https://wiki.cosmos.esa.int/planck-legacy-archive/api.php?action=feedcontributions&user=Jtauber&feedformat=atomPlanck Legacy Archive Wiki - User contributions [en-gb]2022-11-30T03:29:07ZUser contributionsMediaWiki 1.31.6https://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=The_Planck_mission_WiP&diff=14387The Planck mission WiP2018-07-17T12:43:37Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:Introduction}}<br />
<br />
<br />
== The Planck mission ==<br />
<br />
[http://www.esa.int/Planck Planck] is a mission of the European<br />
Space Agency - ESA. The Planck satellite carried instruments provided by two scientific Consortia funded by ESA member<br />
states (in particular the lead countries: France and Italy) with contributions from [https://www.nasa.gov/ NASA] (USA), and<br />
telescope reflectors provided in a collaboration between ESA and a scientific Consortium led and<br />
funded by Denmark.<br />
<br />
Planck was conceived in 1992, in the wake of the release of the results from the<br />
Cosmic Background Explorer ([https://science.nasa.gov/missions/cobe COBE]) satellite, notably its measurement of the shape of the spectrum of the <br />
[http://pdg.lbl.gov/2017/reviews/rpp2016-rev-cosmic-microwave-background.pdf cosmic microwave background] <br />
(CMB), and its<br />
detection of the spatial anisotropies of the temperature of the CMB. The<br />
latter result in particular led to an explosion in the number of ground-based and suborbital<br />
experiments dedicated to mapping of the anisotropies, and to proposals for space experiments both in<br />
Europe and the USA.<br />
<br />
The main objective of Planck was to measure the spatial anisotropies of the temperature of the CMB, with an accuracy set by fundamental astrophysical limits. Its level of performance enabled Planck to extract essentially all the information in the CMB temperature anisotropies. Planck also measured to high accuracy the polarization of the CMB anisotropies, which encodes not only a wealth of cosmological information, but also provides a unique probe of the thermal history of the Universe during the time when the first stars and galaxies formed. In addition, the Planck sky surveys produced a wealth of information on the properties of extragalactic sources and on the dust and gas in our own Galaxy. The scientific objectives of Planck as conceived in 2005 (4 years before launch) were described in detail in the {{PlanckPapers|Bluebook}}.<br />
<br />
The development of Planck began with two proposals presented to the<br />
European Space Agency (ESA) in May of 1993, for the [https://dms.cosmos.esa.int/cs/livelink/Open/3557509 Cosmic Background Radiation Anisotropy Satellite] (COBRAS)<br />
and the [https://dms.cosmos.esa.int/cs/livelink/Open/3557510 Satellite for Measurement of Background Anisotropies] (SAMBA). Each of these proposed a payload formed by an offset<br />
Gregorian telescope focussing light from the sky onto an array of<br />
detectors (based on high-electron-mobility transistor [HEMT] low<br />
noise amplifiers for COBRAS and very low temperature bolometers for<br />
SAMBA) fed by corrugated horns. The two proposals were used by an<br />
ESA-led team to design a payload where a single COBRAS-like<br />
telescope fed two instruments, a COBRAS-like Low Frequency<br />
Instrument (LFI), and a SAMBA-like High Frequency Instrument (HFI),<br />
sharing a common focal plane. A period of study of this concept<br />
culminated in the selection by ESA in 1996 of the COBRAS/SAMBA<br />
satellite (described in the so-called {{PlanckPapers|Redbook}})<br />
into its programme of scientific satellites. At the time of<br />
selection the launch of COBRAS/SAMBA was expected to be in 2003.<br />
Shortly after the mission was approved, it was renamed in honour of<br />
the German scientist [https://www.cosmos.esa.int/web/planck/max-planck Max Planck] (1858-1947), winner of the Nobel<br />
Prize for Physics in 1918.<br />
<br />
Shortly after its selection, the development of Planck was joined<br />
with that of ESA's [https://www.cosmos.esa.int/web/herschel Herschel Space Telescope], based on a number of<br />
potential commonalities, the most important of which was that both<br />
missions targeted orbits around the second Lagrangian point of the<br />
Sun-Earth system and could therefore share a single heavy launcher.<br />
In practice the joint development meant that a single ESA<br />
engineering team led the development of both satellites by a<br />
single industrial prime contractor, leading to the use of many<br />
identical hardware and software subsystems in both satellites, and a<br />
synergistic sharing of engineering skills and manpower. The<br />
industrial prime contractor, Thales Alenia Space France, was<br />
competitively selected in early 2001. Thales Alenia Space France was<br />
supported by two major subcontractors: Thales Alenia Space Italy for<br />
the Service Module of both Planck and Herschel; and EADS Astrium<br />
GmbH for the Herschel Payload Module. There were also contributions from many other industrial<br />
subcontractors from all ESA member states (the industrial team is described [http://sci.esa.int/planck/34787-industrial-team/ here] ). <br />
<br />
In early 1999, ESA selected two Consortia of scientific institutes to provide the two Planck<br />
instruments that were part of the payload described in the {{PlanckPapers|Redbook}}: the Low Frequency Instrument<br />
was developed by a consortium led by N. Mandolesi of the [http://www.iasfbo.inaf.it/en/ Istituto di Astrofisica Spaziale e Fisica<br />
Cosmica] (CNR) in Bologna (Italy); and the High Frequency Instrument by a consortium led by J.-L.<br />
Puget of the [https://www.ias.u-psud.fr/ Institut d'Astrophysique Spatiale] (CNRS) in Orsay (France). <br />
<br />
In early 2000, ESA and the [http://www.space.dtu.dk/english Danish National Space Institute] (DNSI) signed a Letter of Agreement for<br />
the provision of the two reflectors that are used in the Planck telescope. DNSI led a Consortium of<br />
Danish institutes, which together with ESA subcontracted the development of the Planck reflectors to<br />
EADS Astrium GmbH (Friedrichshafen, D), now part of the Airbus group, who have manufactured the reflectors using state-of-the-art<br />
carbon-fibre technology.<br />
<br />
In total, more than 40 European<br />
institutes, and some from the USA and Canada joined forces to constitute the [https://www.cosmos.esa.int/web/planck/planck-collaboration Planck Collaboration], and carry out the development, testing, and in-flight operations of these<br />
instruments, as well as the ensuing data analysis<br />
and initial scientific exploitation. <br />
<br />
[[file:Planck_Logos.jpg|thumb|center|500px|The Planck Collaboration's institutes and agencies.]]<br />
<br />
<br />
The development history of the Planck satellite is summarised [https://www.cosmos.esa.int/web/planck/mission-history here].<br />
It culminated with the successful launch of Planck and Herschel on 14<br />
May 2009.<br />
After a period dedicated to Commissioning and Performance Verification, Planck started its planned survey observations on 12 August 2009. <br />
It carried on observing for a period of about 30 months, around twice the span originally required, and completed five full-sky surveys with both instruments. The Low Frequency Instrument (LFI), which was able to work at higher temperatures than HFI, continued to survey the sky for a large part of 2013, providing even more data to improve the final Planck results. <br />
The last command to the Planck satellite was sent on the 23 October 2013, marking the end of operations.<br />
<br />
<!-- [[file:PlanckMissionTimelineV2.png|thumb|480px|Timeline of the Planck operations and archiving.]] --><br />
<br />
== The Planck data products and papers ==<br />
<br />
The Data Products of Planck have been released in four different stages of increasing scope and quality.<br />
<br />
* The first set of scientific data, the Early Release Compact Source Catalogue (ERCSC; {{PlanckPapers|planck2011-1-10}}), was published in January 2011. At the same time, a set of 26 papers related to astrophysical foregrounds was published in a special issue of Astronomy and Astrophysics (Vol. 536, 2011), among which there is an overview paper ({{PlanckPapers|planck2011-1-1}}). <br />
* The second set of data products (sometimes referred to as Planck Release 1 or “PR1,” because it was the first release of cosmologically useful data) was based on data acquired during the so-called nominal mission, i.e. from start of routine operations to 28 November 2010. These products were based on temperature analysis of the whole sky, and were released in March of 2013. The data and associated scientific results are described in a set of 32 papers in another special issue of A&A (Vol. 571, 2014), among which there is another overview ({{PlanckPapers|planck2013-p01}}). <br />
* The third set of data products (and second set of cosmological data, hence “PR2”) and scientific results released by Planck, was based on the data acquired during the complete Planck mission from 12 August 2009 to 23 October 2013, and hereafter referred to as the “2015 products.” They are based on both temperature and polarization analysis of the entire sky, and were released between February and July 2015. The data and associated scientific results are described in a set of 28 papers published in a third special issue of A&A (Vol. 594, 2016). Again there is an overview paper paper ({{PlanckPapers|planck2014-a01}}).<br />
* The fourth set of scientific data (and third set of cosmological data, hence "PR3") was based on the full mission, focussing on inclusion of the polarization data. The data and associated scientific results are described in a series of 11 papers, including a final "Legacy" which also includes an overview of this release ({{PlanckPapers|planck2016-l01}}.<br />
<br />
In addition to the above listed four groups of data-release-related papers, the Planck Collaboration has published more than 50 “Intermediate” papers containing further astrophysical investigations. These papers are usually based on data products that are either already public or about to become public at the time of publication. <br />
<br />
All of the Planck Collaboration papers are listed in and can be downloaded from [https://www.cosmos.esa.int/web/planck/publications]. At the current time, we encourage people interested in an overview on Planck to start with the latest overview paper ({{PlanckPapers|planck2016-l01}}), and follow references to more specific areas of interest.<br />
<br />
== The Planck Legacy Archive ==<br />
<br />
The [http://pla.esac.esa.int/ Planck Legacy Archive] (PLA) contains all public products originating from the Planck mission, and provides an online interface to select and retrieve them. The majority of the scientific data products from Planck have been produced by the LFI and HFI Data Processing Centres on behalf of the [[Planck Collaboration|Planck Collaboration]]. <br />
<br />
The data products distributed by PLA are classified into the following categories.<br />
* "Timelines" contain time series of data acquired. The types of data provided are:<br />
** "semi-raw timelines" containing data samples per detector, which have been very minimally processed after retrieval from the satellite;<br />
** "calibrated timelines" containing data samples per detector after cleaning and calibration.<br />
* "Rings" are timelines that have been binned into individual periods of fixed spin axis pointing. Each ring traces a quasi-large circle on the sky.<br />
* "Maps" are generally all-sky maps in HEALPix format. There are two major types of Planck maps:<br />
** "frequency maps" are maps as observed at one of the nine frequency channels of Planck, containing at least temperature, and in the later versions also polarization, and existing in many varieties of maps, depending on which detectors and/or time coverage is included in their production;<br />
** "component maps" are maps of diffuse emission of specific physical components, including the CMB, Galactic, and extragalactic foregrounds, which are constructed from Planck observations using different methods.<br />
* The "Likelihood code" is the software used by the Planck Collaboration to extract the values of cosmological parameters from the Planck data. The code is bundled with the data set (from Planck and other experiments) that it needs to run.<br />
* "Catalogues" contain lists of compact or point-like sources extracted from the Planck maps. The basic Planck catalogues have been extracted without regard to the type of source, but some specialized lists of specific source types are also available. <br />
* "Cosmological data" contain results of some of the cosmological analyses that formed the main objective of Planck, i.e. CMB angular power spectra, cosmological model parameters, etc.<br />
<br />
In addition to the above, the PLA also includes a wide variety of additional products:<br />
* external scientific data that were used in the generation of Planck products;<br />
* data characterizing the Planck payload;<br />
* operational data.<br />
<br />
All of the Planck products are labelled according to their release: ERCSC-A 2012; PR1 2013; PR2 2015; and PR3 2018. In addition, the product most recommended for use is labelled as the "Legacy" product. The PLA interface allows the user to search the Archive using a wide variety of parameters. It also provides the possibility to extract parts of the products, e.g. a section of the sky, and in some cases to modify them. The PLA also makes it easy to transfer products to generic data analysis tools for further analysis, e.g. Aladin for maps, and Topcat for catalogues.<br />
<br />
Finally, the PLA also contains some selected data products that are based on Planck data, but have not been produced by the Planck Collaboration. These data are labelled as "Community" products. <br />
<br />
All the PLA products can be accessed via its [http://pla.esac.esa.int/pla/#home graphical interface]. Some of the products can also be extracted via a [http://pla.esac.esa.int/pla/#aio machine interface].<br />
<br />
== This Explanatory Supplement ==<br />
<br />
This Explanatory Supplement (ES) has been built by the Planck Collaboration and the Planck Science Office. It contains:<br />
* general technical information on the Planck satellite, its payload, and its operations;<br />
* specific information for each of the products being distributed by the PLA.<br />
<br />
The ES can be accessed online independently or can be called directly from the PLA interface (in this case it will direct the user to the appropriate sections). In general, it will display descriptions appropriate to the "Legacy" products. However, descriptions specific for each of the four Planck releases can be found at the end of each of the ES sections; the background colour of the ES page identifies the release it refers to. <br />
<br />
We emphasize that the ES contains a bare minimum of necessary information on the data products. We strongly recommend that users read the scientific papers by the Planck Collaboration that are closest to their own application. Those papers contain the most relevant and useful information on the quality and limitations of the Planck products, which has often not been fully captured in the ES.<br />
<br />
==For more information==<br />
<br />
A complete list of Planck publications can be found [http://www.sciops.esa.int/index.php?project=PLANCK&page=Planck_Published_Papers here].<br />
<br />
Suggestions or questions should be sent to the [https://support.cosmos.esa.int/pla/ Helpdesk].<br />
<br />
==Acknowledgments==<br />
The development of Planck has been supported by: ESA; CNES and<br />
CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA);<br />
STFC and UKSA (UK); CSIC, MICINN, JA, and RES (Spain); Tekes, AoF, and CSC<br />
(Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO<br />
(Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); and PRACE<br />
(EU). A description of the Planck Collaboration and a list of its members,<br />
including the technical or scientific activities in which they have been<br />
involved, can be found at [http://www.cosmos.esa.int/web/planck/planck-collaboration this site].<br />
<br />
<br />
==References==<br />
<References /><br />
<br />
<br />
[[Category:PSOBook]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=The_Planck_mission_WiP&diff=14386The Planck mission WiP2018-07-17T12:42:56Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:Introduction}}<br />
<br />
<br />
== The Planck mission ==<br />
<br />
[http://www.esa.int/Planck Planck] is a mission of the European<br />
Space Agency - ESA. The Planck satellite carried instruments provided by two scientific Consortia funded by ESA member<br />
states (in particular the lead countries: France and Italy) with contributions from [https://www.nasa.gov/ NASA] (USA), and<br />
telescope reflectors provided in a collaboration between ESA and a scientific Consortium led and<br />
funded by Denmark.<br />
<br />
Planck was conceived in 1992, in the wake of the release of the results from the<br />
Cosmic Background Explorer ([https://science.nasa.gov/missions/cobe COBE]) satellite, notably its measurement of the shape of the spectrum of the <br />
[http://pdg.lbl.gov/2017/reviews/rpp2016-rev-cosmic-microwave-background.pdf cosmic microwave background] <br />
(CMB), and its<br />
detection of the spatial anisotropies of the temperature of the CMB. The<br />
latter result in particular led to an explosion in the number of ground-based and suborbital<br />
experiments dedicated to mapping of the anisotropies, and to proposals for space experiments both in<br />
Europe and the USA.<br />
<br />
The main objective of Planck was to measure the spatial anisotropies of the temperature of the CMB, with an accuracy set by fundamental astrophysical limits. Its level of performance enabled Planck to extract essentially all the information in the CMB temperature anisotropies. Planck also measured to high accuracy the polarization of the CMB anisotropies, which encodes not only a wealth of cosmological information, but also provides a unique probe of the thermal history of the Universe during the time when the first stars and galaxies formed. In addition, the Planck sky surveys produced a wealth of information on the properties of extragalactic sources and on the dust and gas in our own Galaxy. The scientific objectives of Planck as conceived in 2005 (4 years before launch) were described in detail in the {{PlanckPapers|Bluebook}}.<br />
<br />
The development of Planck began with two proposals presented to the<br />
European Space Agency (ESA) in May of 1993, for the [https://dms.cosmos.esa.int/cs/livelink/Open/3557509 Cosmic Background Radiation Anisotropy Satellite] (COBRAS)<br />
and the [https://dms.cosmos.esa.int/cs/livelink/Open/3557510 Satellite for Measurement of Background Anisotropies] (SAMBA). Each of these proposed a payload formed by an offset<br />
Gregorian telescope focussing light from the sky onto an array of<br />
detectors (based on high-electron-mobility transistor [HEMT] low<br />
noise amplifiers for COBRAS and very low temperature bolometers for<br />
SAMBA) fed by corrugated horns. The two proposals were used by an<br />
ESA-led team to design a payload where a single COBRAS-like<br />
telescope fed two instruments, a COBRAS-like Low Frequency<br />
Instrument (LFI), and a SAMBA-like High Frequency Instrument (HFI),<br />
sharing a common focal plane. A period of study of this concept<br />
culminated in the selection by ESA in 1996 of the COBRAS/SAMBA<br />
satellite (described in the so-called {{PlanckPapers|Redbook}})<br />
into its programme of scientific satellites. At the time of<br />
selection the launch of COBRAS/SAMBA was expected to be in 2003.<br />
Shortly after the mission was approved, it was renamed in honour of<br />
the German scientist [https://www.cosmos.esa.int/web/planck/max-planck Max Planck] (1858-1947), winner of the Nobel<br />
Prize for Physics in 1918.<br />
<br />
Shortly after its selection, the development of Planck was joined<br />
with that of ESA's [https://www.cosmos.esa.int/web/herschel Herschel Space Telescope], based on a number of<br />
potential commonalities, the most important of which was that both<br />
missions targeted orbits around the second Lagrangian point of the<br />
Sun-Earth system and could therefore share a single heavy launcher.<br />
In practice the joint development meant that a single ESA<br />
engineering team led the development of both satellites by a<br />
single industrial prime contractor, leading to the use of many<br />
identical hardware and software subsystems in both satellites, and a<br />
synergistic sharing of engineering skills and manpower. The<br />
industrial prime contractor, Thales Alenia Space France, was<br />
competitively selected in early 2001. Thales Alenia Space France was<br />
supported by two major subcontractors: Thales Alenia Space Italy for<br />
the Service Module of both Planck and Herschel; and EADS Astrium<br />
GmbH for the Herschel Payload Module. There were also contributions from many other industrial<br />
subcontractors from all ESA member states (the industrial team is described [http://sci.esa.int/planck/34787-industrial-team/ here] ). <br />
<br />
In early 1999, ESA selected two Consortia of scientific institutes to provide the two Planck<br />
instruments that were part of the payload described in the {{PlanckPapers|Redbook}}: the Low Frequency Instrument<br />
was developed by a consortium led by N. Mandolesi of the [http://www.iasfbo.inaf.it/en/ Istituto di Astrofisica Spaziale e Fisica<br />
Cosmica] (CNR) in Bologna (Italy); and the High Frequency Instrument by a consortium led by J.-L.<br />
Puget of the [https://www.ias.u-psud.fr/ Institut d'Astrophysique Spatiale] (CNRS) in Orsay (France). <br />
<br />
In early 2000, ESA and the [http://www.space.dtu.dk/english Danish National Space Institute] (DNSI) signed a Letter of Agreement for<br />
the provision of the two reflectors that are used in the Planck telescope. DNSI led a Consortium of<br />
Danish institutes, which together with ESA subcontracted the development of the Planck reflectors to<br />
EADS Astrium GmbH (Friedrichshafen, D), now part of the Airbus group, who have manufactured the reflectors using state-of-the-art<br />
carbon-fibre technology.<br />
<br />
In total, more than 40 European<br />
institutes, and some from the USA and Canada joined forces to constitute the [https://www.cosmos.esa.int/web/planck/planck-collaboration Planck Collaboration], and carry out the development, testing, and in-flight operations of these<br />
instruments, as well as the ensuing data analysis<br />
and initial scientific exploitation. <br />
<br />
[[file:Planck_Logos.jpg|thumb|center|500px|The Planck Collaboration's institutes and agencies.]]<br />
<br />
<br />
The development history of the Planck satellite is summarised [https://www.cosmos.esa.int/web/planck/mission-history here].<br />
It culminated with the successful launch of Planck and Herschel on 14<br />
May 2009.<br />
After a period dedicated to Commissioning and Performance Verification, Planck started its planned survey observations on 12 August 2009. <br />
It carried on observing for a period of about 30 months, around twice the span originally required, and completed five full-sky surveys with both instruments. The Low Frequency Instrument (LFI), which was able to work at higher temperatures than HFI, continued to survey the sky for a large part of 2013, providing even more data to improve the final Planck results. <br />
The last command to the Planck satellite was sent on the 23 October 2013, marking the end of operations.<br />
<br />
<!-- [[file:PlanckMissionTimelineV2.png|thumb|480px|Timeline of the Planck operations and archiving.]] --><br />
<br />
== The Planck data products and papers ==<br />
<br />
The Data Products of Planck have been released in four different stages of increasing scope and quality.<br />
<br />
* The first set of scientific data, the Early Release Compact Source Catalogue (ERCSC; {{PlanckPapers|planck2011-1-10}}), was published in January 2011. At the same time, a set of 26 papers related to astrophysical foregrounds was published in a special issue of Astronomy and Astrophysics (Vol. 536, 2011), among which there is an overview paper ({{PlanckPapers|planck2011-1-1}}). <br />
* The second set of data products (sometimes referred to as Planck Release 1 or “PR1,” because it was the first release of cosmologically useful data) was based on data acquired during the so-called nominal mission, i.e. from start of routine operations to 28 November 2010. These products were based on temperature analysis of the whole sky, and were released in March of 2013. The data and associated scientific results are described in a set of 32 papers in another special issue of A&A (Vol. 571, 2014), among which there is another overview ({{PlanckPapers|planck2013-p01}}). <br />
* The third set of data products (and second set of cosmological data, hence “PR2”) and scientific results released by Planck, was based on the data acquired during the complete Planck mission from 12 August 2009 to 23 October 2013, and hereafter referred to as the “2015 products.” They are based on both temperature and polarization analysis of the entire sky, and were released between February and July 2015. The data and associated scientific results are described in a set of 28 papers published in a third special issue of A&A (Vol. 594, 2016). Again there is an overview paper paper ({{PlanckPapers|planck2014-a01}}).<br />
* The fourth set of scientific data (and third set of cosmological data, hence "PR3") was based on the full mission, focussing on inclusion of the polarization data. The data and associated scientific results are described in a series of 11 papers, including a final "Legacy" which also includes an overview of this release ({{PlanckPapers|planck2016-l01}}.<br />
<br />
In addition to the above listed four groups of data-release-related papers, the Planck Collaboration has published more than 50 “Intermediate” papers containing further astrophysical investigations. These papers are usually based on data products that are either already public or about to become public at the time of publication. <br />
<br />
All of the Planck Collaboration papers are listed in and can be downloaded from [https://www.cosmos.esa.int/web/planck/publications]. At the current time, we encourage people interested in an overview on Planck to start with the latest overview paper ({{PlanckPapers|planck2016-l01}}), and follow references to more specific areas of interest.<br />
<br />
== The Planck Legacy Archive ==<br />
<br />
The [http://pla.esac.esa.int/ Planck Legacy Archive] (PLA) contains all public products originating from the Planck mission, and provides an online interface to select and retrieve them. The majority of the scientific data products from Planck have been produced by the LFI and HFI Data Processing Centres on behalf of the [[Planck Collaboration|Planck Collaboration]]. <br />
<br />
The data products distributed by PLA are classified into the following categories.<br />
* "Timelines" contain time series of data acquired. The types of data provided are:<br />
** "semi-raw timelines" containing data samples per detector, which have been very minimally processed after retrieval from the satellite;<br />
** "calibrated timelines" containing data samples per detector after cleaning and calibration.<br />
* "Rings" are timelines that have been binned into individual periods of fixed spin axis pointing. Each ring traces a quasi-large circle on the sky.<br />
* "Maps" are generally all-sky maps in HEALPix format. There are two major types of Planck maps:<br />
** "frequency maps" are maps as observed at one of the nine frequency channels of Planck, containing at least temperature, and in the later versions also polarization, and existing in many varieties of maps, depending on which detectors and/or time coverage is included in their production;<br />
** "component maps" are maps of diffuse emission of specific physical components, including the CMB, Galactic, and extragalactic foregrounds, which are constructed from Planck observations using different methods.<br />
* The "Likelihood code" is the software used by the Planck Collaboration to extract the values of cosmological parameters from the Planck data. The code is bundled with the data set (from Planck and other experiments) that it needs to run.<br />
* "Catalogues" contain lists of compact or point-like sources extracted from the Planck maps. The basic Planck catalogues have been extracted without regard to the type of source, but some specialized lists of specific source types are also available. <br />
* "Cosmological data" contain results of some of the cosmological analyses that formed the main objective of Planck, i.e. CMB angular power spectra, cosmological model parameters, etc.<br />
<br />
In addition to the above, the PLA also includes a wide variety of additional products:<br />
* external scientific data that were used in the generation of Planck products;<br />
* data characterizing the Planck payload;<br />
* operational data.<br />
<br />
All of the Planck products are labelled according to their release: ERCSC-A 2012; PR1 2013; PR2 2015; and PR3 2018. In addition, the product most recommended for use is labelled as the "Legacy" product. The PLA interface allows the user to search the Archive using a wide variety of parameters. It also provides the possibility to extract parts of the products, e.g. a section of the sky, and in some cases to modify them. The PLA also makes it easy to transfer products to generic data analysis tools for further analysis, e.g. Aladin for maps, and Topcat for catalogues.<br />
<br />
Finally, the PLA also contains some selected data products that are based on Planck data, but have not been produced by the Planck Collaboration. These data are labelled as "Community" products. <br />
<br />
All the PLA products can be accessed via its [http://pla.esac.esa.int/pla/#home graphical interface]. Some of the products can also be extracted via a [http://pla.esac.esa.int/pla/#aio machine interface].<br />
<br />
== This Explanatory Supplement ==<br />
<br />
This Explanatory Supplement (ES) has been built by the Planck Collaboration and the Planck Science Office. It contains:<br />
* general technical information on the Planck satellite, its payload, and its operations;<br />
* specific information for each of the products being distributed by the PLA.<br />
<br />
The ES can be accessed online independently or can be called directly from the PLA interface (in this case it will direct the user to the appropriate sections). In general, it will display descriptions appropriate to the "Legacy" products. However, descriptions specific for each of the four Planck releases can be found at the end of each of the ES sections; the background colour of the ES page identifies the release it refers to. <br />
<br />
We emphasize that the ES contains a bare minimum of necessary information on the data products. We strongly recommend that users read the scientific papers by the Planck Collaboration that are closest to their own application. Those papers contain the most relevant and useful information on the quality and limitations of the Planck products, which has often not been fully captured in the ES.<br />
<br />
==For more information==<br />
<br />
A complete list of Planck publications can be found [http://www.sciops.esa.int/index.php?project=PLANCK&page=Planck_Published_Papers here].<br />
<br />
Suggestions or questions should be sent to the [https://support.cosmos.esa.int/pla/ Helpdesk].<br />
<br />
==Acknowledgments==<br />
The development of \Planck\ has been supported by: ESA; CNES and<br />
CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA);<br />
STFC and UKSA (UK); CSIC, MICINN, JA, and RES (Spain); Tekes, AoF, and CSC<br />
(Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO<br />
(Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); and PRACE<br />
(EU). A description of the \Planck\ Collaboration and a list of its members,<br />
including the technical or scientific activities in which they have been<br />
involved, can be found at [http://www.cosmos.esa.int/web/planck/planck-collaboration this site].<br />
<br />
<br />
==References==<br />
<References /><br />
<br />
<br />
[[Category:PSOBook]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=The_Planck_mission_WiP&diff=14385The Planck mission WiP2018-07-17T10:52:18Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:Introduction}}<br />
<br />
<br />
== The Planck mission ==<br />
<br />
[http://www.esa.int/Planck Planck] is a mission of the European<br />
Space Agency - ESA. The Planck satellite carried instruments provided by two scientific Consortia funded by ESA member<br />
states (in particular the lead countries: France and Italy) with contributions from [https://www.nasa.gov/ NASA] (USA), and<br />
telescope reflectors provided in a collaboration between ESA and a scientific Consortium led and<br />
funded by Denmark.<br />
<br />
Planck was conceived in 1992, in the wake of the release of the results from the<br />
Cosmic Background Explorer ([https://science.nasa.gov/missions/cobe COBE]) satellite, notably its measurement of the shape of the spectrum of the <br />
[http://pdg.lbl.gov/2017/reviews/rpp2016-rev-cosmic-microwave-background.pdf cosmic microwave background] <br />
(CMB), and its<br />
detection of the spatial anisotropies of the temperature of the CMB. The<br />
latter result in particular led to an explosion in the number of ground-based and suborbital<br />
experiments dedicated to mapping of the anisotropies, and to proposals for space experiments both in<br />
Europe and the USA.<br />
<br />
The main objective of Planck was to measure the spatial anisotropies of the temperature of the CMB, with an accuracy set by fundamental astrophysical limits. Its level of performance enabled Planck to extract essentially all the information in the CMB temperature anisotropies. Planck also measured to high accuracy the polarization of the CMB anisotropies, which encodes not only a wealth of cosmological information, but also provides a unique probe of the thermal history of the Universe during the time when the first stars and galaxies formed. In addition, the Planck sky surveys produced a wealth of information on the properties of extragalactic sources and on the dust and gas in our own Galaxy. The scientific objectives of Planck as conceived in 2005 (4 years before launch) were described in detail in the {{PlanckPapers|Bluebook}}.<br />
<br />
The development of Planck began with two proposals presented to the<br />
European Space Agency (ESA) in May of 1993, for the [https://dms.cosmos.esa.int/cs/livelink/Open/3557509 Cosmic Background Radiation Anisotropy Satellite] (COBRAS)<br />
and the [https://dms.cosmos.esa.int/cs/livelink/Open/3557510 Satellite for Measurement of Background Anisotropies] (SAMBA). Each of these proposed a payload formed by an offset<br />
Gregorian telescope focussing light from the sky onto an array of<br />
detectors (based on high-electron-mobility transistor [HEMT] low<br />
noise amplifiers for COBRAS and very low temperature bolometers for<br />
SAMBA) fed by corrugated horns. The two proposals were used by an<br />
ESA-led team to design a payload where a single COBRAS-like<br />
telescope fed two instruments, a COBRAS-like Low Frequency<br />
Instrument (LFI), and a SAMBA-like High Frequency Instrument (HFI),<br />
sharing a common focal plane. A period of study of this concept<br />
culminated in the selection by ESA in 1996 of the COBRAS/SAMBA<br />
satellite (described in the so-called {{PlanckPapers|Redbook}})<br />
into its programme of scientific satellites. At the time of<br />
selection the launch of COBRAS/SAMBA was expected to be in 2003.<br />
Shortly after the mission was approved, it was renamed in honour of<br />
the German scientist [https://www.cosmos.esa.int/web/planck/max-planck Max Planck] (1858-1947), winner of the Nobel<br />
Prize for Physics in 1918.<br />
<br />
Shortly after its selection, the development of Planck was joined<br />
with that of ESA's [https://www.cosmos.esa.int/web/herschel Herschel Space Telescope], based on a number of<br />
potential commonalities, the most important of which was that both<br />
missions targeted orbits around the second Lagrangian point of the<br />
Sun-Earth system and could therefore share a single heavy launcher.<br />
In practice the joint development meant that a single ESA<br />
engineering team led the development of both satellites by a<br />
single industrial prime contractor, leading to the use of many<br />
identical hardware and software subsystems in both satellites, and a<br />
synergistic sharing of engineering skills and manpower. The<br />
industrial prime contractor, Thales Alenia Space France, was<br />
competitively selected in early 2001. Thales Alenia Space France was<br />
supported by two major subcontractors: Thales Alenia Space Italy for<br />
the Service Module of both Planck and Herschel; and EADS Astrium<br />
GmbH for the Herschel Payload Module. There were also contributions from many other industrial<br />
subcontractors from all ESA member states (the industrial team is described [http://sci.esa.int/planck/34787-industrial-team/ here] ). <br />
<br />
In early 1999, ESA selected two Consortia of scientific institutes to provide the two Planck<br />
instruments that were part of the payload described in the {{PlanckPapers|Redbook}}: the Low Frequency Instrument<br />
was developed by a consortium led by N. Mandolesi of the [http://www.iasfbo.inaf.it/en/ Istituto di Astrofisica Spaziale e Fisica<br />
Cosmica] (CNR) in Bologna (Italy); and the High Frequency Instrument by a consortium led by J.-L.<br />
Puget of the [https://www.ias.u-psud.fr/ Institut d'Astrophysique Spatiale] (CNRS) in Orsay (France). <br />
<br />
In early 2000, ESA and the [http://www.space.dtu.dk/english Danish National Space Institute] (DNSI) signed a Letter of Agreement for<br />
the provision of the two reflectors that are used in the Planck telescope. DNSI led a Consortium of<br />
Danish institutes, which together with ESA subcontracted the development of the Planck reflectors to<br />
EADS Astrium GmbH (Friedrichshafen, D), now part of the Airbus group, who have manufactured the reflectors using state-of-the-art<br />
carbon-fibre technology.<br />
<br />
In total, more than 40 European<br />
institutes, and some from the USA and Canada joined forces to constitute the [https://www.cosmos.esa.int/web/planck/planck-collaboration Planck Collaboration], and carry out the development, testing, and in-flight operations of these<br />
instruments, as well as the ensuing data analysis<br />
and initial scientific exploitation. <br />
<br />
[[file:Planck_Logos.jpg|thumb|center|500px|The Planck Collaboration's institutes and agencies.]]<br />
<br />
<br />
The development history of the Planck satellite is summarised [https://www.cosmos.esa.int/web/planck/mission-history here].<br />
It culminated with the successful launch of Planck and Herschel on 14<br />
May 2009.<br />
After a period dedicated to Commissioning and Performance Verification, Planck started its planned survey observations on 12 August 2009. <br />
It carried on observing for a period of about 30 months, around twice the span originally required, and completed five full-sky surveys with both instruments. The Low Frequency Instrument (LFI), which was able to work at higher temperatures than HFI, continued to survey the sky for a large part of 2013, providing even more data to improve the final Planck results. <br />
The last command to the Planck satellite was sent on the 23 October 2013, marking the end of operations.<br />
<br />
<!-- [[file:PlanckMissionTimelineV2.png|thumb|480px|Timeline of the Planck operations and archiving.]] --><br />
<br />
== The Planck data products and papers ==<br />
<br />
The Data Products of Planck have been released in four different stages of increasing scope and quality.<br />
<br />
* The first set of scientific data, the Early Release Compact Source Catalogue (ERCSC; {{PlanckPapers|planck2011-1-10}}), was published in January 2011. At the same time, a set of 26 papers related to astrophysical foregrounds was published in a special issue of Astronomy and Astrophysics (Vol. 536, 2011), among which there is an overview paper ({{PlanckPapers|planck2011-1-1}}). <br />
* The second set of data products (sometimes referred to as Planck Release 1 or “PR1,” because it was the first release of cosmologically useful data) was based on data acquired during the so-called nominal mission, i.e. from start of routine operations to 28 November 2010. These products were based on temperature analysis of the whole sky, and were released in March of 2013. The data and associated scientific results are described in a set of 32 papers in another special issue of A&A (Vol. 571, 2014), among which there is another overview ({{PlanckPapers|planck2013-p01}}). <br />
* The third set of data products (and second set of cosmological data, hence “PR2”) and scientific results released by Planck, was based on the data acquired during the complete Planck mission from 12 August 2009 to 23 October 2013, and hereafter referred to as the “2015 products.” They are based on both temperature and polarization analysis of the entire sky, and were released between February and July 2015. The data and associated scientific results are described in a set of 28 papers published in a third special issue of A&A (Vol. 594, 2016). Again there is an overview paper paper ({{PlanckPapers|planck2014-a01}}).<br />
* The fourth set of scientific data (and third set of cosmological data, hence "PR3") was based on the full mission, focussing on inclusion of the polarization data. The data and associated scientific results are described in a series of 11 papers, including a final "Legacy" which also includes an overview of this release ({{PlanckPapers|planck2016-l01}}.<br />
<br />
In addition to the above listed four groups of data-release-related papers, the Planck Collaboration has published more than 50 “Intermediate” papers containing further astrophysical investigations. These papers are usually based on data products that are either already public or about to become public at the time of publication. <br />
<br />
All of the Planck Collaboration papers are listed in and can be downloaded from [https://www.cosmos.esa.int/web/planck/publications]. At the current time, we encourage people interested in an overview on Planck to start with the latest overview paper ({{PlanckPapers|planck2016-l01}}), and follow references to more specific areas of interest.<br />
<br />
== The Planck Legacy Archive ==<br />
<br />
The [http://pla.esac.esa.int/ Planck Legacy Archive] (PLA) contains all public products originating from the Planck mission, and provides an online interface to select and retrieve them. The majority of the scientific data products from Planck have been produced by the LFI and HFI Data Processing Centres on behalf of the [[Planck Collaboration|Planck Collaboration]]. <br />
<br />
The data products distributed by PLA are classified into the following categories.<br />
* "Timelines" contain time series of data acquired. The types of data provided are:<br />
** "semi-raw timelines" containing data samples per detector, which have been very minimally processed after retrieval from the satellite;<br />
** "calibrated timelines" containing data samples per detector after cleaning and calibration.<br />
* "Rings" are timelines that have been binned into individual periods of fixed spin axis pointing. Each ring traces a quasi-large circle on the sky.<br />
* "Maps" are generally all-sky maps in HEALPix format. There are two major types of Planck maps:<br />
** "frequency maps" are maps as observed at one of the nine frequency channels of Planck, containing at least temperature, and in the later versions also polarization, and existing in many varieties of maps, depending on which detectors and/or time coverage is included in their production;<br />
** "component maps" are maps of diffuse emission of specific physical components, including the CMB, Galactic, and extragalactic foregrounds, which are constructed from Planck observations using different methods.<br />
* The "Likelihood code" is the software used by the Planck Collaboration to extract the values of cosmological parameters from the Planck data. The code is bundled with the data set (from Planck and other experiments) that it needs to run.<br />
* "Catalogues" contain lists of compact or point-like sources extracted from the Planck maps. The basic Planck catalogues have been extracted without regard to the type of source, but some specialized lists of specific source types are also available. <br />
* "Cosmological data" contain results of some of the cosmological analyses that formed the main objective of Planck, i.e. CMB angular power spectra, cosmological model parameters, etc.<br />
<br />
In addition to the above, the PLA also includes a wide variety of additional products:<br />
* external scientific data that were used in the generation of Planck products;<br />
* data characterizing the Planck payload;<br />
* operational data.<br />
<br />
All of the Planck products are labelled according to their release: ERCSC-A 2012; PR1 2013; PR2 2015; and PR3 2018. In addition, the product most recommended for use is labelled as the "Legacy" product. The PLA interface allows the user to search the Archive using a wide variety of parameters. It also provides the possibility to extract parts of the products, e.g. a section of the sky, and in some cases to modify them. The PLA also makes it easy to transfer products to generic data analysis tools for further analysis, e.g. Aladin for maps, and Topcat for catalogues.<br />
<br />
Finally, the PLA also contains some selected data products that are based on Planck data, but have not been produced by the Planck Collaboration. These data are labelled as "Community" products. <br />
<br />
All the PLA products can be accessed via its [http://pla.esac.esa.int/pla/#home graphical interface]. Some of the products can also be extracted via a [http://pla.esac.esa.int/pla/#aio machine interface].<br />
<br />
== This Explanatory Supplement ==<br />
<br />
This Explanatory Supplement (ES) has been built by the Planck Collaboration and the Planck Science Office. It contains:<br />
* general technical information on the Planck satellite, its payload, and its operations;<br />
* specific information for each of the products being distributed by the PLA.<br />
<br />
The ES can be accessed online independently or can be called directly from the PLA interface (in this case it will direct the user to the appropriate sections). In general, it will display descriptions appropriate to the "Legacy" products. However, descriptions specific for each of the four Planck releases can be found at the end of each of the ES sections; the background colour of the ES page identifies the release it refers to. <br />
<br />
We emphasize that the ES contains a bare minimum of necessary information on the data products. We strongly recommend that users read the scientific papers by the Planck Collaboration that are closest to their own application. Those papers contain the most relevant and useful information on the quality and limitations of the Planck products, which has often not been fully captured in the ES.<br />
<br />
==For more information==<br />
<br />
A complete list of Planck publications can be found [http://www.sciops.esa.int/index.php?project=PLANCK&page=Planck_Published_Papers here].<br />
<br />
Suggestions or questions should be sent to the [https://support.cosmos.esa.int/pla/ Helpdesk].<br />
<br />
==Acknowledgments==<br />
<br />
<br />
<br />
==References==<br />
<References /><br />
<br />
<br />
[[Category:PSOBook]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=Main_Page&diff=14384Main Page2018-07-17T10:50:10Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE: 2018 Planck Explanatory Supplement}}<br />
<!---'''<span style="font-size:180%"> <span style="color:Blue"> This is the 2018 Explanatory Supplement page for the Planck Legacy Archive </span><br />
* Instructions for new users: [[Help:READ ME FIRST|Read me first]]<br />
* See [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for a detailed User Guide of the MediaWiki software;<br />
* See [[Help:Contents|Explanatory Supplement Help page]] for Planck-specific guidelines.---><br />
<br />
The Explanatory Supplement is a reference text accompanying the public data products which result from the European Space Agency’s Planck mission, and includes descriptions of all the products available via the Planck Legacy Archive. The Explanatory Supplement has been produced by the [[Planck Collaboration]].<br />
<br />
There are have been three major data releases of Planck products: <br />
*PR1 in 2013 (all files are identified by the label *.R1.??) ;<br />
*PR2 in 2015 (all files are identified by the label *.R2.??) ;<br />
*PR3 in 2018 (all files are identified by the label *.R3.??) .<br />
<br />
This is the Explanatory Supplement which accompanies the 2018 release. By default, it describes all the products issued in the 2018 release. In addition, the descriptions of the 2013 and 2015 products can also be found within this Explanatory Supplement, at the end of each section under the heading '''Previous Releases'''. Generally speaking, pages describing the 2018 releases have a white background; pages describing previous generations of products have a different color background: salmon for 2015, and green for 2013. <br />
<br />
Note that not all the products issued in 2015 have been updated in the 2018 release. The Planck Legacy Archive presents by default the latest ("legacy") version of a product to the user; this latest version is mostly from 2018, but in some cases could be from 2015.<br />
<br />
The Index of the Explanatory Supplement is listed below; the Index and individual section headings can also be accessed directly via the menu bar at the left of this page.<br />
<br />
<!--- ############# ---><br />
#[[Introduction_WiP|Introduction]]<br />
##[[The Planck mission_WiP|The Planck mission]] <br />
##[[The satellite_WiP|The spacecraft]]<br />
##[[Ground Segment and Operations|Ground segment and Early operations]]<br />
##[[Survey_scanning_and_performance|Survey scanning and Routine operations]]<br />
##[[Questions and Answers|Questions and answers]]<br />
<!--- ############# ---><br />
#[[The Instruments|The instruments]]<br />
##[[HFI design, qualification, and performance|HFI design, qualification, and performance]]<br />
###[[HFI_cryogenics | Cryogenics]]<br />
###[[HFI_cold_optics_%26_spectral_response | HFI cold optics and spectral response]]<br />
###[[HFI_detection_chain | Detection chain]]<br />
###[[HFI_operations | Operations]]<br />
###[[HFI_performance_summary | Performance summary]]<br />
###[[HFI_instrument_annexes | Annexes]]<br />
##[[LFI overview|LFI design, qualification, and performance]]<span style="color:red"></span><br />
###[[LFI design, qualification, and performance#LFIDescription| Instrument description]]<br />
###[[LFI design, qualification, and performance#LFITests| Ground tests]]<br />
###[[LFI design, qualification, and performance#LFICalibration| In-flight calibration]]<br />
###[[LFI design, qualification, and performance#LFIPerformance| Performance summary]]<br />
###[[LFI design, qualification, and performance#LFISystematics| Systematic effects]]<br />
###[[LFI design, qualification, and performance#SCS| Sorption cooler]]<br />
###[[LFIAppendix| Annexes]]<br />
<!--- ############# ---><br />
#[[Data processing]]<br />
##[[The HFI DPC| HFI data processing]]<br />
###[[Pre-processing | Pre-processing]]<br />
###[[TOI processing|TOI processing]]<br />
###[[Beams | Beams]]<br />
###[[Spectral response | Spectral response]]<br />
###[[HFI-systematics | Systematic effects]]<br />
###[[Map-making | Mapmaking]]<br />
###[[HFI-Validation | Internal overall validation]]<br />
###[[Summary_of_HFI_data_characteristics | Summary of HFI data characteristics]]<br />
###[[HFI_sims | HFI simulations]]<br />
##[[The LFI DPC| LFI data processing]] <span style="color:red"></span><br />
###[[Pre-processing_LFI| Pre-processing]]<br />
###[[TOI processing_LFI| TOI processing]] <span style="color:red"></span><br />
###[[Beams_LFI | Beams]] <span style="color:red"></span><br />
###[[Galactic stray light removal]]<br />
###[[Map-making_LFI | Mapmaking]] <span style="color:red"></span><br />
###[[LFI systematic effect uncertainties | Systematic effects uncertainties]]<br />
###[[LFI-Validation | Internal overall validation]] <span style="color:red"></span><br />
<!--- ###[[L3_LFI | Power spectra]] ---><br />
###[[Summary_LFI | Summary of LFI data characteristics ]]<br />
##[[HFI/LFI joint data processing]]<br />
###[[Detector pointing| Detector pointing]]<br />
<!--- ###[[NoiseCovarMatrices | Noise covariance matrices and low-resolution maps ]] ---><br />
###[[Compact Source catalogues | Compact source catalogues]]<br />
###[[Astrophysical component separation]]<br />
###[[C2 | CMB power spectra and Planck likelihood code]]<br />
<!--- ############# ---><br />
#[[Planck Legacy Archive: mission products]]<br />
##[[Timelines_and_rings | Timelines and Rings]]<br />
###[[Timelines | Timelines]]<br />
###[[Healpix_Rings| HEALPix rings]]<br />
<!--- ###[[Healpix_Rings_LFI| LFI HEALPix rings]]---><br />
<!--- ###[[Healpix_Rings_HFI| HFI HEALPix rings]]---><br />
##[[Maps|Maps]] <br />
###[[Frequency maps | Frequency maps in Temperature and Polarization]]<br />
###[[CMB maps | CMB maps]]<br />
###[[Foreground maps | Foreground maps]]<br />
####[[Foreground_maps#2018_Astrophysical_Components | Overview]]<br />
####[[Foreground_maps#Commander-derived_astrophysical_foreground_maps | Commander-derived astrophysical foreground maps]]<br />
####[[Foreground_maps#SMICA-derived_astrophysical_foreground_maps | SMICA-derived astrophysical foreground maps]]<br />
####[[Foreground_maps#GNILC_thermal_dust_maps | GNILC thermal dust maps]]<br />
###[[Correction maps | Correction maps]]<br />
###[[Masks | Masks]]<br />
###[[Simulation data | Simulation data]]<br />
###[[External maps | External maps]]<br />
####[[External_maps#WMAP| WMAP]]<br />
####[[External_maps#Haslam| Haslam]]<br />
####[[External_maps#IRIS| IRIS]]<br />
####[[External_maps#WISE| WISE]]<br />
####[[External_maps#IRAM| IRAM - Crab nebula]] <br />
###[[DatesObs|Dates of observations]] <br />
##[[Catalogues | Catalogues]] <br />
###[[Catalogues#Catalogue of Compact Sources|PCCS]]<br />
###[[Catalogues#SZ Catalogue | PSZ]]<br />
###[[Catalogues#Catalogue_of_Planck_Galactic_Cold_Clumps | PGCC]]<br />
###[[Catalogues#.282015.29_Planck_List_of_high-redshift_source_candidates | PHZ]]<br />
##[[Cosmology | Cosmology]]<br />
###[[CMB spectrum & Likelihood Code | CMB spectrum and likelihood code]] <!--- <span style="color:red">Likelihood code description should be added here (and parentheses removed from title)</span>---><br />
###[[Cosmological Parameters | Cosmological parameters and MC chains]]<br />
###[[Lensing | Lensing]]<br />
## [[Beams_section|Beams]]<br />
###[[Scanning Beams | Scanning beams]]<br />
###[[Optical Beams | Optical beams]]<br />
###[[Effective Beams | Effective beams]]<br />
###[[Beam Window Functions | Beam window functions]]<br />
##[[The RIMO|Instrument model]]<br />
##[[Planets related data | Planet-related data]] <br />
##[[Software utilities | Software utilities]]<br />
<!---###[[Planck Sky Model | Planck Sky Model simulation tool]]---><br />
<!---###[[Mapmaking | Mapmaking from timelines and ring tools]] ---><br />
<!---###[[Febecop tools | FEBeCoP effective beam extraction and convolution tools]] ---><br />
###[[Unit conversion and Color correction | Unit conversion and colour correction]] <br />
###[[SMICA weights propagation code | SMICA weights propagation code ]] <br />
<!--- ##[[NoiseCovariance | Noise covariance matrices and low-resolution maps ]]<span style="color:red">(Keskitalo)</span ---><br />
<!---##[[Scientific data used to generate Planck products | Scientific data used to generate Planck products]] <span style="color:red">Not ready for release</span>---><br />
<!--- ############# ---><br />
#[[Planck Added Value Tools | Planck value-added tools]] <br />
#[[Operational data]]<br />
<!---##[[Thermal|Thermal and cooler system]]---><br />
##[[Survey history | Survey history data]]<br />
##[[Satellite history | Satellite history data]]<br />
##[[Planck operational state history]]<br />
<!---##[[FOG|Fibre-optic gyro]]---><br />
##[[SREM|Space radiation environment monitor]]<br />
#[[Appendix]]<br />
##[[Glossary]]<br />
##[[List of acronyms]]<br />
[[Category:PSOBook]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=14383CMB spectrum & Likelihood Code2018-07-16T21:48:39Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:CMB spectra and likelihood code}}<br />
<br />
== 2018 CMB spectra==<br />
<br />
<br />
===General description===<br />
====TT====<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, including 86% of the sky ({{PlanckPapers|planck2016-l06}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood {{PlanckPapers|planck2016-l05}}, with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology. Associated 1&sigma; errors include beam uncertainties. Commander is described in more detail in {{PlanckPapers|planck2016-l04}}, and Plik is described in more detail in {{PlanckPapers|planck2016-l05}}.<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.51.48.png|thumb|600px|center]]<br />
<br />
====TE, EE, and EB, BB ====<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. In the multipole range 2 ≤ l ≤ 29, we plot the power spectra estimates from the SimAll likelihood (though only the EE spectrum is used in the baseline parameter analysis at l ≤ 29), see {{PlanckPapers|planck2016-l06}}). The spectra are obtained using a cross quasi maximum likelihood algorithm (QML) on the 100 and 143 GHz maps and validated against high fidelity end-to-end simulations.<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.52.35.png|thumb|600px|center]]<br />
[[File:Screen Shot 2018-07-16 at 05.52.24.png|thumb|600px|center]]<br />
<br />
<br />
In the range &#8467; = 2-29, we also release the <i>BB</i>, and <i>EB</i> power spectra derived from the same maps. Error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2016-l03}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
==== Best-fit model ====<br />
<br />
We also provide best-fit LCDM CMB power spectra from the baseline Planck TT,TE,EE+lowE+lensing. The spectra must be divided by the best-fit Planck map-based calibration parameter squared, calPlanck**2, to be compared to the coadded CMB spectra. The best-fit calPlanck value can be found in the file "COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt".<br />
<br />
===Production process===<br />
The Plik high-multipole likelihood (described in detail in {{PlanckPapers|planck2016-l05}}) is a Gaussian approximation of the probability distributions of the <i>TT</i>, <i>EE</i>, and <i>TE</i> angular power spectra, with semi-analytic covariance matrices calculated assuming a fiducial cosmology. It includes multipoles in the range 30 to 2508 for TT and 30 to 1996 for <i>TE</i> and <i>EE</i> and is constructed from half-mission cross-spectra measured from the 100-, 143-, and 217-GHz HFI frequency maps. For more details see {{PlanckPapers|planck2016-l06}}.<br />
<br />
<br />
<br />
===Inputs===<br />
<br />
The T T likelihood uses four half-mission cross-spectra with different multipole cuts to avoid multipole regions where noise dominates due to the limited resolution of the beams and to en-sure foreground contamination is correctly handled by our fore-ground model: 100 × 100 ( &#8467; = 30–1197); 143 × 143 (&#8467; = 30– 1996); 143 × 217 (&#8467; = 30–2508); and 217 × 217 (&#8467; = 30–2508). The TE and EE likelihoods also include the 100 × 143 and 100 × 217 cross-spectra to improve the signal-to-noise ratio, and have different multipole cuts: 100 × 100 (&#8467; = 30–999); 100 × 143 (&#8467; = 30–999); 100 × 217 (&#8467; = 505–999); 143 × 143 (&#8467; = 30– 1996); 143 × 217 (&#8467; = 505–1996); and 217 × 217 (&#8467; = 505– 1996). The 353, 545 and 857 GHz temperature and polarization maps are also used to build the dust templates, and contribute to the galactic and point source masks determination.<br />
<br />
=== File names and meta-data ===<br />
<br />
The CMB spectra and their uncertainties are distributed in ASCII text files named ''COM_PowerSpect_CMB_nn_R3.01.fits'', where nn stands for the type of spectrum the file contains:<br />
* COM_PowerSpect_CMB-EE-full_R3.01.txt<br />
* COM_PowerSpect_CMB-TE-full_R3.01.txt<br />
* COM_PowerSpect_CMB-TT-full_R3.01.txt<br />
* COM_PowerSpect_CMB-low-ell-BB-full_R3.01.txt<br />
* COM_PowerSpect_CMB-low-ell-EB-full_R3.01.txt<br />
<br />
In addition we provide one file containing all the parameters of the Plik runs which yielded the spectra. This file is named<br />
* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt<br />
<br />
The theoretical spectrum of the best-fit model itself is provided in a separate file named<br />
* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt<br />
<br />
The data file columns give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>, and the lower and upper 68% uncertainties.<br />
<br />
<br />
== 2018 Likelihood==<br />
<br />
The 2018 Likelihood code will be released at a later time.<br />
<br />
== Previous Releases: (2015) and (2013) CMB spectrum and Likelihood ==<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%"><br />
'''2015 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''2015 CMB spectra'''<br />
<br />
'''General description'''<br />
<br />
'''TT'''<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2014-a12}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP &Lambda;CDM run. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]<br />
<br />
'''TE, EE, and TB, EB, BB '''<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
'''Production process'''<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
'''Inputs'''<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
''' File names and meta-data '''<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
'''Likelihood'''<br />
<br />
The 2015 baseline likelihood release consists of a code package and a single data package. Four extended data packages are also available enabling exploration of alternatives to the baseline results.<br />
The code compiles to a library allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets. A data set permits the computation of a single likelihood among:<br />
* the high-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the low-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the CMB lensing reconstruction.<br />
By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.<br />
<br />
Only the baseline data package, ''COM_Likelihood_Data-baseline_R2.00.tar.gz'', will be fully described on this page. It contains six data sets, which are enough to compute all of the baseline Planck results that are discussed in {{PlanckPapers|planck2014-a14}}. In particular it allows for the computation of the CMB and lensing likelihood from either the Temperature data only, or the Temperature + Polarization combination.<br />
<br />
The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in {{PlanckPapers|planck2014-a13}} and {{PlanckPapers|planck2014-a17}}. Their full description is contained in the documentation included in each of the extended data packages.<br />
<br />
'''Library and tools'''<br />
<br />
'''Description'''<br />
The library consists of code written in C and Fortran 90. It can be called from both of<br />
those languages. Optionally, a python wrapper can be built as well. Scripts to<br />
simplify the linking of the library with other codes are part of the package, as<br />
well as some example codes that can be used to test the correct installation of<br />
the code and the integrity of the data packages. Optionally, a script is also available, allowing<br />
the user to modify the multipole range of the TT likelihoods and reproduce the hybridization<br />
test performed in the paper.<br />
A description of the tool, the API of the library, as well as different <br />
installation procedure are detailed in the ''readme.md'' file in the code package.<br />
<br />
'''File name'''<br />
The code can be extracted from <br />
''COM_Likelihood_Code-v2.0_R2.00.tar.bz2''.<br />
<br />
Please read the file ''readme.md'' for installation instructions.<br />
<br />
'''Data sets - Baseline data'''<br />
All of the released baseline data are distributed within a single file,<br />
''COM_Likelihood_Data-baseline_R2.00.tar.gz''.<br />
<br />
This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.<br />
<br />
Each data set is stored in its own directory. The directory structure follows similar rules<br />
for each data set, and stores data, template, and meta-data for each particular likelihood.<br />
<br />
As in 2013, the CMB likelihood is cut into low-&#8467; and high-&#8467; parts. Moreover, <br />
for each of those, we distribute both a T-only datafile and a joint T+P one. In the case <br />
of the high-&#8467; part, we also distribute two specific versions of the likelihood, <br />
that allow for estimate of T and T+P marginalized over the nuisance parameters.<br />
Combining both the low-&#8467; and high-&#8467; files, one can compute the likelihood over the<br />
range &#8467;=2-2508 in TT and &#8467;=2-1996 in TE and EE. A full description of the low-&#8467; <br />
and high-&#8467; likelihood is available in {{PlanckPapers|planck2014-a13}}.<br />
<br />
Similarly, for the case of lensing, we also distribute the likelihood using both<br />
the reconstruction based on the <i>T</i> map only, or on <i>T</i>+<i>P</i> maps. <br />
A full description of the lensing likelihood is available in {{PlanckPapers|planck2014-a17}}.<br />
<br />
All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that his parameter is explored in the Gaussian prior 1.0000&plusmn;0.0025.<br />
<br />
''' Low-&#8467; likelihoods '''<br />
<br />
'''TT only - commander'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=2-29.<br />
Using the optional tool in the code package, it can be modified to cover any multipole range <br />
up to &#8467;&lt;200. <br />
<br />
''' Production process'''<br />
The likelihood is based on the results of the Commander approach, which implements a <br />
Bayesian component separation method in pixel space, sampling the posterior distribution <br />
of the parameters of a model that describes both the CMB and the foreground emissions<br />
in a combination of the Planck maps, the WMAP map, and the 408-MHz survey. The samples<br />
of this exploration are used to infer the foreground marginalized low-&#8467; likelihood <br />
for any <i>TT</i> CMB spectrum. <br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
'''File name and usage'''<br />
The commander likelihood is distributed in <br />
''plc_2.0/low_l/commander/commander_rc2_v1.1_l2_29_B.clik''<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the vector really starts at &#8467;=0, although<br />
the first two entries are null.<br />
<br />
'''TEB '''<br />
This file allows for the computation of the CMB joint TT,EE, BB and TE likelihood <br />
in the range &#8467;=2-29. It should not be used with the low-&#8467; TT-only likelihood.<br />
<br />
''' Production process'''<br />
The file allows for the computation of the pixel based likelihood of <i>T</i>, <i>E</i>, and <i>B</i> <br />
maps. The <i>T</i> map is the best-fit map obtained from the commander algorithm, as described above, <br />
while the <i>E</i> and <i>B</i> maps are obtained from the 70GHz LFI full mission data, but excluding the second and fourth surveys. Foreground contamination is<br />
dealt with by marginalizing over templates based on the 30-GHz LFI and 353-GHz HFI maps.<br />
The covariance matrix comes from the Planck detector sensitivity modulated on the <br />
sky by the scanning strategy. The covariance matrix is further enlarged to account <br />
for the foreground template removal. <br />
To speed up the computation by about an order of magnitude, the problem is <br />
projected into <i>C</i><sub>&#8467;</sub> space using the Sherman-Morrison-Woodbury identity. Only the <br />
projected quantities are stored in the data package.<br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask {{PlanckPapers|planck2014-a12}}.<br />
<br />
<br />
'''File name and usage'''<br />
The low ell TEB likelihood is distributed in <br />
''plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive), followed by the <i>EE</i> (&#8467;=0 to 29), <br />
<i>BB</i> (&#8467;=0 to 29) and <i>TE</i> (&#8467;=0 to 29) spectra, and by an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the entries really start at &#8467;=0, although the<br />
&#8467;=0 and &#8467;=1 values will be null.<br />
<br />
''' High-&#8467; likelihoods '''<br />
<br />
'''TT only - Plik'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=30-2508.<br />
Using the optional tool in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>TT</i> cross-spectra. <br />
Only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission <i>T</i> maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by a vector of 16 nuisance parameters.<br />
Those are, in order:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217;<br />
* calib_100T, the relative calibration between the 100 and 143 spectra;<br />
* calib_217T, the relative calibration between the 217 and 143 spectra;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT+TE+EE - Plik'''<br />
This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range &#8467;=30-2508 for TT and &#8467;=30-1996 for TE and EE.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>T</i> and <i>E</i> cross-spectra. <br />
In temperature, only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used, while<br />
in <i>TE</i> and <i>EE</i> all of them are used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission T+P maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz and 353-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates;<br />
* best-fit CMB+foreground model for the beam-leakage template.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, plik TTTEEE likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik''.<br />
<br />
This file should not be used with any other TT-only high-&#8467; file.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed the <i>EE</i> and <i>TE</i> spectra (same range) and by a vector of 94 nuisance parameters.<br />
Those are, in g:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100TT;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143TT;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217TT;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217TT;<br />
* galf_EE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100EE;<br />
* galf_EE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143EE;<br />
* galf_EE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217EE;<br />
* galf_EE_A_143, the dust residual contamination at &#8467;=500 in 143&times;143EE;<br />
* galf_EE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217EE;<br />
* galf_EE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217EE;<br />
* galf_EE_index, the dust EE template slope, which should be set to -2.4;<br />
* galf_TE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100TE;<br />
* galf_TE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143TE;<br />
* galf_TE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217TE;<br />
* galf_TE_A_143, the dust residual contamination at &#8467;=500 in 143x143TE;<br />
* galf_TE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217TE;<br />
* galf_TE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217TE;<br />
* galf_TE_index, the dust EE template slope, which should be set to -2.4;<br />
* bleak_epsilon_0_0T_0E, beam-leakage parameter, espilon_0, 100&times;100 TE;<br />
* bleak_epsilon_1_0T_0E, beam-leakage parameter, espilon_1, 100&times;100 TE;<br />
* bleak_epsilon_2_0T_0E, beam-leakage parameter, espilon_2, 100&times;100 TE;<br />
* bleak_epsilon_3_0T_0E, beam-leakage parameter, espilon_3, 100&times;100 TE;<br />
* bleak_epsilon_4_0T_0E, beam-leakage parameter, espilon_4, 100&times;100 TE;<br />
* bleak_epsilon_0_0T_1E, beam-leakage parameter, espilon_0, 100&times;143 TE;<br />
* bleak_epsilon_1_0T_1E, beam-leakage parameter, espilon_1, 100&times;143 TE;<br />
* bleak_epsilon_2_0T_1E, beam-leakage parameter, espilon_2, 100&times;143 TE;<br />
* bleak_epsilon_3_0T_1E, beam-leakage parameter, espilon_3, 100&times;143 TE;<br />
* bleak_epsilon_4_0T_1E, beam-leakage parameter, espilon_4, 100&times;143 TE;<br />
* bleak_epsilon_0_0T_2E, beam-leakage parameter, espilon_0, 100&times;217 TE;<br />
* bleak_epsilon_1_0T_2E, beam-leakage parameter, espilon_1, 100&times;217 TE;<br />
* bleak_epsilon_2_0T_2E, beam-leakage parameter, espilon_2, 100&times;217 TE;<br />
* bleak_epsilon_3_0T_2E, beam-leakage parameter, espilon_3, 100&times;217 TE;<br />
* bleak_epsilon_4_0T_2E, beam-leakage parameter, espilon_4, 100&times;217 TE;<br />
* bleak_epsilon_0_1T_1E, beam-leakage parameter, espilon_0, 143&times;143 TE;<br />
* bleak_epsilon_1_1T_1E, beam-leakage parameter, espilon_1, 143&times;143 TE;<br />
* bleak_epsilon_2_1T_1E, beam-leakage parameter, espilon_2, 143&times;143 TE;<br />
* bleak_epsilon_3_1T_1E, beam-leakage parameter, espilon_3, 143&times;143 TE;<br />
* bleak_epsilon_4_1T_1E, beam-leakage parameter, espilon_4, 143&times;143 TE;<br />
* bleak_epsilon_0_1T_2E, beam-leakage parameter, espilon_0, 143&times;217 TE;<br />
* bleak_epsilon_1_1T_2E, beam-leakage parameter, espilon_1, 143&times;217 TE;<br />
* bleak_epsilon_2_1T_2E, beam-leakage parameter, espilon_2, 143&times;217 TE;<br />
* bleak_epsilon_3_1T_2E, beam-leakage parameter, espilon_3, 143&times;217 TE;<br />
* bleak_epsilon_4_1T_2E, beam-leakage parameter, espilon_4, 143&times;217 TE;<br />
* bleak_epsilon_0_2T_2E, beam-leakage parameter, espilon_0, 217&times;217 TE;<br />
* bleak_epsilon_1_2T_2E, beam-leakage parameter, espilon_1, 217&times;217 TE;<br />
* bleak_epsilon_2_2T_2E, beam-leakage parameter, espilon_2, 217&times;217 TE;<br />
* bleak_epsilon_3_2T_2E, beam-leakage parameter, espilon_3, 217&times;217 TE;<br />
* bleak_epsilon_4_2T_2E, beam-leakage parameter, espilon_4, 217&times;217 TE;<br />
* bleak_epsilon_0_0E_0E, beam-leakage parameter, espilon_0, 100&times;100 EE;<br />
* bleak_epsilon_1_0E_0E, beam-leakage parameter, espilon_1, 100&times;100 EE;<br />
* bleak_epsilon_2_0E_0E, beam-leakage parameter, espilon_2, 100&times;100 EE;<br />
* bleak_epsilon_3_0E_0E, beam-leakage parameter, espilon_3, 100&times;100 EE;<br />
* bleak_epsilon_4_0E_0E, beam-leakage parameter, espilon_4, 100&times;100 EE;<br />
* bleak_epsilon_0_0E_1E, beam-leakage parameter, espilon_0, 100&times;143 EE;<br />
* bleak_epsilon_1_0E_1E, beam-leakage parameter, espilon_1, 100&times;143 EE;<br />
* bleak_epsilon_2_0E_1E, beam-leakage parameter, espilon_2, 100&times;143 EE;<br />
* bleak_epsilon_3_0E_1E, beam-leakage parameter, espilon_3, 100&times;143 EE;<br />
* bleak_epsilon_4_0E_1E, beam-leakage parameter, espilon_4, 100&times;143 EE;<br />
* bleak_epsilon_0_0E_2E, beam-leakage parameter, espilon_0, 100&times;217 EE;<br />
* bleak_epsilon_1_0E_2E, beam-leakage parameter, espilon_1, 100&times;217 EE;<br />
* bleak_epsilon_2_0E_2E, beam-leakage parameter, espilon_2, 100&times;217 EE;<br />
* bleak_epsilon_3_0E_2E, beam-leakage parameter, espilon_3, 100&times;217 EE;<br />
* bleak_epsilon_4_0E_2E, beam-leakage parameter, espilon_4, 100&times;217 EE;<br />
* bleak_epsilon_0_1E_1E, beam-leakage parameter, espilon_0, 143&times;143 EE;<br />
* bleak_epsilon_1_1E_1E, beam-leakage parameter, espilon_1, 143&times;143 EE;<br />
* bleak_epsilon_2_1E_1E, beam-leakage parameter, espilon_2, 143&times;143 EE;<br />
* bleak_epsilon_3_1E_1E, beam-leakage parameter, espilon_3, 143&times;143 EE;<br />
* bleak_epsilon_4_1E_1E, beam-leakage parameter, espilon_4, 143&times;143 EE;<br />
* bleak_epsilon_0_1E_2E, beam-leakage parameter, espilon_0, 143&times;217 EE;<br />
* bleak_epsilon_1_1E_2E, beam-leakage parameter, espilon_1, 143&times;217 EE;<br />
* bleak_epsilon_2_1E_2E, beam-leakage parameter, espilon_2, 143&times;217 EE;<br />
* bleak_epsilon_3_1E_2E, beam-leakage parameter, espilon_3, 143&times;217 EE;<br />
* bleak_epsilon_4_1E_2E, beam-leakage parameter, espilon_4, 143&times;217 EE;<br />
* bleak_epsilon_0_2E_2E, beam-leakage parameter, espilon_0, 217&times;217 EE;<br />
* bleak_epsilon_1_2E_2E, beam-leakage parameter, espilon_1, 217&times;217 EE;<br />
* bleak_epsilon_2_2E_2E, beam-leakage parameter, espilon_2, 217&times;217 EE;<br />
* bleak_epsilon_3_2E_2E, beam-leakage parameter, espilon_3, 217&times;217 EE;<br />
* bleak_epsilon_4_2E_2E, beam-leakage parameter, espilon_4, 217&times;217 EE;<br />
* calib_100T, the relative calibration between 100 and 143 TT spectra;<br />
* calib_217T, the relative calibration between 217 and 143 TT spectra;<br />
* calib_100P, the calibration of the 100 EE spectra, which should be set to 1;<br />
* calib_143P, the calibration of the 143 EE spectra, which should be set to 1;<br />
* calib_217P, the calibration of the 217 EE spectra, which should be set to 1;<br />
* A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* galf_EE_A_100 = 0.060&plusmn;0.012;<br />
* galf_EE_A_100_143 = 0.050&plusmn;0.015;<br />
* galf_EE_A_100_217 = 0.110&plusmn;0.033;<br />
* galf_EE_A_143 = 0.10&plusmn;0.02;<br />
* galf_EE_A_143_217 = 0.240&plusmn;0.048;<br />
* galf_EE_A_217 = 0.72&plusmn;0.14;<br />
* galf_EE_index = -2.4;<br />
* galf_TE_A_100 = 0.140&plusmn;0.042;<br />
* galf_TE_A_100_143 = 0.120&plusmn;0.036;<br />
* galf_TE_A_100_217 = 0.30&plusmn;0.09;<br />
* galf_TE_A_143 = 0.240&plusmn;0.072;<br />
* galf_TE_A_143_217 = 0.60&plusmn;0.018;<br />
* galf_TE_A_217 = 1.80&plusmn;0.54;<br />
* galf_TE_index = -2.4;<br />
* bleak_epsilon_0_0T_0E = 0;<br />
* bleak_epsilon_1_0T_0E = 0;<br />
* bleak_epsilon_2_0T_0E = 0;<br />
* bleak_epsilon_3_0T_0E = 0;<br />
* bleak_epsilon_4_0T_0E = 0;<br />
* bleak_epsilon_0_0T_1E = 0;<br />
* bleak_epsilon_1_0T_1E = 0;<br />
* bleak_epsilon_2_0T_1E = 0;<br />
* bleak_epsilon_3_0T_1E = 0;<br />
* bleak_epsilon_4_0T_1E = 0;<br />
* bleak_epsilon_0_0T_2E = 0;<br />
* bleak_epsilon_1_0T_2E = 0;<br />
* bleak_epsilon_2_0T_2E = 0;<br />
* bleak_epsilon_3_0T_2E = 0;<br />
* bleak_epsilon_4_0T_2E = 0;<br />
* bleak_epsilon_0_1T_1E = 0;<br />
* bleak_epsilon_1_1T_1E = 0;<br />
* bleak_epsilon_2_1T_1E = 0;<br />
* bleak_epsilon_3_1T_1E = 0;<br />
* bleak_epsilon_4_1T_1E = 0;<br />
* bleak_epsilon_0_1T_2E = 0;<br />
* bleak_epsilon_1_1T_2E = 0;<br />
* bleak_epsilon_2_1T_2E = 0;<br />
* bleak_epsilon_3_1T_2E = 0;<br />
* bleak_epsilon_4_1T_2E = 0;<br />
* bleak_epsilon_0_2T_2E = 0;<br />
* bleak_epsilon_1_2T_2E = 0;<br />
* bleak_epsilon_2_2T_2E = 0;<br />
* bleak_epsilon_3_2T_2E = 0;<br />
* bleak_epsilon_4_2T_2E = 0;<br />
* bleak_epsilon_0_0E_0E = 0;<br />
* bleak_epsilon_1_0E_0E = 0;<br />
* bleak_epsilon_2_0E_0E = 0;<br />
* bleak_epsilon_3_0E_0E = 0;<br />
* bleak_epsilon_4_0E_0E = 0;<br />
* bleak_epsilon_0_0E_1E = 0;<br />
* bleak_epsilon_1_0E_1E = 0;<br />
* bleak_epsilon_2_0E_1E = 0;<br />
* bleak_epsilon_3_0E_1E = 0;<br />
* bleak_epsilon_4_0E_1E = 0;<br />
* bleak_epsilon_0_0E_2E = 0;<br />
* bleak_epsilon_1_0E_2E = 0;<br />
* bleak_epsilon_2_0E_2E = 0;<br />
* bleak_epsilon_3_0E_2E = 0;<br />
* bleak_epsilon_4_0E_2E = 0;<br />
* bleak_epsilon_0_1E_1E = 0;<br />
* bleak_epsilon_1_1E_1E = 0;<br />
* bleak_epsilon_2_1E_1E = 0;<br />
* bleak_epsilon_3_1E_1E = 0;<br />
* bleak_epsilon_4_1E_1E = 0;<br />
* bleak_epsilon_0_1E_2E = 0;<br />
* bleak_epsilon_1_1E_2E = 0;<br />
* bleak_epsilon_2_1E_2E = 0;<br />
* bleak_epsilon_3_1E_2E = 0;<br />
* bleak_epsilon_4_1E_2E = 0;<br />
* bleak_epsilon_0_2E_2E = 0;<br />
* bleak_epsilon_1_2E_2E = 0;<br />
* bleak_epsilon_2_2E_2E = 0;<br />
* bleak_epsilon_3_2E_2E = 0;<br />
* bleak_epsilon_4_2E_2E = 0;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* calib_100P = 1;<br />
* calib_143P = 1; <br />
* calib_217P = 1; <br />
* A_pol = 1;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT only - Plik lite'''<br />
This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range &#8467;=30-2508. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT</i> spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-&#8467; likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TT likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.<br />
<br />
'''TT EE TE - Plik lite'''<br />
This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range &#8467;=30-2508 for temperature and &#8467;=30-1996 for TE and EE. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT<i/>, <i>TE</i>, and <i>EE</i> spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TTTEEE likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TTTEEE, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the <i>EE</i>, and <i>TE</i> spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
''' Lensing likelihoods '''<br />
<br />
'''T only'''<br />
This file allows for the computation of the baseline lensing likelihood, using only the SMICA <i>T</i><br />
map-based lensing reconstruction. Only the lensing multipole range &#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of a model-dependent correction to the normalization and<br />
the "N1 bias." To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant "mean field" and "N0" contribution, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> CMB map;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i> spectrum is needed to compute the normalization and N1 corrections.<br />
<br />
'''T+P'''<br />
This file allows for the computation of the baseline lensing likelihood, using both the <br />
<i>T</i> and <i>P</i> SMICA map-based lensing reconstruction. Only the lensing multipole range&#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of model dependent correction to the normalization and<br />
the N1 bias. To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> and <i>P</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured outside a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> and <i>E</i> CMB maps;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T+P-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive), the <i>EE</i> and <i>TE</i> power spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i>, <i>EE</i>, and <i>TE</i> spectra are needed to compute the normalization and N1 corrections.<br />
<br />
'''Data sets - Extended data'''<br />
<br />
Four other data files are available.<br />
Those extend the baseline delivery by adding:<br />
* TE, EE and other joint high-&#8467 Plik likelihoods, ''COM_Likelihood_Data-extra-plik-HM-ext_R2.00.tar.gz'';<br />
* TT and TTTEEE unbinned high-&#8467 Plik likelihood, ''COM_Likelihood_Data-extra-plik-unbinned_R2.00.tar.gz'';<br />
* TT, TE, EE, and TTTEEE Plik likelihood using the detset cross-spectra instead of the half-mission one, and including empirical correlated noise correction for the TT spectra, ''COM_Likelihood_Data-extra-plik-DS_R2.00.tar.gz'';<br />
* extended &#8467 range lensing likelihood, ''COM_Likelihood_Data-extra-lensing-ext_R2.00.tar.gz''.<br />
<br />
Note that although these products are discussed in the Planck papers, they are not used for the baseline results.<br />
<br />
Each file contains a '''readme.md''' description of the content and the use of the different likelihood files.<br />
<br />
<br />
<br />
<!-- <br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the {{PlanckPapers|planck2013-p08|1|Power spectrum & Likelihood Paper}} (for the CMB based likelihood) and in the {{PlanckPapers|planck2013-p12|1|Lensing Paper}} (for the lensing likelihood) .<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The Commander likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 &plusmn; 0.2 and a_gs = 0.4 &plusmn; 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first-order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first-order renormalization procedure. This means that the code will need both the TT and &phi;&phi; power spectrum up to &#8467; = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between &#8467; = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
</span><br />
<span style="color:red">OUTSTANDING: description of likelihood masks </span><br />
'''Production process'''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each data set comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<sup>-6</sup> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander''<nowiki>:</nowiki><br />
* all Planck channel maps;<br />
* compact source catalogues;<br />
* common masks;<br />
* beam transfer functions for all channels.<br />
<br />
; ''lowlike''<nowiki>:</nowiki><br />
* WMAP9 likelihood data;<br />
* Low-<math>\ell</math> Commander map.<br />
<br />
; ''CAMspec''<nowiki>:</nowiki><br />
* 100-, 143- and 217-GHz detector and detsets maps;<br />
* 857GHz channel map;<br />
* compact source catalogue;<br />
* common masks (0,1 and 3);<br />
* beam transfer function and error eigenmodes and covariance for 100-, 143- and 217-GHz detectors and detsets;<br />
* theoretical templates for the tSZ and kSZ contributions;<br />
* color corrections for the CIB emission for the 143- and 217-GHz detectors and detsets;<br />
* fiducial CMB model (bootstrapped from WMAP7 best-fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz.<br />
<br />
; ''lensing''<nowiki>:</nowiki><br />
* the lensing map;<br />
* beam error eigenmodes and covariance for the 143- and 217-GHz channel maps;<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt''<nowiki>:</nowiki><br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here];<br />
* the tSZ and kSZ template are changed to match those of CAMspec.<br />
<br />
''' File names and Meta-data '''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta-data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
--><br />
<br />
'''Likelihood Masks'''<br />
<br />
'''General description'''<br />
<br />
We provide the masks for Temperature and Polarisation used to exclude the regions of strongest foreground emission in the CMB maps when computing the empirical spectra that we use to form the high-&#8467 likelihood. The masks are provided for each frequency between 100 and 217 GHz, masking the appropriate part of the Galactic Plane and, for temperature only, the relevant population of point sources. Note that to compute the empirical power spectrum of the maps, one should also take into account missing pixels in a particular map. This is not included in the masks we distribute.<br />
<br />
'''Production Process'''<br />
Complete production process for those masks is described in {{PlanckPapers|planck2014-a13}}.<br />
<br />
The temperature masks are the combination of a Galactic mask, a point source mask and (for 100Ghz and 217GHz) a CO mask. Extended objects, planets, etc are included in the point source mask. <br />
The polarization masks are simply the Galactic masks.<br />
<br />
The Galactic masks are obtained by thresholding a CMB corrected and <math>10^o</math> smoothed 353GHz map. The threshold is tuned so as to retain a given fraction of the sky, between 50% and 80%. Each mask is apodized by a <math>4^o.71</math> FWHM gaussian window function using the distance map. Special care is taken to smooth this distance map, in order to avoid strong caustics. The apodization down-weights an effective 10% of the sky. Following {{PlanckPapers|planck2014-a13}}, the Galactic masks are named by the effective unmasked sky area G70, G60, G50 and G41.<br />
<br />
The point source masks are different for each frequency. They are based on the 2015 Planck catalog and cut out all the sources detected at S/N = 5 or higher in each channel. Each source is masked with a circular aperture of size 3xFWHM of that channel (i.e. 3x9.′66 at 100GHz, 3x7.′22 at 143GHz, and 3x4.′90 at 217GHz). Note that we include in the point source masks all sources above our threshold, including possible galactic ones. The mask is further apodized with a gaussian window function with FWHM=30'. <br />
<br />
The CO masks is used only at 100GHz and 217GHz, since there is no (strong) CO line in the 147 GHz channel. They are based on the Type 3 CO map from the Planck2013 delivery. The CO map is smoothed to 120' and a threshold is applied to mask all regions above <math>1 K_{RJ} km s^{−1}</math>. The mask is further apodized to 30'.<br />
<br />
Mask combinations are performed by multiplying a galactic, a point source, and possibly a CO mask together.<br />
<br />
The Temperature masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter T and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: T66 = G70+Point source mask 100Ghz+CO mask<br />
* 143Ghz: T57 = G60+Point source mask 143Ghz<br />
* 217Ghz: T47 = G50+Point source mask 217Ghz+CO mask<br />
<br />
The Polarization masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter P and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: P70 = G70<br />
* 143Ghz: P50 = G50<br />
* 217Ghz: P41 = G41<br />
<br />
'''Inputs'''<br />
* Galactic masks: The SMICA CMB temperature map, the 353GHz temperature map.<br />
* Point source masks: The Planck 2015 catalog, the FWHM of each of the frequencies.<br />
* CO mask: the Type 3 CO map from the Planck 2013 delivery.<br />
<br />
''' File names and meta-data '''<br />
The masks are distributed in a single tar file ''COM_Likelihood_Masks_R2.00.tar.gz''.<br />
The files extract to 6 files<br />
* temperature_100.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 100Ghz, i.e. T66<br />
* temperature_143.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 143Ghz, i.e. T57<br />
* temperature_217.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 217Ghz, i.e. T47<br />
* polarization_100.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 100Ghz, i.e. P70<br />
* polarization_143.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 143Ghz, i.e. P50<br />
* polarization_217.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 217Ghz, i.e. P41<br />
<br />
<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #EEE8AA;width:80%"><br />
'''2013 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''General description'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles <math> \ell </math> = 2-2479. Over the multipole range <math> \ell </math> = 2–49, the power spectrum is derived from a component-separation algorithm, ''Commander'', applied to maps in the frequency range 30–353 GHz over 91% of the sky {{PlanckPapers|planck2013-p06}}. The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction. For multipoles greater than <math>\ell=50</math>, instead, the spectrum is derived from the ''CAMspec'' likelihood {{PlanckPapers|planck2013-p08}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds. Associated 1-sigma errors include beam and foreground uncertainties. Both ''Commander'' and ''CAMspec'' are described in more details in the sections below.<br />
<br />
[[File: mission_spectrum.png|thumb|center|700px|'''CMB spectrum. Logarithmic x-scale up to <math>\ell=50</math>, linear at higher <math>\ell</math>; all points with error bars. The red line is the Planck best-fit primordial power spectrum (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}).''']]<br />
<br />
'''Likelihood'''<br />
<br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the Power spectrum & Likelihood Paper {{PlanckPapers|planck2013-p08}} (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) {{PlanckPapers|planck2013-p12}}.<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The ''Commander'' likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 ± 0.2 and a_gs = 0.4 ± 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. This means that the code will need both the TT and $\phi\phi$ power spectrum up to <math>\ell</math> = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between <math>\ell</math> = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
<br />
'''Production process'''<br />
<br />
'''CMB spectra'''<br />
<br />
The <math>\ell</math> < 50 part of the Planck power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters {{PlanckPapers|planck2013-p06}}. The power spectrum at any multipole <math>\ell</math> is given as the maximum probability point for the posterior <math>C_\ell</math> distribution, marginalized over the other multipoles, and the error bars are 68% confidence level {{PlanckPapers|planck2013-p08}}. <br />
<br />
The <math>\ell</math> > 50 part of the CMB temperature power spectrum has been derived by the CamSpec likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of {{PlanckPapers|planck2013-p08}}. Frequency spectra are computed as noise weighted averages of the cross-spectra between single detector and sets of detector maps. Mask and multipole range choices for each frequency spectrum are summarized in Table 4 of {{PlanckPapers|planck2013-p08}}. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of {{PlanckPapers|planck2013-p08}} and Sec. 4 of {{PlanckPapers|planck2013-p11}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with unresolved foreground and beam uncertainties. Both spectrum and associated covariance matrix are given as uniformly weighted band averages in 74 bins. <br />
<br />
'''Likelihood'''<br />
<br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each dataset comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<math>^{-6}</math> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
; Low-l spectrum (<math>\ell < 50</math>):<br />
* frequency maps from 30–353 GHz<br />
* common mask {{PlanckPapers|planck2013-p06}}<br />
* compact sources catalog<br />
<br />
; High-l spectrum (<math>50 < \ell < 2500</math>): <br />
<br />
* 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 2 in {{PlanckPapers|planck2013-p08}})<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of {{PlanckPapers|planck2013-p11}})<br />
* Beam transfer function uncertainties {{PlanckPapers|planck2013-p03c}}<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander'' :<br />
* all Planck channels maps<br />
* compact source catalogs<br />
* common masks<br />
* beam transfer functions for all channels<br />
<br />
; ''lowlike'' :<br />
* WMAP9 likelihood data<br />
* Low-<math>\ell</math> Commander map<br />
<br />
; ''CAMspec'' :<br />
* 100, 143 and 217 GHz detector and detsets maps<br />
* 857GHz channel map<br />
* compact source catalog<br />
* common masks (0,1 & 3)<br />
* beam transfer function and error eigenmodes and covariance for 100, 143 and 217 GHz detectors & detsets<br />
* theoretical templates for the tSZ and kSZ contributions<br />
* color corrections for the CIB emission for the 143 and 217GHz detectors and detsets<br />
* fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz<br />
<br />
; ''lensing'' :<br />
* the lensing map<br />
* beam error eigenmodes and covariance for the 143 and 217GHz channel maps<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt'' :<br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]<br />
* the tSZ andkSZ template are changed to match those of CAMspec<br />
<br />
''' File names and Meta data '''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The CMB spectrum and its covariance matrix are distributed in a single FITS file named <br />
* ''{{PLASingleFile | fileType=cosmo | name=COM_PowerSpect_CMB_R1.10.fits | link=COM_PowerSpect_CMB_R1.10.fits}}'' <br />
<br />
which contains 3 extensions<br />
<br />
; LOW-ELL (BINTABLE)<br />
: with the low ell part of the spectrum, not binned, and for l=2-49. The table columns are<br />
# ''ELL'' (integer): multipole number<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERRUP'' (float): the upward uncertainty<br />
# ''ERRDOWN'' (float): the downward uncertainty<br />
<br />
; HIGH-ELL (BINTABLE)<br />
: with the high-ell part of the spectrum, binned into 74 bins covering <math>\langle l \rangle = 47-2419\ </math> in bins of width <math>l=31</math> (with the exception of the last 4 bins that are wider). The table columns are as follows:<br />
# ''ELL'' (integer): mean multipole number of bin<br />
# ''L_MIN'' (integer): lowest multipole of bin<br />
# ''L_MAX'' (integer): highest multipole of bin<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERR'' (float): the uncertainty<br />
<br />
; COV-MAT (IMAGE)<br />
: with the covariance matrix of the high-ell part of the spectrum in a 74x74 pixel image, i.e., covering the same bins as the ''HIGH-ELL'' table.<br />
<br />
The spectra give $D_\ell = \ell(\ell+1)C_\ell / 2\pi$ in units of $\mu\, K^2$, and the covariance matrix is in units of $\mu\, K^4$. The spectra are shown in the figure below, in blue and red for the low- and high-<math>\ell</math> parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.<br />
<br />
[[File: CMBspect.jpg|thumb|center|700px|'''CMB spectrum. Linear x-scale; error bars only at high <math>\ell</math>.''']]<br />
<br />
'''Likelihood'''<br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
<br />
</div><br />
</div><br />
<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
[[Category:Mission products|008]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_maps&diff=14382CMB maps2018-07-16T16:40:06Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:2018 CMB maps}}<br />
<br />
== Overview ==<br />
This section describes the CMB maps produced from the Planck data. These products are derived from some or all of the nine frequency channel maps using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of each product and how it is obtained, followed by a description of the FITS file containing the data and associated information.<br />
All the details can be found in {{PlanckPapers|planck2016-l04}} and, for earlier releases, in {{PlanckPapers|planck2013-p06}} and {{PlanckPapers|planck2014-a11}}.<br />
<br />
<br />
<br />
==2018 CMB maps==<br />
CMB maps have been produced using four different methods: COMMANDER, NILC, SEVEM, and SMICA, as described in the [[Astrophysical_component_separation#CMB_and_foreground_separation | CMB and foreground separation]] section and also in Appendices A-D of {{PlanckPapers|planck2016-l04}} and references therein.<br />
<br />
For each method we provide the following:<br />
* Full-mission CMB intensity map, with corresponding confidence mask and effective beam transfer function.<br />
* Full-mission CMB polarisation map, with corresponding confidence mask and effective beam transfer function. <br />
* In-painted CMB intensity and polarisation maps, intended for PR purposes.<br />
In addition, and for characterisation purposes, we include four other sets of maps from two data splits: odd/even ring and first/second half-mission. Half-difference maps can be used to provide an approximate noise estimates for the full mission, but they should be used with caution. Each split has caveats in this regard: there are noise correlations between the odd/even split maps, and unobserved pixels in both splits. Masks flagging unobserved pixels are provided for each split, and we strongly encourage use of these when analysing split maps. <br />
<br />
In addition, for SMICA, we also provide a CMB map from which Sunyaev-Zeldovich (SZ) sources have been projected out, while SEVEM provides cleaned single-frequency maps at 70, 100, 143 and 217 GHz for both intensity and polarization.<br />
<br />
All CMB products are provided at an angular resolution of 5 arcmin FWHM, and HEALPix resolution <i>N</i><sub>side</sub>=2048, with the exception of the SEVEM cleaned single-frequency maps which are provided at their native resolution, and in units of K<sub>cmb</sub>. <br />
<br />
For a complete description of the above data structures, see [[#File names and structure | below]]; the content of the first extensions is illustrated and commented in the table below.<br />
<br />
The gallery below shows the inpainted full-mission CMB maps (T, Q and U) from each pipeline. The temperature maps are shown at 5 arcmin FWHM resolution, while the polarization maps are shown at 80 arcmin FWHM resolution, in order to suppress instrumental noise. <br />
<br />
<center><br />
<gallery style="padding:0 0 0 0;" perrow=3 widths=300px heights=180> <br />
File:cmb_inpaint_T_commander_v1.png | '''Commander temperature'''<br />
File:cmb_inpaint_Q_commander_v1.png | '''Commander Stokes Q'''<br />
File:cmb_inpaint_U_commander_v1.png | '''Commander Stokes U'''<br />
File:cmb_inpaint_T_nilc_v1.png | '''NILC temperature'''<br />
File:cmb_inpaint_Q_nilc_v1.png | '''NILC Stokes Q'''<br />
File:cmb_inpaint_U_nilc_v1.png | '''NILC Stokes U'''<br />
File:cmb_inpaint_T_sevem_v2.png | '''SEVEM temperature'''<br />
File:cmb_inpaint_Q_sevem_v2.png | '''SEVEM Stokes Q'''<br />
File:cmb_inpaint_U_sevem_v2.png | '''SEVEM Stokes U'''<br />
File:cmb_inpaint_T_smica_v1.png | '''SMICA temperature'''<br />
File:cmb_inpaint_Q_smica_v1.png | '''SMICA Stokes Q'''<br />
File:cmb_inpaint_U_smica_v1.png | '''SMICA Stokes U'''<br />
</gallery><br />
</center><br />
<br />
===Product description ===<br />
<br />
====COMMANDER====<br />
<br />
;Principle<br />
<br />
: COMMANDER is a Planck software code implementing Bayesian parametric component separation. Each astrophysical signal component is modelled in terms of a small number of free parameters per pixel, typically in terms of an amplitude at a given reference frequency and a small set of spectral parameters, and these are fitted to the data with an MCMC Gibbs sampling algorithm. A new feature in the Planck 2018 analysis is support for multi-resolution analysis, allowing reconstruction of both CMB and foreground maps at full angular resolution. Only CMB products are provided from Commander in the Planck 2018 release (see {{PlanckPapers|planck2016-l04}} for details), while for polarization both CMB and foreground products are provided. For temperature, a dedicated low-resolution CMB map is also provided as part of the Planck likelihood package.<br />
<br />
; Resolution (effective beam)<br />
<br />
: The Commander sky maps have different angular resolutions depending on data products:<br />
:* CMB temperature and polarization and thermal dust polarization maps are provided at 5 arcmin FWHM resolution<br />
:* Synchrotron polarization maps are provided at 40 arcmin FWHM resolution<br />
:* The low-resolution CMB likelihood map is provided at an angular resolution of 40 arcmin FWHM.<br />
<br />
; Confidence mask<br />
<br />
: The Commander temperature confidence mask is produced by thresholding the chi-square map characterizing the global fits, combined with direct CO amplitude thresholding to eliminate known leakage effects. In addition, we exclude all pixels brighter than 10mK in the 30GHz map, in order to remove particularly bright radio sources. Finally, we remove by hand the Virgo and Coma clusters, as well as the Crab nebula. A total of 88% of the sky is admitted for analysis.<br />
<br />
: The Commander polarization mask is produced in a similar manner, starting by thresholding the chi-squared map. In addition, we exclude all pixels for which the thermal dust polarization amplitude is brighter than 20µK<sub>RJ</sub> at 353GHz, as well as particularly bright objects in the PCCS2 source catalog. Finally, we remove a small region that is particularly contaminated by cosmic ray glitches. A total of 86% of the sky is admitted for analysis.<br />
<br />
; Pre-processing and data selection<br />
<br />
: The primary Commander 2018 analysis is carried out at full angular resolution, and no smoothing to a common resolution is applied to the maps, in constrast to the procedure employed in previous releases. The temperature analysis employs all nine Planck frequency maps between 30 and 857 GHz, while the polarization analysis employs the seven frequency maps between 30 and 353 GHz. No external data are used in the 2018 Commander analysis.<br />
<br />
; Priors<br />
<br />
: The following priors are enforced in the Commander analysis:<br />
* The 30 GHz zero-level is fixed to zero, while the 44 and 70 GHz zero-levels are fitted freely with uniform priors. HFI zero-levels are fitted with a strong CIB prior.<br />
* Dipoles are fitted only at 70 and 100 GHz; all other are fixed to zero.<br />
* Gaussian priors are enforced on spectral parameters, with values informed by the values derived in the high signal-to-noise areas of the sky<br />
* The Jeffreys ignorance prior is enforced on spectral parameters in addition to the informative Gaussian priors<br />
<br />
; Fitting procedure<br />
<br />
: Given data and priors, Commander either maximizes, or samples from, the Bayesian posterior, P(theta|data). Because this is a highly non-Gaussian and correlated distribution, involving millions of parameters, these operations are performed by means of the Gibbs sampling algorithm, in which joint samples from the full distributions are generated by iteratively sampling from the corresponding conditional posterior distributions, P(theta_i| data, theta_{j/=i}). All parameters are optimized jointly.<br />
<br />
====NILC====<br />
<br />
;Principle<br />
<br />
: Needlet Internal Linear Combination (or NILC in short) is a blind component separation method for the measurement of Cosmic Microwave Background (CMB) from the multi-frequency observations of sky. It is an implementation of an Internal Linear Combination (ILC) of the frequency channels under consideration with minimum error variance on a frame of spherical wavelets called needlets, allowing localized filtering in both pixel space and harmonic space. The method includes multipoles up to 4000. Temperature and, E-mode and B-mode of polarization maps are produced independently. The Q and U maps of CMB polarization have been reconstructed from the corresponding E-mode and B-mode maps.<br />
<br />
; Resolution (effective beam)<br />
<br />
: The effective beam is equivalent to a Gaussian circular beam with FWHM=5 arcminutes. <br />
<br />
; Confidence mask<br />
<br />
: For each needlet scale, we identify the frequency channel that contributes the most to the final reconstruction of CMB for that band. Then we scale the sky maps for 30GHz and 353GHz to that frequency channel to obtain the scaled-sky map and compute the root mean square (RMS) of full mission CMB map. The mask is obtained by setting a cut-off at each needlet scale. The cutoff values are 500 times the RMS value of CMB for temperature and 1500 times the RMS value of CMB for polarization for each scale. The final mask is reconstructed from the union of all the masks obtained at different needlet scales. The confidence masks cover the most contaminated regions of the sky, leaving approximately 78.6 per cent of useful sky for temperature and 82 per cent for polarization.<br />
<br />
; Pre-processing<br />
<br />
: All sky maps are convolved/deconvolved in harmonic space, to a common beam resolution corresponding to a Gaussian beam of 5 arc-minutes FWHM. A very small preprocessing mask has been used on the temperature sky maps. Prior to implement the pipeline on the sky maps, the masked regions are filled using PSM tools which uses an increasing number of neighboring pixels to fill regions deeper in the hole. At each iteration it uses pixels at up to twice the diameter of the pixel times number of iteration. No preprocessing has been done on polarization sky maps.<br />
<br />
; Linear combination<br />
<br />
: Needlet ILC weights are computed for each of T, E and B, for each scale and for each pixel of the needlet representation at that scale. For each of T, E and B, a full-sky CMB map, at 5 arc-minutes beam resolution, is synthesized from the NILC needlet coefficients.<br />
<br />
; Post-processing<br />
<br />
: E and B maps are re-combined into Q and U products using standard HEALPix tools.<br />
<br />
====SEVEM====<br />
<br />
; Principle<br />
<br />
: SEVEM produces cleaned CMB maps at several frequencies by using a procedure based on template fitting in real space. The templates used in the SEVEM pipeline are typically constructed by subtracting two close Planck frequency channel maps, after first smoothing them to a common resolution to ensure that the CMB signal is properly removed. A linear combination of the templates <math>t_j</math> is then subtracted from (hitherto unused) map d to produce a cleaned CMB map at that frequency. This is done in real space at each position on the sky: <math> T_c(\mathbf{x}, ν) = d(\mathbf{x}, ν) − \sum_{j=1}^{n_t} α_j t(\mathbf{x}) </math><br />
where <math>n_t</math> is the number of templates. The <math>α_j</math> coefficients are obtained by minimising the variance of the cleaned map <math>T_c</math> outside a given mask. Note that the same expression applies for I, Q and U. Although we exclude very contaminated regions during the minimization, the subtraction is performed for all pixels and, therefore, the cleaned maps cover the full-sky (although foreground residuals are expected to be particularly large in those areas excluded by the minimisation). In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust. A subset of the cleaned single frequency maps are then combined to obtain the final CMB map.<br />
<br />
There are several possible configurations of SEVEM with regard to the number of frequency maps which are cleaned or the number of templates that are used in the fitting. Note that the production of cleaned maps at different frequencies is of great interest by itself in order to test the robustness of the results, and these intermediate products (cleaned maps at individual frequencies for intensity and polarization) are also provided in the archive. Therefore, to define the best strategy, one needs to find a compromise between the number of maps that can be cleaned and the number of templates that can be constructed.<br />
<br />
;Intensity<br />
<br />
For the CMB intensity case, we have cleaned the 70, 100, 143 and 217 GHz maps using a total of five templates. In particular, three templates constructed as the difference of two consecutive Planck channels smoothed to a common resolution [30GHz &ndash; 44GHz], [44GHz &ndash; 70GHz] and [543GHz &ndash; 535GHz] as well as a fourth template given by the 857 GHz channel are used to clean the 100, 143 and 217 GHz maps. Before constructing the templates, the six frequency channels involved in the templates are inpainted at the corresponding point source positions detected at each frequency using the Mexican Hat Wavelet algorithm (these positions are given in the provided point sources masks). The size of the holes to be inpainted is determined taking into account the beam size of the channel as well as the flux of each source. The inpainting algorithm is based on simple diffuse inpainting, which fills one pixel with the mean value of the neighbouring pixels in an iterative way. To avoid inconsistencies when subtracting two channels, each frequency map is inpainted on the sources detected in that map and on the second map (if any) used to construct the template. Then the maps are smoothed to a common resolution, by convolving the first map with the beam of the second one and viceversa. For the fourth template, we simply filter the inpainted 857 GHz map with the 545 GHz beam. The cleaned 70 GHz map is produced similarly by considering two templates, the [30GHz &ndash; 44GHz] map and a second template obtained as [353GHz &ndash; 143GHz] constructed at the original resolution of the 70 GHz map.<br />
<br />
The coefficients to clean the frequency maps are obtained by minimising the variance outside the analysis mask, that covers the 1 per cent brightest emission of the sky as well as point sources detected at all frequency channels. Once the maps are cleaned, each of them is inpainted on the point sources positions detected at that (raw) channel. Then, the Mexican Hat Wavelet algorithm is run again, now on the cleaned maps. A number of new sources are found and are also inpainted at each channel. The resolution of the cleaned map is the same as that of the original data. Our final CMB map is then constructed by combining the 143 and 217 GHz maps by weighting the maps in harmonic space taking into account the noise level, the resolution and a rough estimation of the foreground residuals of each map (obtained from realistic simulations). This final map has a resolution corresponding to a Gaussian beam of fwhm=5 arcminutes and <i>N</i><sub>side</sub>=2048 and the maximum considered multipole is <math>\ell=4000</math>. The monopole and dipole over the full-sky have been subtracted from the final CMB map.<br />
<br />
In addition, the cleaned CMB maps produced at 70, 100, 143 and 217 GHz frequencies are also provided. The resolution of these maps is the same as that of the uncleaned frequency channels and have been constructed at <i>N</i><sub>side</sub>=1024 for 70 GHz and <i>N</i><sub>side</sub>=2048 for the rest of the maps. They have been inpainted at the position of the point sources detected in the raw and cleaned maps (these positions are given in the corresponding inpainting masks). The monopole and dipole over the full-sky have also been removed from each of the cleaned maps.<br />
<br />
The confidence mask is produced by studying the differences between several SEVEM CMB reconstructions, which correspond to maps cleaned at different frequencies or using different analysis masks. The obtained mask leaves a useful sky fraction of approximately 84 per cent.<br />
<br />
;Polarization<br />
<br />
To clean the polarization maps, a procedure similar to the one used for intensity data is applied to the Q and U maps independently. Cleaned maps at 70, 100, 143 and 217 GHz are also produced but, given that a smaller number of frequency channels is available for polarization, the templates selected to clean the maps are different. In particular, we clean the 70 GHz map using two templates and the rest of the channels using different combinations of three templates. <br />
<br />
Following the same procedure as for the intensity case, those channels involved in the construction of the templates are inpainted in the position of the sources detected in the raw frequency maps. The sources are selected from a non-blind search, based on the Filtered Fusion technique, using as candidates those sources detected in intensity. These inpainted maps are then used to construct a total of six templates, one of them at two different resolutions. To trace the synchrotron emission, we construct a template as the subtraction of the 30 GHz minus the 44 GHz map, after being convolved with the beam of each other. For the dust emission, the following templates are considered: [217GHz &ndash; 143GHz], [217GHz &ndash; 100GHz] and [143GHz &ndash; 100GHz] at 1 degree resolution, [353GHz &ndash; 217GHz] and [353GHz &ndash; 143GHz] at 10 arcminutes resolution. The last template is also constructed at the resolution of the 70 GHz channel, in order to clean that map. <br />
<br />
Different combinations of these templates (see Table C.3 in {{PlanckPapers|planck2016-l04}} for details) are then used to clean the raw 70, 100, 143 and 217 GHz channels (at its native resolution). The corresponding linear coefficients are estimated independently for Q and U by minimising the variance of the cleaned maps outside a mask, that covers the point sources detected in polarization and the 3 per cent brightest Galactic emission. Once the maps have been cleaned, inpainting of the point sources detected at the corresponding raw maps is carried out. Then the non-blind search for point sources is run again on the cleaned maps and the new identified sources are also inpainted. The 100, 143 and 217 GHz cleaned maps are then combined in harmonic space, using E and B decomposition, to produce the final CMB maps for the Q and U components at a resolution of 5' (Gaussian beam) for a HEALPix parameter <i>N</i><sub>side</sub>=2048. The maximum considered multipole is <math>\ell=3000</math>. Each map is weighted taking into account its noise and resolution. In addition, the lowest multipoles of the 217 GHz cleaned map are down-weighting, since they are expected to be more contaminated by the presence of residual systematics.<br />
<br />
The cleaned CMB maps at individual frequency channels produced as intermediate steps of SEVEM are also provided for Q and U, at their native resolution. The four pairs of Q/U maps have been inpainted in the positions of the detected point sources (given by the corresponding inpainting masks).<br />
<br />
The confidence mask is constructed as the product of two different masks. One of them is obtained from the 353 GHz data channel and excludes those regions more contaminated by thermal dust. The second mask is constructed by thresholding a map of the ratio between the locally estimated RMS of P in the cleaned CMB map, over the same quantity expected for a map containg CMB plus noise. The combination of these two masks leaves a useful sky fraction of approximately 80 per cent.<br />
<br />
;Resolution<br />
<br />
: The cleaned CMB maps for intensity and polarization are constructed at <i>N</i><sub>side</sub>=2048 and at the standard resolution of 5 arcminutes (Gaussian beam). The maximum considered multipole is <math>\ell=4000</math> for intensity and <math>\ell=3000</math> for polarization.<br />
<br />
; Confidence masks<br />
<br />
: The confidence masks cover the most contaminated regions of the sky, leaving approximately 84 per cent of useful sky for intensity, and 80 per cent for polarization.<br />
<br />
; Point source masks<br />
<br />
: The point source masks contain the holes corresponding to the point sources detected at each raw Planck frequency channel in intensity and polarization. The number of sources detected are given in the upper part of Table C.1 of {{PlanckPapers|planck2016-l04}}. There is one mask for intensity and another one for polarization per frequency channel. When using the Planck channels in the construction of the templates, these have been inpainted in the positions of the point sources given in these masks, to reduce the emission from this contaminant in the templates and its propagation to the final cleaned CMB maps.<br />
<br />
; Inpainting masks<br />
: The inpainting masks include the positions of the point sources that have been inpainted in the cleaned single-frequency maps. They contain point sources detected at the original raw data at those frequencies plus the sources detected in the cleaned frequency maps (see Table C.1 of {{PlanckPapers|planck2016-l04}}). There is a mask for intensity and another one for polarization for each of the cleaned frequency maps (70, 100, 143 and 217 GHz) as well as the corresponding masks for the combined map. The latter are constructed as the product of the individual frequency masks of those cleaned channels that are combined in the final CMB map (i.e., the product of 143 and 217 GHz masks for intensity and of 100, 143 and 217 GHz for polarization). Note that the inpainted positions are not excluded by default by the SEVEM confidence mask, but only if they are considered unreliable with the general procedure used to construct the SEVEM confidence mask.<br />
<br />
<br />
=====Foreground-subtracted maps=====<br />
<br />
In addition to the regular CMB maps, SEVEM provides maps cleaned of the foregrounds for selected frequency channels (categorized as fgsub-sevem in the archive). In particular, for both intensity and polarization there are cleaned CMB maps available at 70, 100, 143 and 217 GHz, provided at the original resolution and <i>N</i><sub>side</sub> of the uncleaned channel (1024 for 70 GHz and 2048 for the rest of the maps).<br />
<br />
====SMICA====<br />
; Principle<br />
: SMICA produces CMB maps by linearly combining Planck input channels with multipole-dependent weights, including multipoles up to <math>\ell = 4000</math>. Temperature and polarization maps are produced independently. In temperature, two distinct CMB renderings are produced and then merged (hybridized) together into a single CMB intensity map. In polarization, the E and B modes are processed independently and the results are combined to produce Q and U maps.<br />
; Resolution (effective beam)<br />
: The SMICA intensity map has an effective beam window function of 5 arc-minutes which is truncated at <math>\ell=4000</math>.<br />
: The SMICA Q and U maps are obtained similarly but are produced at <math>N_{side}</math>=1024 with an effective beam of 10 arc-minutes.<br />
; Confidence mask<br />
: A confidence mask is provided which excludes some parts of the Galactic plane, some very bright areas and masked point sources. This mask provides a qualitative (and subjective) indication of the cleanliness of a pixel.<br />
<br />
; Intensity.<br />
<br />
SMICA operation starts with a pre-processing step to deal with regions of very strong emission<br />
(such as the Galactic center) and point sources. <br />
The nine pre-processed Planck frequency channels from 30 to 857 GHz are then masked<br />
and harmonically transformed up to <math>\ell = 4000</math> to form spectral statistics (all auto- and cross- angular spectra). Two different masks are used to compute the spectral statistics. The first one preserves most of the sky while the second preserves CMB-dominated areas. These two sets of spectral statistics are used to determine two sets of harmonic weights which are thus adapted to two different levels of contamination. <br />
Two CMB intensity maps are produced and then merged into a single intensity product.<br />
The merging process is devised so that the information at high Galactic latitude and medium-to-high multipole<br />
is provided by the CMB map computed from high Galatic latitude statistics<br />
(note that this map does not include the LFI channels)<br />
while the remaining information is provided by the other CMB map (which does include all Planck channels).<br />
See {{PlanckPapers|planck2016-l04}} for more details.<br />
<br />
; Polarisation.<br />
<br />
The SMICA pipeline for polarization uses all the 7 polarized Planck channels.<br />
The E and B modes of the frequency maps are processed independently by SMICA<br />
to produce E and B modes of the CMB map from which Q and U maps are derived.<br />
The foreground model fitted by SMICA is 6-dimensional which is the maximal dimension<br />
supported by SMICA when operating in blind mode, that is, assuming nothing about the<br />
foregrounds except that they can be represented by a superposition of 6 components<br />
with unconstrained emission laws, unconstrained angular spectra and unconstrained angular correlation.<br />
See {{PlanckPapers|planck2016-l04}} for more details.<br />
<br />
====Common Masks====<br />
<br />
Common masks have been defined for analysis of the CMB temperature and polarization maps. In previous releases, these were constructed simply as the union of the individual pipeline confidence masks. In the 2018 release, a more direct approach has been adopted, by thresholding the standard deviation map evaluated between each of the four cleaned CMB maps. This standard deviation mask is then augmented with the Commander and SEVEM confidence masks, as well as with the SEVEM and SMICA in-painting masks.<br />
<br />
In addition, we provide masks for unobserved pixels for the half-mission and odd-even data splits, as well as an in-painting mask. The latter is not intended for scientific analysis, but for producing visually acceptable CMB representation for PR purposes.<br />
<br />
In total, we provide the following masks:<br />
<br />
* COM_Mask_CMB-common-Mask-Int_2048_R3.00.fits -- Temperature confidence mask with f<sub>sky</sub> = 77.9%. This is the preferred mask for temperature science analysis.<br />
* COM_Mask_CMB-common-Mask-Pol_2048_R3.00.fits -- Polarization confidence mask with f<sub>sky</sub> = 78.1%. This is the preferred mask for polarization science analysis.<br />
* COM_Mask_CMB-HM-Misspix-Mask-Int_2048_R3.00.fits -- Temperature half-mission missing pixels mask with f<sub>sky</sub> = 96.0%. This should be applied in analyses of the half-mission split temperature maps.<br />
* COM_Mask_CMB-HM-Misspix-Mask-Pol_2048_R3.00.fits -- Polarization half-mission missing pixels mask with f<sub>sky</sub> = 96.1%. This should be applied in analyses of the half-mission split polarization maps.<br />
* COM_Mask_CMB-HM-Misspix-Mask-Int_2048_R3.00.fits -- Temperature half-mission missing pixels mask with f<sub>sky</sub> = 98.1%. This should be applied in analyses of the half-mission split temperature maps.<br />
* COM_Mask_CMB-HM-Misspix-Mask-Pol_2048_R3.00.fits -- Polarization half-mission missing pixels mask with f<sub>sky</sub> = 98.1%. This should be applied in analyses of the half-mission split polarization maps.<br />
* COM_Mask_CMB-Inpainting-Mask-Int_2048_R3.00.fits -- Temperature CMB in-painting mask with f<sub>sky</sub> = 97.9%.<br />
<br />
====CMB-subtracted frequency maps ("Foreground maps")====<br />
<br />
These are the full-sky, full-mission frequency maps in intensity and polarization from which the CMB has been subtracted. The maps contain foregrounds and noise. They are provided for each frequency channel and for each component separation method. They are grouped into 8 files, two for each method of which there is one for each instrument. The maps are are at N<sub>side</sub> = 1024 for the three LFI channels and at N<sub>side</sub> = 2048 for the six HFI channels. The filenames are:<br />
<br />
* ''LFI_Foregrounds-{method}_1024_Rn.nn.fits'' (145 MB each)<br />
* ''HFI_Foregrounds-{method}_2048_Rn.nn.fits'' (1.2 GB each)<br />
<br />
To remove the CMB, the respective CMB map was first deconvolved with the 5 arcmin beam, then convolved with the beam of the frequency channel, and finally subtracted from the frequency map. This was done using the <math>B_\rm{l}</math> in harmonic space, assuming a symmetric beam.<br />
<br />
The CMB-subtracted maps have complicated noise properties. The CMB maps contain a noise contribution from each of the frequency maps, depending on the weights with which they were combined. Therefore subtracting the CMB map from a frequency channel contributes additional noise from the other frequency channels. This caveat is particularly important for polarization, for which the noise in the cleaned CMB maps is large. After subtraction this noise term is perfectly correlated between frequency channels, with a perfect blackbody spectrum with T=2.7255K. Caution is therefore warranted when using these maps for scientific analysis.<br />
<br />
The frequency maps from which the CMB have been subtracted are:<br />
<br />
* ''LFI_SkyMap_0nn_1024_R3.00_full.fits''<br />
* ''HFI_SkyMap_nnn_2048_R3.00_full.fits''<br />
<br />
Note that the zodiacal light correction described [https://wiki.cosmos.esa.int/planckpla2015/index.php/Map-making#Zodiacal_light_correction here] was applied to the HFI temperature maps before the CMB subtraction.<br />
<br />
<br />
<br />
====Masks====<br />
Summary table with the various masks that have been either been used or produced by the component separation methods to pre- or post-process the CMB maps.<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:left"<br />
|-<br />
|- bgcolor="ffdead" <br />
! Common mask filename || Field || Description || <br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_Mask_CMB-common-Mask-Int_2048_R3.00.fits|link=COM_Mask_CMB-common-Mask-Int_2048_R3.00.fits}} || TMASK || Common temperature confidence mask.<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_Mask_CMB-common-Mask-Pol_2048_R3.00.fits|link=COM_Mask_CMB-common-Mask-Pol_2048_R3.00.fits}} || PMASK || Common polarization confidence mask.<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_Mask_CMB-HM-Misspix-Mask-Int_2048_R3.00.fits|link=COM_Mask_CMB-HM-Misspix-Mask-Int_2048_R3.00.fits}} || TMASK || Missing pixels temperature mask for the half-mission data split.<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_Mask_CMB-HM-Misspix-Mask-Pol_2048_R3.00.fits|link=COM_Mask_CMB-HM-Misspix-Mask-Pol_2048_R3.00.fits}} || PMASK || Missing pixels polarization mask for the half-mission data split.<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_Mask_CMB-OE-Misspix-Mask-Int_2048_R3.00.fits|link=COM_Mask_CMB-OE-Misspix-Mask-Int_2048_R3.00.fits}} || TMASK || Missing pixels temperature mask for the odd-even data split.<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_Mask_CMB-OE-Misspix-Mask-Pol_2048_R3.00.fits|link=COM_Mask_CMB-OE-Misspix-Mask-Pol_2048_R3.00.fits}} || PMASK || Missing pixels polarization mask for the odd-even data split.<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_Mask_CMB-Inpainting-Mask-Int_2048_R3.00.fits|link=COM_Mask_CMB-Inpainting-Mask-Int_2048_R3.00.fits}} || TMASK || Temperature inpainting mask.<br />
|- bgcolor="800000"<br />
|<br />
! ||<br />
|<br />
|- bgcolor="ffdead" <br />
! Pipeline specific mask filename || Field || Description<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_CMB_IQU-commander_2048_R3.00_full.fits|link=COM_CMB_IQU-commander_2048_R3.00_full.fits}} || TMASK || Commander temperature confidence mask.<br />
|-<br />
| || PMASK || Commander polarization confidence mask.<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_CMB_IQU-nilc_2048_R3.00_full.fits|link=COM_CMB_IQU-nilc_2048_R3.00_full.fits}} || TMASK || NILC temperature confidence mask.<br />
|-<br />
| || PMASK || NILC polarization confidence mask.<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_CMB_IQU-sevem_2048_R3.00_full.fits|link=COM_CMB_IQU-sevem_2048_R3.00_full.fits}} || TMASK || SEVEM temperature confidence mask.<br />
|-<br />
| || PMASK || SEVEM polarization confidence mask.<br />
|-<br />
| || TMASKINP || SEVEM polarization (pre-processing) in-painting mask.<br />
|-<br />
| || PMASKINP || SEVEM polarization (pre-processing) in-painting mask.<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_CMB_IQU-smica_2048_R3.00_full.fits|link=COM_CMB_IQU-smica_2048_R3.00_full.fits}} || TMASK || SMICA temperature confidence mask.<br />
|-<br />
| || PMASK || SMICA polarization confidence mask.<br />
|-<br />
| || TMASKINP || SMICA polarization (pre-processing) in-painting mask.<br />
|-<br />
| || PMASKINP || SMICA polarization (pre-processing) in-painting mask.<br />
|-<br />
|}<br />
<br />
===Inputs===<br />
The input maps are the sky temperature maps described in the [[Frequency Maps | Sky temperature maps]] section. All pipelines use all maps between 30 and 857 GHz in temperature, and all maps between 30 and 353 GHz in polarization.<br />
<br />
===CMB file names===<br />
<br />
The CMB products are provided as a set of five files per pipeline, one file covering some part of the entire mission (full mission; first half-mission; second half-mission; odd rings; and even rings), with a filename structure on the form<br />
*''COM_CMB_IQU-{method}-2048-R3.00_{full,hm1,hm2,oe1,oe2}.fits''<br />
The first extension contains the full-sky CMB maps in the fields called I_STOKES, Q_STOKES, U_STOKES. The full-mission files additionally contains an ASCII table with the effective beam transfer function in the second extension. The structure of each file is given as follows:<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''CMB R3.00 map file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | Ext. 1. or 2. EXTNAME = ''COMP-MAP'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_Stokes || Real*4 || uK_cmb || I map <br />
|- <br />
|Q_Stokes || Real*4 || uK_cmb || Q map <br />
|-<br />
|U_Stokes || Real*4 || uK_cmb || U map <br />
|-<br />
|TMASK || Int || none || Temperature confidence mask (full-mission only) <br />
|-<br />
|PMASK || Int || none || Polarisation confidence mask (full-mission only) <br />
|-<br />
|TMASKINP || Int || none || Temperature confidence mask (full-mission SEVEM, SMICA only) <br />
|-<br />
|PMASKINP || Int || none || Polarisation confidence mask (full-mission SEVEM, SMICA only) <br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CMB || Astrophysical compoment name<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (COMMANDER/NILC/SEVEM/SMICA)<br />
|-<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Optional Ext. 2. or 3. EXTNAME = ''BEAM_TF'' (BINTABLE). ONLY FULL-MISSION DATA FILES<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INT_BEAM || Real*4 || none || Effective beam transfer function. <br />
|-<br />
|POL_BEAM || Real*4 || none || Effective beam transfer function.<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Int || value || First multipole of beam WF<br />
|-<br />
|LMAX_I || Int || value || Last multipole for Int beam TF<br />
|-<br />
|LMAX_P || Int || value || Last multipole for Pol beam TF<br />
|-<br />
|METHOD || String ||name || Cleaning method <br />
|-<br />
|}<br />
<br />
<br />
All maps are provided in thermodynamic units (K<sub>cmb</cmb>), with Nside=2048 and a nominal angular resolution of 5' FWHM.<br />
<br />
===CMB simulations===<br />
<br />
End-to-end simulations corresponding to each of the CMB data products are provided in terms of 999 CMB realization and 300 noise realizations individually propagated through each pipeline. These files are called <br />
*''dx12_v3_{method}_{cmb,noise,noise_hm1,noise_hm2,noise_oe1,noise_oe2}_mc_?????_raw.fits''<br />
*''dx12_v3_sevem_{freq}_{cmb,noise,noise_hm1,noise_hm2,noise_oe1,noise_oe2}_mc_?????_raw.fits'' for SEVEM cleaned cmb maps at single frequencies.<br />
*''dx12_v3_smica_nosz_{cmb,noise,noise_hm1,noise_hm2,noise_oe1,noise_oe2}_mc_?????_raw.fits'' for SMICA SZ-free cmb maps.<br />
<br />
Note that only 999 CMB realizations are available, as one realization was corrupted during processing.<br />
<br />
== Previous Releases: (2015) and (2013) CMB Maps ==<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%"><br />
'''2015 Release of CMB maps'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''CMB maps'''<br />
<br />
CMB maps have been produced using four different methods: COMMANDER, NILC, SEVEM, and SMICA, as described in the [[Astrophysical_component_separation#CMB_and_foreground_separation | CMB and foreground separation]] section and also in Appendices A-D of {{PlanckPapers|planck2014-a11}} and references therein.<br />
<br />
'''As discussed extensively in {{PlanckPapers|planck2014-a01}}, {{PlanckPapers|planck2014-a07}}, {{PlanckPapers|planck2014-a09}}, and {{PlanckPapers|planck2014-a11}}, the residual systematics in the Planck 2015 polarization maps have been dramatically reduced compared to 2013, by as much as two orders of magnitude on large angular scales. Nevertheless, on angular scales greater than 10 degrees, correponding to l < 20, systematics are still non-negligible compared to the expected cosmological signal.'''<br />
<br />
'''It was not possible, for this data release, to fully characterize the large-scale residuals from the data or from simulations. Therefore all results published by the Planck Collaboration in 2015 which are based on CMB polarization have used maps which have been high-pass filtered to remove the large angular scales. We warn all users of the CMB polarization maps that they cannot yet be used for cosmological studies at large angular scales.'''<br />
<br />
'''For convenience, we provide as default polarized CMB maps from which all angular scales at l < 30 have been filtered out. '''<br />
<br />
For each method we provide the following:<br />
* Full-mission CMB intensity map, confidence mask and beam transfer function.<br />
* Full-mission CMB polarisation map, <br />
* A confidence mask.<br />
* A beam transfer function.<br />
In addition, and for characterisation purposes, we include six other sets of maps from three data splits: first/second half-ring, odd/even years and first/second half-mission. For the year-1,2 and half-mission-1,2 data splits we provide half-sum and half-difference maps which are produced by running the corresponding sums and differences inputs through the pipelines. The half-difference maps can be used to provide an approximate noise estimates for the full mission, but they should be used with caution. Each split has caveats in this regard: there are noise correlations between the half-ring maps, and missing pixels in the other splits. The Intensity maps are provided at Nside = 2048, at 5 arcmin resolution, while the Polarisation ones are provided at Nside = 1024, at 10 arcmin resolution. All maps are in units of K<sub>cmb</sub>.<br />
<br />
In addition, for each method we provide three sets of files, each categorized by the "R2.0X" label as follows:<br />
<br />
; ''R2.02''<br />
<pre style="white-space: pre-wrap; <br />
white-space: -moz-pre-wrap; <br />
white-space: -pre-wrap; <br />
white-space: -o-pre-wrap; <br />
word-wrap: break-word;"><br />
This set of intensity and polarisation maps are provided at a resolution of Nside=1024. The Stokes Q and U maps are high-pass filtered to contain only modes above l > 30, as explained above and as used for analysis by the Planck Collaboration; THESE ARE THE POLARISATION MAPS WHICH SHOULD BE USED FOR COSMOLOGICAL ANALYSIS. Each type of map is packaged into a separate fits file (as for "R2.01"), resulting in file sizes which are easier to download (as opposed to the "R2.00" files), and more convenient to use with commonly used analysis software.<br />
</pre><br />
<br />
; ''R2.01''<br />
<pre style="white-space: pre-wrap; <br />
white-space: -moz-pre-wrap; <br />
white-space: -pre-wrap; <br />
white-space: -o-pre-wrap; <br />
word-wrap: break-word;"><br />
This is the most complete set of 2015 CMB maps, containing Intensity products at a resolution of Nside=2048, and both Intensity and Polarisation at resolution of Nside=1024. For polarisation (Q and U), they contain all angular resolution modes. WE CAUTION USERS ONCE AGAIN THAT THE STOKES Q AND U MAPS ARE NOT CONSIDERED USEABLE FOR COSMOLOGICAL ANALYSIS AT l < 30. The structure of these files is the same as for "R2.02".<br />
</pre><br />
<br />
; ''R2.00''<br />
<pre style="white-space: pre-wrap; <br />
white-space: -moz-pre-wrap; <br />
white-space: -pre-wrap; <br />
white-space: -o-pre-wrap; <br />
word-wrap: break-word;"><br />
This set of files is equivalent to the "R2.01" set, but are packaged into only two large files. Warning: downloading these files could be very lengthy...<br />
</pre><br />
<br />
For a complete description of the above data structures, see [[#File names and structure | below]]; the content of the first extensions is illustrated and commented in the table below.<br />
<br />
<br />
The gallery below shows the Intensity, noise from half-mission, half-difference, and confidence mask for the four pipelines, in the order COMMANDER, NILC, SEVEM and SMICA, from top to bottom. The Intensity maps' scale is [–500.+500] μK, and the noise spans [–25,+25] μK. We do not show the Q and U maps since they have no significant visible structure to contemplate.<br />
<br />
<center><br />
<gallery style="padding:0 0 0 0;" perrow=3 widths=300px heights=180> <br />
File:CMB_commander_tsig.png | '''commander temperature'''<br />
File:CMB_commander_tnoi.png | '''commander noise'''<br />
File:CMB_commander_tmask.png | '''commander mask'''<br />
File:CMB_nilc_tsig.png | '''nilc temperature'''<br />
File:CMB_nilc_tnoi.png | '''nilc noise'''<br />
File:CMB_nilc_tmask.png | '''nilc mask'''<br />
File:CMB_sevem_tsig.png | '''sevem temperature'''<br />
File:CMB_sevem_tnoi.png | '''sevem noise'''<br />
File:CMB_sevem_tmask.png | '''sevem mask'''<br />
File:CMB_smica_tsig.png | '''smica temperature'''<br />
File:CMB_smica_tnoi.png | '''smica noise'''<br />
File:CMB_smica_tmask.png | '''smica mask'''</gallery><br />
</center><br />
<br />
'''Product description '''<br />
<br />
'''COMMANDER'''<br />
<br />
;Principle<br />
<br />
: COMMANDER is a Planck software code implementing pixel based Bayesian parametric component separation. Each astrophysical signal component is modelled in terms of a small number of free parameters per pixel, typically in terms of an amplitude at a given reference frequency and a small set of spectral parameters, and these are fitted to the data with an MCMC Gibbs sampling algorithm. Instrumental parameters, including calibration, bandpass corrections, monopole and dipoles, are fitted jointly with the astrophysical components. A new feature in the Planck 2015 analysis is that the astrophysical model is derived from a combination of Planck, WMAP and a 408 MHz (Haslam et al. 1982) survey, providing sufficient frequency support to resolve the low-frequency components into synchrotron, free-free and spinning dust. For full details, see {{PlanckPapers|planck2014-a12}}.<br />
<br />
; Resolution (effective beam)<br />
<br />
: The Commander sky maps have different angular resolutions depending on data products:<br />
* The components of the full astrophysical sky model derived from the complete data combination (Planck, WMAP, 408 MHz) have a 1 degree FWHM resolution, and are pixelized at N<sub>side</sub>=256. The corresponding CMB map defines the input map for the low-l Planck 2015 temperature likelihood. <br />
* The Commander CMB temperature map derived from Planck-only observations has an angular resolution of ~5 arcmin and is pixelized at N<sub>side</sub>=2048. This map is produced by harmonic space hybridiziation, in which independent solutions derived at 40 arcmin (using 30-857 GHz data), 7.5 arcmin (using 143-857 GHz data), and 5 arcmin (using 217-857 GHz data) are coadded into a single map.<br />
* The Commander CMB polarization map has an angular resolution of 10 arcmin and is pixelized at N<sub>side</sub>=1024. As for the temperature case, this map is produced by harmonic space hybridiziation, in which independent solutions derived at 40 arcmin (using 30-353 GHz data) and 10 arcmin (using 100-353 GHz data) are coadded into a single map.<br />
<br />
; Confidence mask<br />
<br />
: The Commander confidence masks are produced by thresholding the chi-square map characterizing the global fits, combined with direct CO amplitude thresholding to eliminate known leakage effects. In addition, we exclude the 9-year WMAP point source mask in the temperature mask. For full details, see Sections 5 and 6 in {{PlanckPapers|planck2014-a12}}. A total of 81% of the sky is admitted for high-resolution temperature analysis, and 83% for polarization analysis. For low-resolution temperature analysis, for which the additional WMAP and 408 MHz observations improve foreground constraints, a total of 93% of the sky is admitted. <br />
<br />
'''NILC'''<br />
<br />
;Principle<br />
<br />
: The Needlet-ILC (hereafter NILC) CMB map is constructed both in total intensity as well as polarization: Q and U Stokes parameters. For total intensity, all Planck frequency channels are included. For polarization, all polarization sensitive frequency channels are included, from 30 to 353 GHz. The solution, for T, Q and U is obtained by applying the Internal Linear Combination (ILC) technique in needlet space, that is, with combination weights which are allowed to vary over the sky and over the whole multipole range. <br />
<br />
; Resolution (effective beam)<br />
<br />
: The spectral analysis, and estimation of the NILC coefficients, is performed up to a maximum <math>\ell=4000</math>. The effective beam is equivalent to a Gaussian circular beam with FWHM=5 arcminutes. <br />
<br />
; Confidence mask<br />
<br />
: The same procedure is followed by SMICA and NILC for producing confidence masks, though with different parametrizations. A low resolution smoothed version of the NILC map, noise subtracted, is thresholded to 73.5 squared micro-K for T, and 6.75 squared micro-K for Q and U.<br />
<br />
<br />
'''SEVEM'''<br />
; Principle<br />
<br />
: SEVEM produces clean CMB maps at several frequencies by using a procedure based on template fitting in real space. The templates are typically constructed from the lowest and highest Planck frequencies and then subtracted from the CMB-dominated channels, with coefficients that are chosen to minimize the variance of the clean map outside a considered mask. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust. Two single frequency clean maps are then combined to obtain the final CMB map.<br />
<br />
;Resolution<br />
<br />
: For intensity the clean CMB map is constructed up to a maximum <math>\ell=4000</math> at Nside=2048 and at the standard resolution of 5 arcminutes (Gaussian beam).<br />
: For polarization the clean CMB map is produced at Nside=1024 with a resolution of 10 arcminutes (Gaussian beam) and a maximum <math>\ell=3071</math>.<br />
<br />
; Confidence masks<br />
<br />
: The confidence masks cover the most contaminated regions of the sky, leaving approximately 85 per cent of useful sky for intensity, and 80 per cent for polarization.<br />
<br />
'''Foregrounds-subtracted maps'''<br />
<br />
In addition to the regular CMB maps, SEVEM provides maps cleaned of the foregrounds for selected frequency channels (categorized as fgsub-sevem in the archive). In particular, for intensity there are clean CMB maps available at 100, 143 and 217 GHz, provided at the original resolution of the uncleaned channel and at Nside=2048. For polarization, there are Q/U clean CMB maps for the 70, 100 and 143 GHz (at Nside=1024). The 70 GHz clean map is provided at its original resolution, whereas the 100 and 143 GHz maps have a resolution given by a Gaussian beam with fwhm=10 arcminutes.<br />
<br />
'''SMICA'''<br />
; Principle<br />
: SMICA produces CMB maps by linearly combining all Planck input channels with multipole-dependent weights. It includes multipoles up to <math>\ell = 4000</math>. Temperature and polarization maps are produced independently.<br />
; Resolution (effective beam)<br />
: The SMICA intensity map has an effective beam window function of 5 arc-minutes which is truncated at <math>\ell=4000</math> and is '''not''' deconvolved from the pixel window function. Thus the delivered beam window function is the product of a Gaussian beam at 5 arcminutes and the pixel window function for <math>N_{side}</math>=2048.<br />
: The SMICA Q and U maps are obtained similarly but are produced at <math>N_{side}</math>=1024 with an effective beam of 10 arc-minutes (to be multiplied by the pixel window function, as for the intensity map).<br />
; Confidence mask<br />
: A confidence mask is provided which excludes some parts of the Galactic plane, some very bright areas and masked point sources. This mask provides a qualitative (and subjective) indication of the cleanliness of a pixel. See section below detailing the production process.<br />
<br />
<br />
'''Common Masks'''<br />
<br />
A number of common masks have been defined for analysis of the CMB temperature and polarization maps. They are based on the confidence masks provided by the component separation methods. One mask for temperature and one mask for polarization have been chosen as the preferred masks based on subsequent analyses.<br />
<br />
The common masks for the CMB temperature maps are:<br />
<br />
* UT78: union of the Commander, SEVEM, and SMICA temperature confidence masks (the NILC mask was not included since it masks much less of the sky). It has f<sub>sky</sub> = 77.6%. This is the preferred mask for temperature.<br />
<br />
* UTA76: in addition to the UT78 mask, it masks pixels where standard deviation between the four CMB maps is greater than 10 &mu;K. It has f<sub>sky</sub> = 76.1%.<br />
<br />
The common masks for the CMB polarization maps are:<br />
<br />
* UP78: the union of the Commander, SEVEM and SMICA polarization confidence masks (the NILC mask was not included since it masks much less of the sky). It has f<sub>sky</sub> = 77.6%.<br />
<br />
* UPA77: In addition to the UP78 mask, it masks pixels where the standard deviation between the four CMB maps, averaged in Q and U, is greater than 4 &mu;K. It has f<sub>sky</sub> = 76.7%.<br />
<br />
* UPB77: in addition to the UP78 mask, it masks polarized point sources detected in the frequency channel maps. It has f<sub>sky</sub> = 77.4%. This is the preferred mask for polarization.<br />
<br />
Additional pre-processing masks used mainly for inpainting of the frequency and/or cmb maps is show below in [https://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_maps#Masks Masks]<br />
<br />
'''CMB-subtracted frequency maps ("Foreground maps")'''<br />
<br />
These are the full-sky, full-mission frequency maps in intensity from which the CMB has been subtracted. The maps contain foregrounds and noise. They are provided for each frequency channel and for each component separation method. They are grouped into 8 files, two for each method of which there is one for each instrument. The maps are are at N<sub>side</sub> = 1024 for the three LFI channels and at N<sub>side</sub> = 2048 for the six HFI channels. The filenames are:<br />
<br />
* ''LFI_Foregrounds-{method}_1024_Rn.nn.fits'' (145 MB each)<br />
* ''HFI_Foregrounds-{method}_2048_Rn.nn.fits'' (1.2 GB each)<br />
<br />
To remove the CMB, the respective CMB map was first deconvolved with the 5 arcmin beam, then convolved with the beam of the frequency channel, and finally subtracted from the frequency map. This was done using the <math>B_\rm{l}</math> in harmonic space, assuming a symmetric beam.<br />
<br />
The CMB-subtracted maps have complicated noise properties. The CMB maps contain a noise contribution from each of the frequency maps, depending on the weights with which they were combined. Therefore subtracting the CMB map from a frequency channel contributes additional noise from the other frequency channels.<br />
<br />
'''Quadrupole Residual Maps'''<br />
<br />
The second-order (kinematic) quadrupole is a frequency-dependent effect. During the production of the frequency maps the frequency-independent part was subtracted, which leaves a frequency-dependent residual quadrupole. The residuals in the component-separated CMB temperature maps have been estimated by simulating the effect in the frequency maps and propagating it through the component separation pipelines. The residuals have an amplitude of around 2 &mu;K peak-to-peak. The maps of the estimated residuals can be used to remove the effect by subtracting them from the CMB maps.<br />
<br />
'''Production process'''<br />
<br />
'''COMMANDER'''<br />
<br />
; Pre-processing<br />
<br />
: All sky maps are first convolved to a common resolution that is larger than the largest beam of any frequency channel. For the combined Planck, WMAP and 408 MHz temperature analysis, the common resolution is 1 degree FWHM; for the Planck-only, all-frequency analysis it is 40 arcmin FWHM; and for the intermediate-resolution analysis it is 7.5 arcmin; while for the full-resolution analysis, we assume all frequencies between 217 and 857 GHz have a common resolution, and no additional convolution is performed. For polarization, only two smoothing scales are employed, 40 and 10 arcmin, respectively. The instrumental noise rms maps are convolved correspondingly, properly accouting for their matrix-like nature. <br />
<br />
; Priors<br />
<br />
: The following priors are enforced in the Commander analysis:<br />
* All foreground amplitudes are enforced to be positive definite in the low-resolution analysis, while no amplitude priors are enforced in the high-resolution analyses<br />
* Monopoles and dipoles are fixed to nominal values for a small set of reference frequencies<br />
* Gaussian priors are enforced on spectral parameters, with values informed by the values derived in the high signal-to-noise areas of the sky<br />
* The Jeffreys ignorance prior is enforced on spectral parameters in addition to the informative Gaussian priors<br />
<br />
; Fitting procedure<br />
<br />
: Given data and priors, Commander either maximizes, or samples from, the Bayesian posterior, P(theta|data). Because this is a highly non-Gaussian and correlated distribution, involving millions of parameters, these operations are performed by means of the Gibbs sampling algorithm, in which joint samples from the full distributions are generated by iteratively sampling from the corresponding conditional posterior distributions, P(theta_i| data, theta_{j/=i}). For the low-resolution analysis, all parameters are optimized jointly, while in the high-resolution analyses, which employs fewer frequency channels, low signal-to-noise parameters are fixed to those derived at low resolution. Examples of such parameters include monopoles and dipoles, calibration and bandpass parameters, thermal dust temperature etc.<br />
<br />
'''NILC'''<br />
<br />
; Pre-processing<br />
<br />
: All sky frequency maps are deconvolved using the DPC beam transfer function provided, and re-convolved with a 5 arcminutes FWHM circular Gaussian beam. In polarization, prior to the smoothing process, all sky E and B maps are derived from Q and U using standard HEALPix tools from each individual frequency channels <br />
<br />
; Linear combination<br />
<br />
: Pre-processed input frequency maps are decomposed in needlet coefficients, specified in the Appendix B of the Planck A11 paper, with shape given by Table B.1. Minimum variance coefficients are then obtained, using all channels for T, from 30 to 353 for E and B. <br />
<br />
; Post-processing<br />
<br />
: E and B maps are re-combined into Q and U products using standard HEALPix tools. <br />
<br />
'''SEVEM'''<br />
<br />
The templates used in the SEVEM pipeline are typically constructed by subtracting two close Planck frequency channel maps, after first smoothing them to a common resolution to ensure that the CMB signal is properly removed. A linear combination of the templates <math>t_j</math> is then subtracted from (hitherto unused) map d to produce a clean CMB map at that frequency. This is done in real space at each position on the sky: <math> T_c(\mathbf{x}, ν) = d(\mathbf{x}, ν) − \sum_{j=1}^{n_t} α_j t(\mathbf{x}) </math><br />
where <math>n_t</math> is the number of templates. The <math>α_j</math> coefficients are obtained by minimising the variance of the clean map <math>T_c</math> outside a given mask. Note that the same expression applies for I, Q and U. Although we exclude very contaminated regions during the minimization, the subtraction is performed for all pixels and, therefore, the cleaned maps cover the full-sky (although we expect that foreground residuals are present in the excluded areas).<br />
<br />
There are several possible configurations of SEVEM with regard to the number of frequency maps which are cleaned or the number of templates that are used in the fitting. Note that the production of clean maps at different frequencies is of great interest in order to test the robustness of the results, and these intermediate products (clean maps at individual frequencies for intensity and polarization) are also provided in the archive. Therefore, to define the best strategy, one needs to find a compromise between the number of maps that can be cleaned independently and the number of templates that can be constructed.<br />
<br />
;Intensity<br />
<br />
For the CMB intensity map, we have cleaned the 100 GHz, 143 GHz and 217 GHz maps using a total of four templates. Three of them are constructed as the difference of two consecutive Planck channels smoothed to a common resolution (30-44, 44-70 and 545-353) while the 857 GHz channel is chosen as the fourth template. First of all, the six frequency channels which are going to be part of the templates are inpainted at the point source positions detected using the Mexican Hat Wavelet algorithm. The size of the holes to be inpainted is determined taking into account the beam size of the channel as well as the flux of each source. The inpainting algorithm is based on simple diffuse inpainting, which fills one pixel with the mean value of the neighbouring pixels in an iterative way. To avoid inconsistencies when subtracting two channels, each frequency map is inpainted on the sources detected in that map and on the second map (if any) used to construct the template. Then the maps are smoothed to a common resolution (the first channel in the subtraction is smoothed with the beam of the second map and viceversa). For the 857 GHz template, we simply filter the inpainted map with the 545 GHz beam.<br />
<br />
The coefficients are obtained by minimising the variance outside the analysis mask, that covers the 1 per cent brightest emission of the sky as well as point sources detected at all frequency channels. Once the maps are cleaned, each of them is inpainted on the point sources positions detected at that (raw) channel. Then, the MHW algorithm is run again, now on the clean maps. A relatively small number of new sources are found and are also inpainted at each channel. The resolution of the clean map is the same as that of the original data. Our final CMB map is then constructed by combining the 143 and 217 GHz maps by weighting the maps in harmonic space taking into account the noise level, the resolution and a rough estimation of the foreground residuals of each map (obtained from realistic simulations). This final map has a resolution corresponding to a Gaussian beam of fwhm=5 arcminutes.<br />
<br />
In addition, the clean CMB maps produced at 100, 143 and 217 GHz frequencies are also provided. The resolution of these maps is the same as that of the uncleaned frequency channels and have been constructed at Nside=2048. They have been inpainted at the position of the detected point sources. Note that these three clean maps should be close to independent, although some level of correlation will be present since the same templates have been used to clean the maps.<br />
<br />
The confidence mask is produced by studying the differences between several SEVEM CMB reconstructions, which correspond to maps cleaned at different frequencies or using different analysis masks. The obtained mask leaves a useful sky fraction of approximately 85 per cent.<br />
<br />
;Polarization<br />
<br />
To clean the polarization maps, a procedure similar to the one used for intensity data is applied to the Q and U maps independently. However, given that a narrower frequency coverage is available for polarization, the selected templates and maps to be cleaned are different. In particular, we clean the 70, 100 and 143 GHz using three templates for each channel. The first step of the pipeline is to inpaint the positions of the point sources using the MHW, in those channels which are going to be used in the construction of templates, following the same procedure as for the intensity case. The inpainting is performed in the frequency maps at their native resolution. These inpainted maps are then used to construct a total of four templates. To trace the synchrotron emission, we construct a template as the subtraction of the 30 GHz minus the 44 GHz <br />
map, after being convolved with the beam of each other. For the dust emission, the following templates are considered: 353-217 GHz (smoothed at 10' resolution), 217-143 GHz (used <br />
to clean 70 and 100 GHz) and 217-100 GHz (to clean 143 GHz). These two last templates are constructed at 1 degree resolution since an additional smoothing becomes necessary in<br />
order to increase the signal-to-noise ratio of the template. Conversely to the <br />
intensity case and due to the lower availability of frequency channels, it becomes necessary to use the maps to be cleaned as part of one of the templates. In this way, the 100 GHz <br />
map is used to clean the 143 GHz frequency channel and viceversa, making the clean maps less independent between them than in the intensity case.<br />
<br />
These templates are then used to clean the non-inpainted 70 (at its native resolution), 100 (at 10' resolution) and 143 GHz maps (also at 10'). The corresponding linear coefficients are estimated independently for Q and U by minimising the variance of the clean maps outside a mask, that covers point sources and the 3 per cent brightest Galactic emission. Once the maps have been cleaned, inpainting of the point sources detected at the corresponding raw maps is carried out. The size of the holes to be inpainted takes<br />
into account the additional smoothing of the 100 and 143 GHz maps. The 100 and 143 GHz clean maps are then combined in harmonic space, using E and B decomposition, to produce the final CMB maps for the Q and U components at a resolution of 10' (Gaussian beam) for a HEALPix parameter Nside=1024. Each map is weighted taking into account its <br />
corresponding noise level at each multipole. Finally, before applying the post-processing HPF to the clean polarization data, the region with the brightest Galactic residuals is inpainted (5 per cent of the sky) to avoid the introduction of ringing around the Galactic centre in the filtering process.<br />
<br />
The clean CMB maps at individual frequency channels produced as intermediate steps of SEVEM are also provided for Q and U, constructed at Nside=1024. The clean 70 GHz map is provided at its native resolution, while the clean maps at 100 and 143 GHz frequencies have a resolution of 10 arcminutes (Gaussian beam). The three maps have been inpainted in the positions of the detected point sources. Note that, due to the availability of a smaller number of templates for polarization than for intensity, these maps are less independent than for the temperature case, since, for instance, the 100 GHz map is used to clean the 143 GHz one and viceversa.<br />
<br />
The confidence mask includes all the pixels above a given threshold in a smoothed version of the clean CMB map, the regions more contaminated by the CO emission and those pixels more affected by the high-pass filtering, leaving a useful sky fraction of approximately 80 per cent.<br />
<br />
<br />
'''SMICA'''<br />
<br />
A) Production of the intensity map.<br />
<br />
; 1) Pre-processing<br />
: Before computing spherical harmonic coefficients, all input maps undergo a pre-processing step to deal with regions of very strong emission (such as the Galactic center) and point sources. The point sources with SNR > 5 in the PCCS catalogue are fitted in each input map. If the fit is successful, the fitted point source is removed from the map; otherwise it is masked and the hole is filled in by a simple diffusive process to ensure a smooth transition and mitigate spectral leakage. The diffusive inpainting process is also applied to some regions of very strong emissions. This is done at all frequencies but 545 and 857 GHz, here all point sources with SNR > 7.5 are masked and filled-in similarly.<br />
; 2) Linear combination<br />
: The nine pre-processed Planck frequency channels from 30 to 857 GHz are harmonically transformed up to <math>\ell = 4000</math> and co-added with multipole-dependent weights as shown in the figure.<br />
; 3) Post-processing<br />
: A confidence mask is determined (see the Planck paper) and all regions which have been masked in the pre-processing step are added to it.<br />
<br />
<!--[[File:Smica_filter_dx11.png|thumb|center|600px|'''Weights given by SMICA to the input intensity maps (after they are re-beamed to 5 arc-minutes and expressed in K<math>_\rm{RJ}</math>), as a function of multipole.''']]--><br />
<br />
B) Production of the Q and U polarisation maps.<br />
<br />
The SMICA pipeline for polarization uses all the 7 polarized Planck channels. The production of the Q and U maps is similar to the production of the intensity map. However, there is no input point source pre-processing of the input maps. The regions of very strong emission are masked out using an apodized mask before computing the E and B modes of the input maps and combining them to produce the E and B modes of the CMB map. Those modes are then used to synthesize the U and Q CMB maps. The E and B parts of the input frequency maps being processed jointly, there are, at each multipole, 2*7=14 coefficients (weights) defined to produce the E modes of the CMB map and as many to produce the B part. The weights are displayed in the figure below. The Q and U maps were originally produced at Nside=2048 with a 5-arc-minute resolution, but were downgraded to Nside=1024 with a 10 arc-minute resolution for this release.<br />
<br />
<!--[[File:Smica_filterEB_dx11.png|thumb|center|600px|'''Weights given by SMICA to the input E and B modes (after they are re-beamed to 5 arcmin and expressed in K<math>_\rm{RJ}</math>), in order to produce the E and B modes of the CMB map. A given frequency channel is encoded in a given color. Solid lines are for E modes and dashed lines are for B modes. The thick lines are for the EE or BB weights; the thin lines are for the EB or BE weights. See the paper for more details.''']]--><br />
<br />
'''Masks'''<br />
<br />
Summary table with the different masks that have been used by the component separation methods to pre-process and to process the frequency maps and the CMB maps.<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|-<br />
|- bgcolor="ffdead" <br />
! Commander 2015 (PR2) || Used for diffuse inpainting of input frequency maps || Used for constrained Gaussian realization inpaiting of CMB map || Description<br />
|-<br />
|T_MASK || NO || NO || T_MASK (the equivalent to PR1 VALMASK) is the confidence mask in temperature that defines the region where the reconstructed CMB is trusted. It can be found inside {{PLASingleFile|fileType=map|name=COM_CMB_IQU-commander-field-Int_2048_R2.01_full.fits|link=COM_CMB_IQU-commander-field-Int_2048_R2.01_full.fits}}.<br />
|-<br />
|P_MASK || NO || NO || P_MASK is the confidence mask in polarization that defines the region where the reconstructed CMB is trusted. It can be found inside {{PLASingleFile|fileType=map|name=COM_CMB_IQU-commander_1024_R2.02_full.fits|link=COM_CMB_IQU-commander_1024_R2.02_full.fits}}.<br />
|-<br />
|INP_MASK_T || NO || YES || Three masks have been used for inpaiting of CMB maps for specific <math>\ell</math> ranges: three different angular resolution maps (40 arcmin, 7.5 arcmin and full resolution), are produced using different data combinations and foreground models. Each of these are inpainted with their own masks with a constrained Gaussian realization before coadding the three maps in harmonic space.<br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrcGalplane_commander_dx11d2_temp_n0256_lmax200_0256_R2.03.fits|link=COM_Mask_PointSrcGalplane_commander_dx11d2_temp_n0256_lmax200_0256_R2.03.fits}}<br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrcGalplane_commander_dx11d2_temp_lmax1000_2048_R2.03.fits|link=COM_Mask_PointSrcGalplane_commander_dx11d2_temp_lmax1000_2048_R2.03.fits}}<br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrcGalplane_commander_dx11d2_temp_fullres_2048_R2.03.fits|link=COM_Mask_PointSrcGalplane_commander_dx11d2_temp_fullres_2048_R2.03.fits}}<br />
|-<br />
|INP_MASK_P || NO || YES || Mask used for inpainting of the CMB map in polarization.<br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrcGalplane_commander_dx11d2_pol_fullres_1024_R2.02.fits|link=COM_Mask_PointSrcGalplane_commander_dx11d2_pol_fullres_1024_R2.02.fits}}<br />
|- bgcolor="800000"<br />
|<br />
! ||<br />
|<br />
|- bgcolor="ffdead" <br />
! SEVEM 2015 (PR2) || Used for Diffuse Inpainting of foregorund subtracted CMB maps (fgsub-sevem) || Used for constrained Gaussian realization inpaiting of CMB map || Description<br />
|-<br />
|T_MASK || NO || NO || T_MASK (the equivalent to PR1 VALMASK) is the confidence mask in temperature that defines the region where the reconstructed CMB is trusted. It can be found inside {{PLASingleFile|fileType=map|name=COM_CMB_IQU-sevem-field-Int_2048_R2.01_full.fits|link=COM_CMB_IQU-sevem-field-Int_2048_R2.01_full.fits}}.<br />
|-<br />
|P_MASK || NO || NO || P_MASK is the confidence mask in polarization that defines the region where the reconstructed CMB is trusted. It can be found inside {{PLASingleFile|fileType=map|name=COM_CMB_IQU-sevem_1024_R2.02_full.fits|link=COM_CMB_IQU-sevem_1024_R2.02_full.fits}}.<br />
|-<br />
|INP_MASK_T || YES || NO || Point source mask for temperature. This mask is the combination of the 143 and 217 T point source masks used for the inpainting of the foreground subtracted CMB maps at those two frequencies. These two maps have been combined to produce the final CMB map. <br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrc_sevem_extended143x217_2048_R2.00.fits|link=COM_Mask_PointSrc_sevem_extended143x217_2048_R2.00.fits}}<br />
|-<br />
|INP_MASK_P || YES || NO || Point source mask for polarization. This mask is the combination of the 100 and 143 point source masks used for the inpainting of the foreground subtracted CMB maps at those two frequencies. These two maps have been combined to produce the final CMB map.<br />
* {{PLASingleFile|fileType=map|name=COM_Mask_PointSrc_sevem_extended100x143_fw10_1024_R2.00.fits|link=COM_Mask_PointSrc_sevem_extended100x143_fw10_1024_R2.00.fits}}<br />
|-<br />
|INP_MASK_T for the cleaned 100, 143 and 217 GHz CMB || YES || NO || Three temperature point source masks used for the inpainting of the foreground subtracted CMB maps at the considered frequencies: <br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrc_sevem_ps100_extended_2048_R2.00.fits|link=COM_Mask_PointSrc_sevem_ps100_extended_2048_R2.00.fits}} (clean 100 GHz)<br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrc_sevem_ps143_extended_2048_R2.00.fits|link=COM_Mask_PointSrc_sevem_ps143_extended_2048_R2.00.fits}} (clean 143 GHz)<br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrc_sevem_ps217_extended_2048_R2.00.fits|link=COM_Mask_PointSrc_sevem_ps217_extended_2048_R2.00.fits}} (clean 217 GHz)<br />
|-<br />
|INP_MASK_P for the cleaned 70, 100 and 143 GHz CMB|| YES || NO || Three polarization point source masks used for the inpainting of the foreground subtracted CMB maps at the considered frequencies:<br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrc_sevem_dx11d_70_pol_varhole_full_99p90_1024_R2.00.fits|link=COM_Mask_PointSrc_sevem_dx11d_70_pol_varhole_full_99p90_1024_R2.00.fits}} (clean 70 GHz);<br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrc_sevem_dx11d_100_pol_99.97pc_radius_3sigma_10arcmin_1024_R2.00.fits|link=COM_Mask_PointSrc_sevem_dx11d_100_pol_99.97pc_radius_3sigma_10arcmin_1024_R2.00.fits}} (clean 100 GHz)<br />
*{{PLASingleFile|fileType=map|name=COM_Mask_PointSrc_sevem_dx11d_143_pol_99.97pc_radius_3sigma_10arcmin_1024_R2.00.fits|link=COM_Mask_PointSrc_sevem_dx11d_143_pol_99.97pc_radius_3sigma_10arcmin_1024_R2.00.fits}} (clean 143 GHz)<br />
|- bgcolor="800000"<br />
|<br />
! ||<br />
|<br />
|- bgcolor="ffdead" <br />
! NILC 2015 (PR2) || Used for diffuse inpainting of input frequency maps || Used for constrained Gaussian realization inpaiting of CMB map || Description<br />
|-<br />
|T_MASK || NO || NO || T_MASK (the equivalent to PR1 VALMASK) is the confidence mask in temperature that defines the region where the reconstructed CMB is trusted. It can be found inside {{PLASingleFile|fileType=map|name=COM_CMB_IQU-nilc-field-Int_2048_R2.01_full.fits|link=COM_CMB_IQU-nilc-field-Int_2048_R2.01_full.fits}}.<br />
|-<br />
|P_MASK || NO || NO || P_MASK is the confidence mask in polarization that defines the region where the reconstructed CMB is trusted. It can be found inside {{PLASingleFile|fileType=map|name=COM_CMB_IQU-nilc_1024_R2.02_full.fits|link=COM_CMB_IQU-nilc_1024_R2.02_full.fits}}.<br />
|-<br />
|INP_MASK || YES || NO || The pre-processing involves inpainting of the holes in INP_MASK in the frequency maps prior to applying NILC on them. The first mask (nside 2048) has been used for the pre-processing of sky maps for HFI channels and second one for LFI channels (nside 1024). They can downloaded here:<br />
{{PLASingleFile|fileType=map|name=COM_Mask_PointSrcGalplane_nilc_dx11_preproc_1024_R2.00.fits|link=COM_Mask_PointSrcGalplane_nilc_dx11_preproc_1024_R2.00.fits}}<br />
{{PLASingleFile|fileType=map|name=COM_Mask_PointSrcGalplane_nilc_dx11_preproc_2048_R2.00.fits|link=COM_Mask_PointSrcGalplane_nilc_dx11_preproc_2048_R2.00.fits}} <br />
|- bgcolor="800000"<br />
|<br />
! ||<br />
|<br />
|- bgcolor="ffdead" <br />
! SMICA 2015 (PR2) || Used for diffuse inpainting of input frequency maps || Used for constrained Gaussian realization inpaiting of CMB map || Description<br />
|-<br />
|T_MASK || NO || YES || T_MASK (the equivalent to PR1 VALMASK) is the confidence mask in temperature that defines the region where the reconstructed CMB is trusted. It can be found inside {{PLASingleFile|fileType=map|name=COM_CMB_IQU-smica-field-Int_2048_R2.01_full.fits|link=COM_CMB_IQU-smica-field-Int_2048_R2.01_full.fits}}.<br />
|-<br />
|P_MASK || NO || YES || P_MASK is the confidence mask in polarization that defines the region where the reconstructed CMB is trusted. It can be found inside {{PLASingleFile|fileType=map|name=COM_CMB_IQU-smica_1024_R2.02_full.fits|link=COM_CMB_IQU-smica_1024_R2.02_full.fits}}.<br />
|-<br />
|I_MASK || YES || NO || I_MASK, as in PR1, defines the regions over which CMB is not built. It is a combination of point source masks, Galactic plane mask and other bright regions like LMC, SMC, etc. It can downloaded here: {{PLASingleFile|fileType=map|name=COM_Mask_PointSrcGalplane_smica_harmonic_mask_2048_R2.00.fits|link=COM_Mask_PointSrcGalplane_smica_harmonic_mask_2048_R2.00.fits}}<br />
|- <br />
|}<br />
<br />
<br />
'''Inputs'''<br />
The input maps are the sky temperature maps described in the [[Frequency Maps | Sky temperature maps]] section. SMICA and SEVEM use all the maps between 30 and 857 GHz; NILC uses the ones between 44 and 857 GHz. Commander-Ruler uses frequency channel maps from 30 to 353 GHz. <br />
<br />
'''File names and structure'''<br />
<br />
Three sets of files FITS files containing the CMB products are available. In the first set all maps (i.e., covering different parts of the mission) and all characterisation products for a given method and a given Stokes parameter are grouped into a single extension, and there are two files per ''method'' (smica, nilc, sevem, and commander), one for the high resolution data (I only, Nside=2048) and one for low resolution data (Q and U only, Nside=1024). Each file also contains the associated confidence mask(s) and beam transfer function. '''These are the R2.00 files''' which have names like<br />
*''COM_CMB_IQU-{method}-field-{Int,Pol}_Nside_R2.00.fits''<br />
There are 7 coverage periods:''full'', ''halfyear-1,2'', ''halfmission-1,2'', or ''ringhalf-1,2'', and 4 characterisation products: ''half-sum'' and half-difference'' for the year and the half-mission periods.<br />
<br />
In the second second set the different coverages are split into different files which in most cases have a single extension with I only (Nside=1024) and I, Q, and U (Nside=1024). This second set was built in order to allow users to use standard codes like ''spice'' or ''anafast'' on them, directly. So this set contains the I maps at Nside=1024, which are not contained in the R2.00; on the other hand this set does not contain the half-sum and half-difference maps. '''These are the 2.01 files''' which have names like <br />
*''COM_CMB_IQU-{method}{-field-Int|Pol}_Nside_R2.01_{coverage}.fits'' for the regular CMB maps, and <br />
*''COM_CMB_IQU-{fff}-{fgsub-sevem}{-field-Int|Pol}_Nside_R2.01_{coverage}.fits'' for the sevem frequency-dependent, foregrounds-subtracted maps,<br />
where ''field-Int|Pol'' is used to indicate that only Int or only Pol data are contained (at present only ''field-Int'' is used for the high-res data), and is not included in the low-res data which contains all three Stokes parameters, and ''coverage'' is one of ''full'', ''halfyear-1,2'', ''halfmission-1,2'', or ''ringhalf-1,2''. Also, the coverage=''full'' files contain also the confidence mask(s) and beam transfer function(s) which are valid for all products of the same method (one for Int and one for Pol when both are available). <br />
<br />
The third set has the same structure as the Nside=1024 products of R2.01, but '''the Q and U maps have been high-pass filtered to remove modes at l < 30 for the reasons indicated earlier. These are the default products for use in polarisation studies. They are the R2.02 files''' which have names like:<br />
*''COM_CMB_IQU-{method}_1024_R2.02_{coverage}.fits'' <br />
<br />
'''Version 2.00 files'''<br />
<br />
These have names like <br />
*''COM_CMB_IQU-{method}-field-{Int,Pol}_Nside_R2.00.fits'', <br />
as indicated above. They contain:<br />
* a minimal primary extension with no data;<br />
* one or two ''BINTABLE'' data extensions with a table of Npix lines by 14 columns in which the first 13 columns is a CMB maps produced from the full or a subset of the data, as described in the table below, and the last column in a confidence mask. There is a single extension for ''Int'' files, and two, for Q and U, for ''Pol'' files. <br />
* a ''BINTABLE'' extension containing the beam transfer function (mistakenly called window function in the files).<br />
<br />
If Nside=1024 the files contain I, Q and U maps, whereas if Nside=2048 only the I map is given.<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''CMB R2.00 map file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | Ext. 1. or 2. EXTNAME = ''COMP-MAP'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I or Q or U || Real*4 || uK_cmb || I or Q or U map <br />
|- <br />
|HM1 || Real*4 || uK_cmb || Half-miss 1 <br />
|-<br />
|HM2 || Real*4 || uK_cmb || Half-miss 2 <br />
|-<br />
|YR1 || Real*4 || uK_cmb || Year 1 <br />
|-<br />
|YR2 || Real*4 || uK_cmb || Year 2 <br />
|-<br />
|HR1 || Real*4 || uK_cmb || Half-ring 1 <br />
|-<br />
|HR2 || Real*4 || uK_cmb || Half-ring 2 <br />
|-<br />
|HMHS || Real*4 || uK_cmb || Half-miss, half sum <br />
|-<br />
|HMHD || Real*4 || uK_cmb || Half-miss, half diff <br />
|-<br />
|YRHS || Real*4 || uK_cmb || Year, half sum <br />
|-<br />
|YRHD || Real*4 || uK_cmb || Year, half diff <br />
|-<br />
|HRHS || Real*4 || uK_cmb || Half-ring half sum <br />
|-<br />
|HRHD || Real*4 || uK_cmb || Half-ring half diff <br />
|-<br />
|MASK || BYTE || || Confidence mask <br />
|-<br />
<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CMB || Astrophysical compoment name<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 1024 or 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (smica/nilc/sevem/commander)<br />
|-<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Ext. 2. or 3. EXTNAME = ''BEAM_WF'' (BINTABLE) . See Note 1<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BEAMWF || Real*4 || none || The effective beam transfer function, including the pixel window function. See Note 2.<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Int || value || First multipole of beam TF<br />
|-<br />
|LMAX || Int || value || Last multipole of beam TF<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|-<br />
|}<br />
<br />
Notes:<br />
# Actually this is a beam ''transfer'' function, so BEAM_TF would have been more appropriate.<br />
# The beam transfer function <math>B_\ell</math> given here includes the pixel window function <math>p_\ell</math> for the Nside=2048 pixelization. It means that, ideally, <math>C_\ell(map) = C_\ell(sky) \, B_\ell^2 \, p_\ell^2</math>. The beam ''Window'' function is given by <math>W_\ell = B_\ell^2</math><br />
<br />
<br />
'''Version 2.01 files'''<br />
<br />
These files have names like:<br />
*''COM_CMB_IQU-{method}{-field-Int|Pol}_Nside_R2.01_{coverage}.fits'' for the regular CMB maps, and <br />
*''COM_CMB_IQU-{fff}-{fgsub-sevem}{-field-Int|Pol}_Nside_R2.01_{coverage}.fits'' for the sevem frequency-dependent, foregrounds-subtracted maps,<br />
as indicated above. They contain:<br />
* a minimal primary extension with no data, but with a NUMEXT keyword giving the number of extensions contained.<br />
* one or two ''BINTABLE'' data extensions with a table of Npix lines by 1-5 columns depending on the file, as described above: the minimum begin I only, the maximum begin I, Q, U, and confidence masks for I and P. <br />
* a ''BINTABLE'' extension containing the beam transfer function(s): one for I, and a second one that applies to both Q and U, if Nslde=1024.<br />
<br />
If Nside=1024 the files contain I, Q and U maps, whereas if Nside=2048 only the I map is given. The basic structure, including information on the most important keywords, is given in the table below. For full details, see the FITS header.<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''CMB R2.01 map file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | Ext. 1. or 2. EXTNAME = ''COMP-MAP'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_Stokes || Real*4 || uK_cmb || I map (Nside=1024,2048) <br />
|- <br />
|Q_Stokes || Real*4 || uK_cmb || Q map (Nside=1024) <br />
|-<br />
|U_Stokes || Real*4 || uK_cmb || U map (Nside=2048) <br />
|-<br />
|TMASK || Int || none || optional Temperature confidence mask <br />
|-<br />
|PMASK || Int || none || optional Polarisation confidence mask <br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CMB || Astrophysical compoment name<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 1024 or 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM)<br />
|-<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Optional Ext. 2. or 3. EXTNAME = ''BEAM_TF'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INT_BEAM || Real*4 || none || Effective beam transfer function. See Note 1.<br />
|-<br />
|POL_BEAM || Real*4 || none || Effective beam transfer function. See Note 1.<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Int || value || First multipole of beam WF<br />
|-<br />
|LMAX_I || Int || value || Last multipole for Int beam TF<br />
|-<br />
|LMAX_P || Int || value || Last multipole for Pol beam TF<br />
|-<br />
|METHOD || String ||name || Cleaning method <br />
|-<br />
|}<br />
Notes:<br />
# The beam transfer function <math>B_\ell</math> given here includes the pixel window function <math>p_\ell</math> for the Nside=2048 pixelization. It means that, ideally, <math>C_\ell(map) = C_\ell(sky) \, B_\ell^2 \, p_\ell^2</math>. The beam ''Window'' function is given by <math>W_\ell = B_\ell^2</math><br />
<br />
'''Version 2.02 files'''<br />
<br />
'''For polarisation work, this is the default set of files to be used for cosmological analysis. Their content is identical to the "R2.01" files, except that angular scales above l < 30 have been filtered out of the Q and U maps. '''<br />
<br />
These files have names like:<br />
*''COM_CMB_IQU-{method}_1024_R2.02_{coverage}.fits'' <br />
as indicated above. They contain:<br />
The files contain <br />
* a minimal primary extension with no data, but with a NUMEXT keyword giving the number of extensions contained.<br />
* one or two ''BINTABLE'' data extensions with a table of Npix lines by 1-5 columns depending on the file, as described above: the minimum begin I only, the maximum begin I, Q, U, and confidence masks for I and P. <br />
* a ''BINTABLE'' extension containing 2 beam transfer functions: one for I and one that applies to both Q and U.<br />
<br />
If Nside=1024 the files contain I, Q and U maps, whereas if Nside=2048 only the I map is given. The basic structure, including information on the most important keywords, is given in the table below. For full details, see the FITS header.<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''CMB R2.02 map file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | Ext. 1. or 2. EXTNAME = ''COMP-MAP'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_Stokes || Real*4 || uK_cmb || I map (Nside=1024) <br />
|- <br />
|Q_Stokes || Real*4 || uK_cmb || Q map (Nside=1024) <br />
|-<br />
|U_Stokes || Real*4 || uK_cmb || U map (Nside=2048) <br />
|-<br />
|TMASK || Int || none || optional Temperature confidence mask <br />
|-<br />
|PMASK || Int || none || optional Polarisation confidence mask <br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CMB || Astrophysical compoment name<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 1024 or 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM)<br />
|-<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Optional Ext. 2. or 3. EXTNAME = ''BEAM_TF'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INT_BEAM || Real*4 || none || Effective beam transfer function. See Note 1.<br />
|-<br />
|POL_BEAM || Real*4 || none || Effective beam transfer function. See Note 1.<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Int || value || First multipole of beam WF<br />
|-<br />
|LMAX_I || Int || value || Last multipole for Int beam TF<br />
|-<br />
|LMAX_P || Int || value || Last multipole for Pol beam TF<br />
|-<br />
|METHOD || String ||name || Cleaning method <br />
|-<br />
|}<br />
Notes:<br />
# The beam transfer function <math>B_\ell</math> given here includes the pixel window function <math>p_\ell</math> for the Nside=2048 pixelization. It means that, ideally, <math>C_\ell(map) = C_\ell(sky) \, B_\ell^2 \, p_\ell^2</math>. The beam ''Window'' function is given by <math>W_\ell = B_\ell^2</math><br />
<br />
'''Common masks'''<br />
<br />
The common masks are stored into two different files for Temperature and Polarisation respectively:<br />
* ''COM_CMB_IQU-common-field-MaskInt_2048_R2.nn.fits'' with the UT78 and UTA76 masks<br />
* ''COM_CMB_IQU-common-field-MaskPol_1024_R2.nn.fits'' with the UP78, UPA77, and UPB77 masks<br />
Both files contain also a map of the missing pixels for the half mission and year coverage periods. The 2 (for Temp) or 3 (for Pol) masks and the missing pixels maps are stored in 4 or 5 column a ''BINTABLE'' extension 1 of each file, named ''MASK-INT'' and ''MASK-POL'', respectively. See the FITS file headers for details.<br />
<br />
'''Quadrupole residual maps'''<br />
<br />
The quadrupole residual maps are stored in files called:<br />
* ''COM_CMB_IQU-kq-resid-{method}-field-Int_2048_R2.02.fits''<br />
<br />
They contain:<br />
* a minimal primary extension with no data, but with a NUMEXT keyword giving the number of extensions contained.<br />
* a single ''BINTABLE'' extension with a single column of Npix lines containing the HEALPIX map indicated<br />
<br />
The basic structure of the data extension is shown below. For full details see the extension header. <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Kinetic quadrupole residual map file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | Ext. 1. EXTNAME = ''COMP-MAP'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTENSITY || Real*4 || K_cmb || the residual map <br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || KQ-RESID || Astrophysical compoment name<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|POLCCONV || String || COSMO || Polarization convention<br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method<br />
|-<br />
|}<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #EEE8AA;width:80%"><br />
'''2013 Release of CMB maps'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''CMB Maps'''<br />
<br />
CMB maps have been produced by the SMICA, NILC, SEVEM and COMMANDER-Ruler pipelines. Of these, the SMICA product is considered the preferred one overall and is labelled ''Main product'' in the Planck Legacy Archive, while the other two are labeled as ''Additional product''.<br />
<br />
SMICA and NILC also produce ''inpainted'' maps, in which the Galactic Plane, some bright regions and masked point sources are replaced with a constrained CMB realization such that the whole map has the same statistical distribution as the observed CMB. <br />
<br />
The results of SMICA, NILC and SEVEM pipeline are distributed as a FITS file containing 4 extensions:<br />
# CMB maps and ancillary products (3 or 6 maps)<br />
# CMB-cleaned foreground maps from LFI (3 maps)<br />
# CMB-cleaned foreground maps from HFI (6 maps)<br />
# Effective beam of the CMB maps (1 vector)<br />
<br />
The results of COMMANDER-Ruler are distributed as two FITS files (the high and low resolution) containing the following extensions: <br />
High resolution N$_\rm{side}$=2048 (note that we don't provide the CMB-cleaned foregrounds maps for LFI and HFI because the Ruler resolution (~7.4') is lower than the HFI highest channel and and downgrading it will introduce noise correlation). <br />
# CMB maps and ancillary products (4 maps)<br />
# Effective beam of the CMB maps (1 vector)<br />
<br />
Low resolution N$_\rm{side}$=256<br />
# CMB maps and ancillary products (3 maps)<br />
# 10 example CMB maps used in the montecarlo realization (10 maps)<br />
# Effective beam of the CMB maps (1 vector)<br />
<br />
For a complete description of the data structure, see the [[#File names and structure | below]]; the content of the first extensions is illustrated and commented in the table below.<br />
<br />
<br />
{| class="wikitable" border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:center" style="background:#efefef;"<br />
|+ style="background:#eeeeee;" | '''The maps (CMB, noise, masks) contained in the first extension'''<br />
|-<br />
!width=40px | Col name<br />
!width=200px| SMICA<br />
!width=200px| NILC<br />
!width=200px| SEVEM <br />
!width=200px| COMMANDER-Ruler H<br />
!width=200px| COMMANDER-Ruler L <br />
!width=300px| Description / notes<br />
|-<br />
| align="left" | 1: I<br />
| [[File: CMB-smica.png|200px]]<br />
| [[File: CMB-nilc.png|200px]]<br />
| [[File: CMB-sevem.png|200px]]<br />
| [[File: CMB-CR_h.png|200px]]<br />
| [[File: CMB-CR_l.png|200px]]<br />
| Raw CMB anisotropy map. These are the maps used in the component separation paper {{PlanckPapers|planck2013-p06}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<br />
| [[File: CMBnoise-CR_h.png|200px]]<br />
| align='center' | not applicable<br />
| Noise map. Obtained by propagating the half-ring noise through the CMB cleaning pipelines.<br />
|-<br />
| 3: VALMASK<br />
| [[File: valmask-smica.png|200px]]<br />
| [[File: valmask-nilc.png|200px]]<br />
| [[File: valmask-sevem.png|200px]]<br />
| [[File: valmask-cr_h.png|200px]]<br />
| [[File: valmask-cr_l.png|200px]]<br />
| Confidence map. Pixels with an expected low level of foreground contamination. These maps are only indicative and obtained by different ad hoc methods. They cannot be used to rank the CMB maps.<br />
|-<br />
| 4: I_MASK<br />
| [[File: cmbmask-smica.png|200px]]<br />
| [[File: cmbmask-nilc.png|200px]]<br />
| align='center' | not applicable<br />
| align='center' | not applicable<br />
| align='center' | not applicable<br />
| Some areas are masked for the production of the raw CMB maps (for NILC: point sources from 44 GHz to 857 GHz; for SMICA: point sources from 30 GHz to 857 GHz, Galatic region and additional bright regions).<br />
|-<br />
| 5: INP_CMB<br />
| [[File: CMBinp-smica.png|200px]]<br />
| [[File: CMBinp-nilc.png|200px]]<br />
| align='center' | not applicable<br />
| align='center' | not applicable<br />
| align='center' | not applicable<br />
| Inpainted CMB map. The raw CMB maps with some regions (as indicated by INP_MASK) replaced by a constrained Gaussian realization. The inpainted SMICA map was used for PR.<br />
|-<br />
| 6: INP_MASK<br />
| [[File: inpmask-smica.png|200px]]<br />
| [[File: inpmask-nilc.png|200px]]<br />
| align='center' | not applicable<br />
| align='center' | not applicable<br />
| align='center' | not applicable<br />
| Mask of the inpainted regions. For SMICA, this is identical to I_MASK. For NILC, it is not.<br />
|}<br />
<br />
The component separation pipelines are described in the [[Astrophysical_component_separation#CMB_and_foreground_separation|CMB and foreground separation]] section and also in Section 3 and Appendices A-D of {{PlanckPapers|planck2013-p06}} and references therein.<br />
<br />
The union (or common) mask is defined as the union of the confidence masks from the four component separation pipelines, the three listed above and Commander-Ruler. It leaves 73% of the sky available, and so it is denoted as U73.<br />
<br />
<br />
'''Product description '''<br />
<br />
'''SMICA'''<br />
<br />
; Principle<br />
: SMICA produces a CMB map by linearly combining all Planck input channels (from 30 to 857 GHz) with weights which vary with the multipole. It includes multipoles up to <math>\ell = 4000</math>.<br />
; Resolution (effective beam)<br />
: The SMICA map has an effective beam window function of 5 arc-minutes truncated at <math>\ell=4000</math> '''and deconvolved from the pixel window'''. It means that, ideally, one would have <math>C_\ell(map) = C_\ell(sky) * B_\ell(5')^2</math>, where <math>C_\ell(map)</math> is the angular spectrum of the map, where <math>C_\ell(sky)</math> is the angular spectrum of the CMB and <math>B_\ell(5')</math> is a 5-arcminute Gaussian beam function. Note however that, by convention, the effective beam window function <math>B_\ell(fits)</math> provided in the FITS file does include a pixel window function. Therefore, it is equal to <math>B_\ell(fits) = B_\ell(5') / p_\ell(2048)</math> where <math>p_\ell(2048)</math> denotes the pixel window function for an Nside=2048 pixelization.<br />
; Confidence mask<br />
: A confidence mask is provided which excludes some parts of the Galactic plane, some very bright areas and the masked point sources. This mask provides a qualitative (and subjective) indication of the cleanliness of a pixel. <br />
; Masks and inpainting<br />
: The raw SMICA CMB map has valid pixels except at the location of masked areas: point sources, Galactic plane, some other bright regions. Those invalid pixels are indicated with the mask named 'I_MASK'. The raw SMICA map has been inpainted, producing the map named "INP_CMB". Inpainting consists in replacing some pixels (as indicated by the mask named INP_MASK) by the values of a constrained Gaussian realization which is computed to ensure good statistical properties of the whole map (technically, the inpainted pixels are a sample realisation drawn under the posterior distribution given the un-masked pixels.<br />
<br />
'''NILC'''<br />
<br />
; Principle<br />
: The Needlet-ILC (hereafter NILC) CMB map is constructed from all Planck channels from 44 to 857 GHz and includes multipoles up to <math>\ell = 3200</math>. It is obtained by applying the Internal Linear Combination (ILC) technique in needlet space, that is, with combination weights which are allowed to vary over the sky and over the whole multipole range.<br />
; Resolution (effective beam)<br />
: As in the SMICA product except that there is no abrupt truncation at <math>\ell_{max}= 3200</math> but a smooth transition to <math>0</math> over the range <math>2700\leq\ell\leq 3200</math>.<br />
; Confidence mask<br />
: A confidence mask is provided which excludes some parts of the Galactic plane, some very bright areas and the masked point sources. This mask provides a qualitative indication of the cleanliness of a pixel. The threshold is somewhat arbitrary.<br />
; Masks and inpainting<br />
: The raw NILC map has valid pixels except at the location of masked point sources. This is indicated with the mask named 'I_MASK'. The raw NILC map has been inpainted, producing the map named "INP_CMB". The inpainting consists in replacing some pixels (as indicated by the mask named INP_MASK) by the values of a constrained Gaussian realization which is computed to ensure good statistical properties of the whole map (technically, the inpainted pixels are a sample realisation drawn under the posterior distribution given the un-masked pixels.<br />
<br />
'''SEVEM'''<br />
<br />
The aim of SEVEM is to produce clean CMB maps at one or several frequencies by using a procedure based on template fitting. The templates are internal, i.e., they are constructed from Planck data, avoiding the need for external data sets, which usually complicates the analyses and may introduce inconsistencies. The method has been successfully applied to Planck simulations{{BibCite|leach2008}} and to WMAP polarisation data{{BibCite|fernandezcobos2012}}. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust. Note that unlike the other products, SEVEM does not provide the mask of regions not used in the productions of the CMB ma (''I_MASK'') nor an inpainted version of the map and its associated mask. On the other hand, it provides ''channel maps'' and 100, 143, and 217 GHz which are used as the building blocks of the final map.<br />
<br />
'''COMMANDER-Ruler'''<br />
<br />
COMMANDER-Ruler is the Planck software implementing a pixel based parametric component separation. Amplitude of CMB and the main diffuse foregrounds along with the relevant spectral parameters for those (see below in the Astrophysical Foreground Section for the latter) are parametrized and fitted in single MCMC chains conducted at $N_\rm{side}$=256 using COMMANDER, implementing a Gibbs Sampling. The CMB amplitude which <br />
is obtained in these runs corresponds to the delivered low resolution CMB component from COMMANDER-Ruler which has a FWHM of 40 arcminutes. The sampling of the foreground parameters is applied to the data at full resolution for obtaining the high resolution CMB component from Ruler which is available on the PLA. In the {{PlanckPapers|planck2013-p06|1|Planck Component Separation paper}} additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps. The products mainly consist of: <br />
<br />
* Maps of the Amplitudes of the CMB at low resolution, $N_\rm{side}$=256, along with the standard deviations of the outputs, beam profiles derived from the production process. <br />
* Maps of the CMB amplitude, along with the standard deviations, at high resolution, $N_\rm{side}$=2048, beam profiles derived from the production process. <br />
* Mask obtained on the basis of the precision in the fitting procedure; the thresholding is evaluated through the COMMANDER-Ruler likelihood analysis and excludes 13% of the sky, see {{PlanckPapers|planck2013-p06}}.<br />
<br />
'''Production process'''<br />
<br />
'''SMICA'''<br />
<br />
; 1) Pre-processing<br />
: All input maps undergo a pre-processing step to deal with point sources. The point sources with SNR > 5 in the PCCS catalogue are fitted in each input map. If the fit is successful, the fitted point source is removed from the map; otherwise it is masked and the hole is filled in by a simple diffusive process to ensure a smooth transition and mitigate spectral leakage. This is done at all frequencies but 545 and 857 GHz, here all point sources with SNR > 7.5 are masked and filled-in similarly.<br />
; 2) Linear combination<br />
: The nine pre-processed Planck frequency channels from 30 to 857 GHzare harmonically transformed up to <math>\ell = 4000</math> and co-added with multipole-dependent weights as shown in the figure.<br />
; 3) Post-processing<br />
: The areas masked in the pre-processing step are replaced by a constrained Gaussian realization.<br />
<br />
Note: The visible power deficit in the raw CMB map around the galactic plane is due to the smooth fill-in of the masked areas in the input maps (the result of the pre-processing). It is not to be confused with the post-processing step of inpainting of the CMB map with a constrained Gaussian realization.<br />
<br />
<br />
[[File:smica.jpg|thumb|center|500px|'''Weights given by SMICA to the input maps (after they are re-beamed to 5 arcmin and expressed in K<math>_\rm{RJ}</math>), as a function of multipole.''']]<br />
<br />
'''NILC'''<br />
<br />
; 1) Pre-processing<br />
: Same pre-processing as SMICA (except the 30 GHz channel is not used).<br />
; 2) Linear combination<br />
: The pre-processed Planck frequency channels from 44 to 857 GHz are linearly combined with weights which depend on location on the sky and on the multipole range up to <math>\ell = 3200</math>. This is achieved using a needlet (redundant spherical wavelet) decomposition. For more details, see {{PlanckPapers|planck2013-p06}}.<br />
; 3) Post-processing<br />
: The areas masked in the pre-processing plus other bright regions step are replaced by a constrained Gaussian realization as in the SMICA post-processing step.<br />
<br />
'''SEVEM'''<br />
<br />
The templates are internal, i.e., they are constructed from Planck data, avoiding the need for external data sets, which usually complicates the analyses and may introduce inconsistencies. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust. The fitting can be done in real or wavelet space (using a fast wavelet adapted to the HEALPix pixelization{{BibCite|casaponsa2011}}) to properly deal with incomplete sky coverage. By expediency, however, we fill in the small number of unobserved pixels at each channel with the mean value of its neighbouring pixels before applying SEVEM.<br />
<br />
We construct our templates by subtracting two close Planck frequency channel maps, after first smoothing them to a common resolution to ensure that the CMB signal is properly removed. A linear combination of the templates <math>t_j</math> is then subtracted from (hitherto unused) map d to produce a clean CMB map at that frequency. This is done either in real or in wavelet space (i.e., scale by scale) at each position on the sky: <math> T_c(\mathbf{x}, ν) = d(\mathbf{x}, ν) − \sum_{j=1}^{n_t} α_j t(\mathbf{x}) </math><br />
where <math>n_t</math> is the number of templates. If the cleaning is performed in real space, the <math>α_j</math> coefficients are obtained by minimising the variance of the clean map <math>T_c</math> outside a given mask. When working in wavelet space, the cleaning is done in the same way at each wavelet scale independently (i.e., the linear coefficients depend on the scale). Although we exclude very contaminated regions during the minimization, the subtraction is performed for all pixels and, therefore, the cleaned maps cover the full-sky (although we expect that foreground residuals are present in the excluded areas).<br />
<br />
An additional level of flexibility can also be considered: the linear coefficients can be the same for all the sky, or several regions with different sets of coefficients can be considered. The regions are then combined in a smooth way, by weighting the pixels at the boundaries, to avoid discontinuities in the clean maps.<br />
Since the method is linear, we may easily propagate the noise properties to the final CMB map. Moreover, it is very fast and permits the generation of thousands of simulations to character- ize the statistical properties of the outputs, a critical need for many cosmological applications. The final CMB map retains the angular resolution of the original frequency map.<br />
<br />
There are several possible configurations of SEVEM with regard to the number of frequency maps which are cleaned or the number of templates that are used in the fitting. Note that the production of clean maps at different frequencies is of great interest in order to test the robustness of the results. Therefore, to define the best strategy, one needs to find a compromise between the number of maps that can be cleaned independently and the number of templates that can be constructed.<br />
<br />
In particular, we have cleaned the 143 GHz and 217 GHz maps using four templates constructed as the difference of the following Planck channels (smoothed to a common resolution): (30-44), (44-70), (545-353) and (857-545). For simplicity, the three maps have been cleaned in real space, since there was not a significant improvement when using wavelets (especially at high latitude). In order to take into account the different spectral behaviour of the foregrounds at low and high galactic latitudes, we have considered two independent regions of the sky, for which we have used a different set of coefficients. The first region corresponds to the 3 per cent brightest Galactic emission, whereas the second region is defined by the remaining 97 per cent of the sky. For the first region, the coefficients are actually estimated over the whole sky (we find that this is more optimal than perform the minimisation only on the 3 per cent brightest region, where the CMB emission is very sub-dominant) while for the second region, we exclude the 3 per cent brightest region of the sky, point sources detected at any frequency and those pixels which have not been observed at all channels.<br />
Our final CMB map has then been constructed by combining the 143 and 217 GHz maps by weighting the maps in harmonic space taking into account the noise level, the resolution and a rough estimation of the foreground residuals of each map (obtained from realistic simulations). This final map has a resolution corresponding to a Gaussian beam of fwhm=5 arcminutes.<br />
<br />
Moreover, additional CMB clean maps (at frequencies between 44 and 353 GHz) have also been produced using different combinations of templates for some of the analyses carried out in {{PlanckPapers|planck2013-p09}} and {{PlanckPapers|planck2013-p14}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in {{PlanckPapers|planck2013-p14}}, while frequencies from 70 to 217 GHz were used for consistency tests in {{PlanckPapers|planck2013-p09}}.<br />
<br />
'''COMMANDER-Ruler'''<br />
<br />
The production process consist in low and high resolution runs according to the description above. <br />
; Low Resolution Runs: Same as the Astrophysics Foregrounds Section below; The CMB amplitude is fitted along with the other foreground parameters and constitutes the CMB Low Resolution Rendering which is in the PLA. <br />
; Ruler Runs: the sampling at high resolution is used to infer the probability distribution of spectral parameters which is exploited at full resolution in order to obtain the High Resolution CMB Rendering which is in the PLA. <br />
<br />
''' Masks '''<br />
<br />
Summary table with the different masks that have been used by the component separation methods to pre-process and to process the frequency maps and the CMB maps.<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|-<br />
|- bgcolor="ffdead" <br />
! Commander 2013 (PR1) || Used for diffuse inpainting of input frequency maps || Used for constrained Gaussian realization inpaiting of CMB map || Description<br />
|-<br />
|VALMASK || NO || NO || VALMASK is the confidence mask that defines the region where the reconstructed CMB is trusted. It can be found inside <br />
<br />
{{PLASingleFile|fileType=map|name=COM_CompMap_CMB-commrul_2048_R1.00.fits|link=COM_CompMap_CMB-commrul_2048_R1.00.fits}} and {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-commrul_0256_R1.00.fits|link=COM_CompMap_CMB-commrul_0256_R1.00.fits}} for low resolution analyses.<br />
|-<br />
|- bgcolor="800000"<br />
|<br />
! ||<br />
|<br />
|- bgcolor="ffdead" <br />
! SEVEM 2013 (PR1) || Used diffuse inpainting of input frequency maps || Used for Constrained Gaussian realization inpaiting of CMB map || Description<br />
|-<br />
|VALMASK || NO || NO || VALMASK is the confidence mask that defines the region where the reconstructed CMB is trusted. It can be found inside <br />
<br />
{{PLASingleFile|fileType=map|name=COM_CompMap_CMB-sevem_2048_R1.12.fits|link=COM_CompMap_CMB-sevem_2048_R1.12.fits}}.<br />
|-<br />
|- bgcolor="800000"<br />
|<br />
! ||<br />
|<br />
|- bgcolor="ffdead"<br />
! NILC 2013 (PR1) || Used for diffuse inpainting of input frequency maps || Used for constrained Gaussian realization inpaiting of CMB map || Description<br />
|-<br />
|VALMASK || NO || NO || VALMASK is the confidence mask that defines the region where the reconstructed CMB is trusted. It can be found inside {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-nilc_2048_R1.20.fits|link=COM_CompMap_CMB-nilc_2048_R1.20.fits}}.<br />
|-<br />
|I_MASK || NO || NO || I_MASK defines the regions over which CMB is not built. It is a combination of point source masks, Galactic plane mask and other bright regions like LMC, SMC, etc. It can be found inside {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-nilc_2048_R1.20.fits|link=COM_CompMap_CMB-nilc_2048_R1.20.fits}}.<br />
|- <br />
|INP_MASK || NO || YES || It can be found inside {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-nilc_2048_R1.20.fits|link=COM_CompMap_CMB-nilc_2048_R1.20.fits}}.<br />
|-<br />
|-<br />
|- bgcolor="800000"<br />
|<br />
! ||<br />
|<br />
|- bgcolor="ffdead" <br />
! SMICA 2013 (PR1) || Used for diffuse inpainting of input frequency maps || Used for constrained Gaussian realization inpaiting of CMB map || Description<br />
|-<br />
|VALMASK || NO || NO || VALMASK is the confidence mask that defines the region where the reconstructed CMB is trusted. It can be found inside <br />
<br />
{{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}.<br />
|-<br />
|I_MASK || YES || YES || I_MASK defines the regions over which CMB is not built. It is a combination of point source masks, Galactic plane mask and other bright regions like LMC, SMC, etc. It can be found inside {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}.<br />
|- <br />
|INP_MASK || YES || YES || INP_MASK for SMICA 2013 release is identical to I_MASK above. <br />
|-<br />
|-<br />
|}<br />
<br />
<br />
'''Inputs'''<br />
<br />
The input maps are the sky temperature maps described in the [[Frequency Maps | Sky temperature maps]] section. SMICA and SEVEM use all the maps between 30 and 857 GHz; NILC uses the ones between 44 and 857 GHz. Commander-Ruler uses frequency channel maps from 30 to 353 GHz. <br />
<br />
'''File names and structure'''<br />
<br />
The FITS files corresponding to the three CMB products are the following:<br />
<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-nilc_2048_R1.20.fits|link=COM_CompMap_CMB-nilc_2048_R1.20.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-sevem_2048_R1.12.fits|link=COM_CompMap_CMB-sevem_2048_R1.12.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-commrul_2048_R1.00.fits|link=COM_CompMap_CMB-commrul_2048_R1.00.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-commrul_0256_R1.00.fits|link=COM_CompMap_CMB-commrul_0256_R1.00.fits}}<br />
<br />
<br />
The files contain a minimal primary extension with no data and four ''BINTABLE'' data extensions. Each column of the ''BINTABLE'' is a (Healpix) map; the column names and the most important keywords of each extension are described in the table below; for the remaining keywords, please see the FITS files directly. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''CMB map file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | Ext. 1. EXTNAME = ''COMP-MAP'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK_cmb || CMB temperature map<br />
|-<br />
|NOISE || Real*4 || uK_cmb || Estimated noise map (note 1)<br />
|-<br />
|I_STDEV|| Real*4 || uK_cmb || Standard deviation, ONLY on COMMANDER-Ruler products<br />
|-<br />
|VALMASK|| Byte || none || Confidence mask (note 2)<br />
|-<br />
|I_MASK|| Byte || none || Mask of regions over which CMB map is not built (Optional - see note 3)<br />
|-<br />
|INP_CMB || Real*4 || uK_cmb || Inpainted CMB temperature map (Optional - see note 3)<br />
|-<br />
|INP_MASK || Byte || none || mask of inpainted pixels (Optional - see note 3)<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CMB || Astrophysical compoment name<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|-<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Ext. 2. EXTNAME = ''FGDS-LFI'' (BINTABLE) - Note 4<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|LFI_030 || Real*4 || K_cmb || 30 GHz foregrounds<br />
|-<br />
|LFI_044 || Real*4 || K_cmb || 44 GHz foregrounds<br />
|-<br />
|LFI_070 || Real*4 || K_cmb || 70 GHz foregrounds<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 1024 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM)<br />
|-<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Ext. 3. EXTNAME = ''FGDS-HFI'' (BINTABLE) - Note 4<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|HFI_100 || Real*4 || K_cmb || 100 GHz foregrounds<br />
|-<br />
|HFI_143 || Real*4 || K_cmb || 143 GHz foregrounds<br />
|-<br />
|HFI_217 || Real*4 || K_cmb || 217 GHz foregrounds<br />
|-<br />
|HFI_353 || Real*4 || K_cmb || 353 GHz foregrounds<br />
|-<br />
|HFI_545 || Real*4 || MJy/sr || 545 GHz foregrounds<br />
|-<br />
|HFI_857 || Real*4 || MJy/sr || 857 GHz foregrounds<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Ext. 4. EXTNAME = ''BEAM_WF'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BEAM_WF || Real*4 || none || The effective beam window function, including the pixel window function. See Note 5.<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Int || value || First multipole of beam WF<br />
|-<br />
|LMAX || Int || value || Lsst multipole of beam WF<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|-<br />
|}<br />
<br />
Notes:<br />
# The half-ring half-difference (HRHD) map is made by passing the half-ring frequency maps independently through the component separation pipeline, then computing half their difference. It approximates a noise realisation, and gives an indication of the uncertainties due to instrumental noise in the corresponding CMB map. <br />
# The confidence mask indicates where the CMB map is considered valid. <br />
# This column is not present in the SEVEM and COMMANDER-Ruler product file. For SEVEM these three columns give the CMB channel maps at 100, 143, and 217 GHz (columns ''C100'', ''C143'', and ''C217'', in units of K_cmb.<br />
# The subtraction of the CMB from the sky maps in order to produce the foregrounds map is done after convolving the CMB map to the resolution of the given frequency. Those columns are not present in the COMMANDER-Ruler product file.<br />
# The beam window function <math>B_\ell</math> given here includes the pixel window function <math>p_\ell</math> for the Nside=2048 pixelization. It means that, ideally, <math>C_\ell(map) = C_\ell(sky) \, B_\ell^2 \, p_\ell^2</math>.<br />
<br />
The low resolution COMMANDER-Ruler CMB product is organized in the following way:<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''CMB low resolution COMMANDER-Ruler map file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | Ext. 1. EXTNAME = ''COMP-MAP'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK_cmb || CMB temperature map obtained as average over 1000 samples<br />
|-<br />
|I_stdev || Real*4 || uK_cmb || Corresponding Standard deviation amongst the 1000 samples<br />
|-<br />
|VALMASK|| Byte || none || Confidence mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|-<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Ext. 2. EXTNAME = ''CMB-Sample'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I_SIM01 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM02 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM03 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM04 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM05 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM06 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM07 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM08 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM09 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|I_SIM10 || Real*4 || K_cmb || CMB Sample, smoothed to 40 arcmin<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || String || HEALPIX ||<br />
|-<br />
|COORDSYS || String || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || String || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 1024 || Healpix Nside<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|- bgcolor="ffdead" <br />
!colspan="4" | Ext. 4. EXTNAME = ''BEAM_WF'' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BEAM_WF || Real*4 || none || The effective beam window function, including the pixel window function.<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Int || value || First multipole of beam WF<br />
|-<br />
|LMAX || Int || value || Lsst multipole of beam WF<br />
|-<br />
|METHOD || String ||name || Cleaning method (SMICA/NILC/SEVEM/COMMANDER-Ruler)<br />
|-<br />
|}<br />
<br />
<br />
The FITS files containing the ''union'' (or common) maks is:<br />
* {{PLASingleFile|fileType=map|name=COM_Mask_CMB-union_2048_R1.10.fits|link=COM_Mask_CMB-common}}<br />
which contains a single ''BINTABLE'' extension with a single column (named ''U73'') for the mask, which is boolean (FITS ''TFORM = B''), in GALACTIC coordinates, NESTED ordering, and Nside=2048.<br />
<br />
For the benefit of users who are only looking for a small file containing the SMICA cmb map with no additional information (noise or masks) we provide such a file here<br />
*{{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica-field-I_2048_R1.20.fits|link=COM_CompMap_CMB-smica-field-I_2048_R1.20.fits}}<br />
This file contains a single extension with a single column containing the SMICA cmb temperature map.<br />
<br />
'''Cautionary notes'''<br />
<br />
# The half-ring CMB maps are produced by the pipelines with parameters/weights fixed to the values obtained from the full maps. Therefore the CMB HRHD maps do not capture all of the uncertainties due to foreground modelling on large angular scales.<br />
# The HRHD maps for the HFI frequency channels underestimate the noise power spectrum at high l by typically a few percent. This is caused by correlations induced in the pre-processing to remove cosmic ray hits. The CMB is mostly constrained by the HFI channels at high l, and so the CMB HRHD maps will inherit this deficiency in power.<br />
# The beam transfer functions do not account for uncertainties in the beams of the frequency channel maps.<br />
<br />
<br />
<br />
</div><br />
</div><br />
<br />
== References ==<br />
<References /><br />
<br />
</div><br />
</div><br />
<br />
<br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=14381CMB spectrum & Likelihood Code2018-07-16T13:40:59Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:CMB spectra and likelihood code}}<br />
<br />
== 2018 CMB spectra==<br />
<br />
<br />
===General description===<br />
====TT====<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 86% of the sky ({{PlanckPapers|planck2016-l06}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood {{PlanckPapers|planck2016-l05}}, with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.51.48.png|thumb|600px|center]]<br />
<br />
====TE, EE, and EB, BB ====<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. In the multipole range 2 ≤ l ≤ 29, we plot the power spectra estimates from the SimAll likelihood (though only the EE spectrum is used in the baseline parameter analysis at l ≤ 29), see {{PlanckPapers|planck2016-l06}}). .<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.52.35.png|thumb|600px|center]]<br />
[[File:Screen Shot 2018-07-16 at 05.52.24.png|thumb|600px|center]]<br />
<br />
<br />
In the range &#8467; = 2-29, we also release the <i>BB</i>, and <i>EB</i> power spectra derived from the same maps. Error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2016-l03}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
==== Best-fit model ====<br />
<br />
We also provide best-fit LCDM CMB power spectra from the baseline Planck TT,TE,EE+lowE+lensing. The spectra must be divided by the best-fit Planck map-based calibration parameter squared, calPlanck**2, to be compared to the coadded CMB spectra. The best-fit calPlanck value can be found in the file "COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt".<br />
<br />
===Production process===<br />
The Plik high-multipole likelihood (described in detail in {{PlanckPapers|planck2016-l05}}) is a Gaussian approximation of the probability distributions of the <i>TT</i>, <i>EE</i>, and <i>TE</i> angular power spectra, with semi-analytic covariance matrices calculated assuming a fiducial cosmology. It includes multipoles in the range 30 to 2508 for TT and 30 to 1996 for <i>TE</i> and <i>EE</i> and is constructed from half-mission cross-spectra measured from the 100-, 143-, and 217-GHz HFI frequency maps. For more details see {{PlanckPapers|planck2016-l06}}.<br />
<br />
<br />
<br />
===Inputs===<br />
<br />
The T T likelihood uses four half-mission cross-spectra with different multipole cuts to avoid multipole regions where noise dominates due to the limited resolution of the beams and to en-sure foreground contamination is correctly handled by our fore-ground model: 100 × 100 ( &#8467; = 30–1197); 143 × 143 (&#8467; = 30– 1996); 143 × 217 (&#8467; = 30–2508); and 217 × 217 (&#8467; = 30–2508). The TE and EE likelihoods also include the 100 × 143 and 100 × 217 cross-spectra to improve the signal-to-noise ratio, and have different multipole cuts: 100 × 100 (&#8467; = 30–999); 100 × 143 (&#8467; = 30–999); 100 × 217 (&#8467; = 505–999); 143 × 143 (&#8467; = 30– 1996); 143 × 217 (&#8467; = 505–1996); and 217 × 217 (&#8467; = 505– 1996). <br />
<br />
=== File names and meta-data ===<br />
<br />
The CMB spectra and their uncertainties are distributed in ASCII text files named ''COM_PowerSpect_CMB_nn_R3.01.fits'', where nn stands for the type of spectrum the file contains:<br />
* COM_PowerSpect_CMB-EE-full_R3.01.txt<br />
* COM_PowerSpect_CMB-TE-full_R3.01.txt<br />
* COM_PowerSpect_CMB-TT-full_R3.01.txt<br />
* COM_PowerSpect_CMB-low-ell-BB-full_R3.01.txt<br />
* COM_PowerSpect_CMB-low-ell-EB-full_R3.01.txt<br />
<br />
In addition we provide one file containing all the parameters of the Plik runs which yielded the spectra. This file is named<br />
* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt<br />
<br />
The theoretical spectrum of the best-fit model itself is provided in a separate file named<br />
* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt<br />
<br />
The data file columns give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>, and the lower and upper 68% uncertainties.<br />
<br />
<br />
== 2018 Likelihood==<br />
<br />
The 2018 Likelihood code will be released at a later time.<br />
<br />
== Previous Releases: (2015) and (2013) CMB spectrum and Likelihood ==<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%"><br />
'''2015 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''2015 CMB spectra'''<br />
<br />
'''General description'''<br />
<br />
'''TT'''<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2014-a12}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP &Lambda;CDM run. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]<br />
<br />
'''TE, EE, and TB, EB, BB '''<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
'''Production process'''<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
'''Inputs'''<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
''' File names and meta-data '''<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
'''Likelihood'''<br />
<br />
The 2015 baseline likelihood release consists of a code package and a single data package. Four extended data packages are also available enabling exploration of alternatives to the baseline results.<br />
The code compiles to a library allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets. A data set permits the computation of a single likelihood among:<br />
* the high-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the low-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the CMB lensing reconstruction.<br />
By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.<br />
<br />
Only the baseline data package, ''COM_Likelihood_Data-baseline_R2.00.tar.gz'', will be fully described on this page. It contains six data sets, which are enough to compute all of the baseline Planck results that are discussed in {{PlanckPapers|planck2014-a14}}. In particular it allows for the computation of the CMB and lensing likelihood from either the Temperature data only, or the Temperature + Polarization combination.<br />
<br />
The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in {{PlanckPapers|planck2014-a13}} and {{PlanckPapers|planck2014-a17}}. Their full description is contained in the documentation included in each of the extended data packages.<br />
<br />
'''Library and tools'''<br />
<br />
'''Description'''<br />
The library consists of code written in C and Fortran 90. It can be called from both of<br />
those languages. Optionally, a python wrapper can be built as well. Scripts to<br />
simplify the linking of the library with other codes are part of the package, as<br />
well as some example codes that can be used to test the correct installation of<br />
the code and the integrity of the data packages. Optionally, a script is also available, allowing<br />
the user to modify the multipole range of the TT likelihoods and reproduce the hybridization<br />
test performed in the paper.<br />
A description of the tool, the API of the library, as well as different <br />
installation procedure are detailed in the ''readme.md'' file in the code package.<br />
<br />
'''File name'''<br />
The code can be extracted from <br />
''COM_Likelihood_Code-v2.0_R2.00.tar.bz2''.<br />
<br />
Please read the file ''readme.md'' for installation instructions.<br />
<br />
'''Data sets - Baseline data'''<br />
All of the released baseline data are distributed within a single file,<br />
''COM_Likelihood_Data-baseline_R2.00.tar.gz''.<br />
<br />
This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.<br />
<br />
Each data set is stored in its own directory. The directory structure follows similar rules<br />
for each data set, and stores data, template, and meta-data for each particular likelihood.<br />
<br />
As in 2013, the CMB likelihood is cut into low-&#8467; and high-&#8467; parts. Moreover, <br />
for each of those, we distribute both a T-only datafile and a joint T+P one. In the case <br />
of the high-&#8467; part, we also distribute two specific versions of the likelihood, <br />
that allow for estimate of T and T+P marginalized over the nuisance parameters.<br />
Combining both the low-&#8467; and high-&#8467; files, one can compute the likelihood over the<br />
range &#8467;=2-2508 in TT and &#8467;=2-1996 in TE and EE. A full description of the low-&#8467; <br />
and high-&#8467; likelihood is available in {{PlanckPapers|planck2014-a13}}.<br />
<br />
Similarly, for the case of lensing, we also distribute the likelihood using both<br />
the reconstruction based on the <i>T</i> map only, or on <i>T</i>+<i>P</i> maps. <br />
A full description of the lensing likelihood is available in {{PlanckPapers|planck2014-a17}}.<br />
<br />
All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that his parameter is explored in the Gaussian prior 1.0000&plusmn;0.0025.<br />
<br />
''' Low-&#8467; likelihoods '''<br />
<br />
'''TT only - commander'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=2-29.<br />
Using the optional tool in the code package, it can be modified to cover any multipole range <br />
up to &#8467;&lt;200. <br />
<br />
''' Production process'''<br />
The likelihood is based on the results of the Commander approach, which implements a <br />
Bayesian component separation method in pixel space, sampling the posterior distribution <br />
of the parameters of a model that describes both the CMB and the foreground emissions<br />
in a combination of the Planck maps, the WMAP map, and the 408-MHz survey. The samples<br />
of this exploration are used to infer the foreground marginalized low-&#8467; likelihood <br />
for any <i>TT</i> CMB spectrum. <br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
'''File name and usage'''<br />
The commander likelihood is distributed in <br />
''plc_2.0/low_l/commander/commander_rc2_v1.1_l2_29_B.clik''<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the vector really starts at &#8467;=0, although<br />
the first two entries are null.<br />
<br />
'''TEB '''<br />
This file allows for the computation of the CMB joint TT,EE, BB and TE likelihood <br />
in the range &#8467;=2-29. It should not be used with the low-&#8467; TT-only likelihood.<br />
<br />
''' Production process'''<br />
The file allows for the computation of the pixel based likelihood of <i>T</i>, <i>E</i>, and <i>B</i> <br />
maps. The <i>T</i> map is the best-fit map obtained from the commander algorithm, as described above, <br />
while the <i>E</i> and <i>B</i> maps are obtained from the 70GHz LFI full mission data, but excluding the second and fourth surveys. Foreground contamination is<br />
dealt with by marginalizing over templates based on the 30-GHz LFI and 353-GHz HFI maps.<br />
The covariance matrix comes from the Planck detector sensitivity modulated on the <br />
sky by the scanning strategy. The covariance matrix is further enlarged to account <br />
for the foreground template removal. <br />
To speed up the computation by about an order of magnitude, the problem is <br />
projected into <i>C</i><sub>&#8467;</sub> space using the Sherman-Morrison-Woodbury identity. Only the <br />
projected quantities are stored in the data package.<br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask {{PlanckPapers|planck2014-a12}}.<br />
<br />
<br />
'''File name and usage'''<br />
The low ell TEB likelihood is distributed in <br />
''plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive), followed by the <i>EE</i> (&#8467;=0 to 29), <br />
<i>BB</i> (&#8467;=0 to 29) and <i>TE</i> (&#8467;=0 to 29) spectra, and by an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the entries really start at &#8467;=0, although the<br />
&#8467;=0 and &#8467;=1 values will be null.<br />
<br />
''' High-&#8467; likelihoods '''<br />
<br />
'''TT only - Plik'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=30-2508.<br />
Using the optional tool in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>TT</i> cross-spectra. <br />
Only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission <i>T</i> maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by a vector of 16 nuisance parameters.<br />
Those are, in order:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217;<br />
* calib_100T, the relative calibration between the 100 and 143 spectra;<br />
* calib_217T, the relative calibration between the 217 and 143 spectra;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT+TE+EE - Plik'''<br />
This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range &#8467;=30-2508 for TT and &#8467;=30-1996 for TE and EE.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>T</i> and <i>E</i> cross-spectra. <br />
In temperature, only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used, while<br />
in <i>TE</i> and <i>EE</i> all of them are used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission T+P maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz and 353-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates;<br />
* best-fit CMB+foreground model for the beam-leakage template.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, plik TTTEEE likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik''.<br />
<br />
This file should not be used with any other TT-only high-&#8467; file.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed the <i>EE</i> and <i>TE</i> spectra (same range) and by a vector of 94 nuisance parameters.<br />
Those are, in g:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100TT;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143TT;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217TT;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217TT;<br />
* galf_EE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100EE;<br />
* galf_EE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143EE;<br />
* galf_EE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217EE;<br />
* galf_EE_A_143, the dust residual contamination at &#8467;=500 in 143&times;143EE;<br />
* galf_EE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217EE;<br />
* galf_EE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217EE;<br />
* galf_EE_index, the dust EE template slope, which should be set to -2.4;<br />
* galf_TE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100TE;<br />
* galf_TE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143TE;<br />
* galf_TE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217TE;<br />
* galf_TE_A_143, the dust residual contamination at &#8467;=500 in 143x143TE;<br />
* galf_TE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217TE;<br />
* galf_TE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217TE;<br />
* galf_TE_index, the dust EE template slope, which should be set to -2.4;<br />
* bleak_epsilon_0_0T_0E, beam-leakage parameter, espilon_0, 100&times;100 TE;<br />
* bleak_epsilon_1_0T_0E, beam-leakage parameter, espilon_1, 100&times;100 TE;<br />
* bleak_epsilon_2_0T_0E, beam-leakage parameter, espilon_2, 100&times;100 TE;<br />
* bleak_epsilon_3_0T_0E, beam-leakage parameter, espilon_3, 100&times;100 TE;<br />
* bleak_epsilon_4_0T_0E, beam-leakage parameter, espilon_4, 100&times;100 TE;<br />
* bleak_epsilon_0_0T_1E, beam-leakage parameter, espilon_0, 100&times;143 TE;<br />
* bleak_epsilon_1_0T_1E, beam-leakage parameter, espilon_1, 100&times;143 TE;<br />
* bleak_epsilon_2_0T_1E, beam-leakage parameter, espilon_2, 100&times;143 TE;<br />
* bleak_epsilon_3_0T_1E, beam-leakage parameter, espilon_3, 100&times;143 TE;<br />
* bleak_epsilon_4_0T_1E, beam-leakage parameter, espilon_4, 100&times;143 TE;<br />
* bleak_epsilon_0_0T_2E, beam-leakage parameter, espilon_0, 100&times;217 TE;<br />
* bleak_epsilon_1_0T_2E, beam-leakage parameter, espilon_1, 100&times;217 TE;<br />
* bleak_epsilon_2_0T_2E, beam-leakage parameter, espilon_2, 100&times;217 TE;<br />
* bleak_epsilon_3_0T_2E, beam-leakage parameter, espilon_3, 100&times;217 TE;<br />
* bleak_epsilon_4_0T_2E, beam-leakage parameter, espilon_4, 100&times;217 TE;<br />
* bleak_epsilon_0_1T_1E, beam-leakage parameter, espilon_0, 143&times;143 TE;<br />
* bleak_epsilon_1_1T_1E, beam-leakage parameter, espilon_1, 143&times;143 TE;<br />
* bleak_epsilon_2_1T_1E, beam-leakage parameter, espilon_2, 143&times;143 TE;<br />
* bleak_epsilon_3_1T_1E, beam-leakage parameter, espilon_3, 143&times;143 TE;<br />
* bleak_epsilon_4_1T_1E, beam-leakage parameter, espilon_4, 143&times;143 TE;<br />
* bleak_epsilon_0_1T_2E, beam-leakage parameter, espilon_0, 143&times;217 TE;<br />
* bleak_epsilon_1_1T_2E, beam-leakage parameter, espilon_1, 143&times;217 TE;<br />
* bleak_epsilon_2_1T_2E, beam-leakage parameter, espilon_2, 143&times;217 TE;<br />
* bleak_epsilon_3_1T_2E, beam-leakage parameter, espilon_3, 143&times;217 TE;<br />
* bleak_epsilon_4_1T_2E, beam-leakage parameter, espilon_4, 143&times;217 TE;<br />
* bleak_epsilon_0_2T_2E, beam-leakage parameter, espilon_0, 217&times;217 TE;<br />
* bleak_epsilon_1_2T_2E, beam-leakage parameter, espilon_1, 217&times;217 TE;<br />
* bleak_epsilon_2_2T_2E, beam-leakage parameter, espilon_2, 217&times;217 TE;<br />
* bleak_epsilon_3_2T_2E, beam-leakage parameter, espilon_3, 217&times;217 TE;<br />
* bleak_epsilon_4_2T_2E, beam-leakage parameter, espilon_4, 217&times;217 TE;<br />
* bleak_epsilon_0_0E_0E, beam-leakage parameter, espilon_0, 100&times;100 EE;<br />
* bleak_epsilon_1_0E_0E, beam-leakage parameter, espilon_1, 100&times;100 EE;<br />
* bleak_epsilon_2_0E_0E, beam-leakage parameter, espilon_2, 100&times;100 EE;<br />
* bleak_epsilon_3_0E_0E, beam-leakage parameter, espilon_3, 100&times;100 EE;<br />
* bleak_epsilon_4_0E_0E, beam-leakage parameter, espilon_4, 100&times;100 EE;<br />
* bleak_epsilon_0_0E_1E, beam-leakage parameter, espilon_0, 100&times;143 EE;<br />
* bleak_epsilon_1_0E_1E, beam-leakage parameter, espilon_1, 100&times;143 EE;<br />
* bleak_epsilon_2_0E_1E, beam-leakage parameter, espilon_2, 100&times;143 EE;<br />
* bleak_epsilon_3_0E_1E, beam-leakage parameter, espilon_3, 100&times;143 EE;<br />
* bleak_epsilon_4_0E_1E, beam-leakage parameter, espilon_4, 100&times;143 EE;<br />
* bleak_epsilon_0_0E_2E, beam-leakage parameter, espilon_0, 100&times;217 EE;<br />
* bleak_epsilon_1_0E_2E, beam-leakage parameter, espilon_1, 100&times;217 EE;<br />
* bleak_epsilon_2_0E_2E, beam-leakage parameter, espilon_2, 100&times;217 EE;<br />
* bleak_epsilon_3_0E_2E, beam-leakage parameter, espilon_3, 100&times;217 EE;<br />
* bleak_epsilon_4_0E_2E, beam-leakage parameter, espilon_4, 100&times;217 EE;<br />
* bleak_epsilon_0_1E_1E, beam-leakage parameter, espilon_0, 143&times;143 EE;<br />
* bleak_epsilon_1_1E_1E, beam-leakage parameter, espilon_1, 143&times;143 EE;<br />
* bleak_epsilon_2_1E_1E, beam-leakage parameter, espilon_2, 143&times;143 EE;<br />
* bleak_epsilon_3_1E_1E, beam-leakage parameter, espilon_3, 143&times;143 EE;<br />
* bleak_epsilon_4_1E_1E, beam-leakage parameter, espilon_4, 143&times;143 EE;<br />
* bleak_epsilon_0_1E_2E, beam-leakage parameter, espilon_0, 143&times;217 EE;<br />
* bleak_epsilon_1_1E_2E, beam-leakage parameter, espilon_1, 143&times;217 EE;<br />
* bleak_epsilon_2_1E_2E, beam-leakage parameter, espilon_2, 143&times;217 EE;<br />
* bleak_epsilon_3_1E_2E, beam-leakage parameter, espilon_3, 143&times;217 EE;<br />
* bleak_epsilon_4_1E_2E, beam-leakage parameter, espilon_4, 143&times;217 EE;<br />
* bleak_epsilon_0_2E_2E, beam-leakage parameter, espilon_0, 217&times;217 EE;<br />
* bleak_epsilon_1_2E_2E, beam-leakage parameter, espilon_1, 217&times;217 EE;<br />
* bleak_epsilon_2_2E_2E, beam-leakage parameter, espilon_2, 217&times;217 EE;<br />
* bleak_epsilon_3_2E_2E, beam-leakage parameter, espilon_3, 217&times;217 EE;<br />
* bleak_epsilon_4_2E_2E, beam-leakage parameter, espilon_4, 217&times;217 EE;<br />
* calib_100T, the relative calibration between 100 and 143 TT spectra;<br />
* calib_217T, the relative calibration between 217 and 143 TT spectra;<br />
* calib_100P, the calibration of the 100 EE spectra, which should be set to 1;<br />
* calib_143P, the calibration of the 143 EE spectra, which should be set to 1;<br />
* calib_217P, the calibration of the 217 EE spectra, which should be set to 1;<br />
* A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* galf_EE_A_100 = 0.060&plusmn;0.012;<br />
* galf_EE_A_100_143 = 0.050&plusmn;0.015;<br />
* galf_EE_A_100_217 = 0.110&plusmn;0.033;<br />
* galf_EE_A_143 = 0.10&plusmn;0.02;<br />
* galf_EE_A_143_217 = 0.240&plusmn;0.048;<br />
* galf_EE_A_217 = 0.72&plusmn;0.14;<br />
* galf_EE_index = -2.4;<br />
* galf_TE_A_100 = 0.140&plusmn;0.042;<br />
* galf_TE_A_100_143 = 0.120&plusmn;0.036;<br />
* galf_TE_A_100_217 = 0.30&plusmn;0.09;<br />
* galf_TE_A_143 = 0.240&plusmn;0.072;<br />
* galf_TE_A_143_217 = 0.60&plusmn;0.018;<br />
* galf_TE_A_217 = 1.80&plusmn;0.54;<br />
* galf_TE_index = -2.4;<br />
* bleak_epsilon_0_0T_0E = 0;<br />
* bleak_epsilon_1_0T_0E = 0;<br />
* bleak_epsilon_2_0T_0E = 0;<br />
* bleak_epsilon_3_0T_0E = 0;<br />
* bleak_epsilon_4_0T_0E = 0;<br />
* bleak_epsilon_0_0T_1E = 0;<br />
* bleak_epsilon_1_0T_1E = 0;<br />
* bleak_epsilon_2_0T_1E = 0;<br />
* bleak_epsilon_3_0T_1E = 0;<br />
* bleak_epsilon_4_0T_1E = 0;<br />
* bleak_epsilon_0_0T_2E = 0;<br />
* bleak_epsilon_1_0T_2E = 0;<br />
* bleak_epsilon_2_0T_2E = 0;<br />
* bleak_epsilon_3_0T_2E = 0;<br />
* bleak_epsilon_4_0T_2E = 0;<br />
* bleak_epsilon_0_1T_1E = 0;<br />
* bleak_epsilon_1_1T_1E = 0;<br />
* bleak_epsilon_2_1T_1E = 0;<br />
* bleak_epsilon_3_1T_1E = 0;<br />
* bleak_epsilon_4_1T_1E = 0;<br />
* bleak_epsilon_0_1T_2E = 0;<br />
* bleak_epsilon_1_1T_2E = 0;<br />
* bleak_epsilon_2_1T_2E = 0;<br />
* bleak_epsilon_3_1T_2E = 0;<br />
* bleak_epsilon_4_1T_2E = 0;<br />
* bleak_epsilon_0_2T_2E = 0;<br />
* bleak_epsilon_1_2T_2E = 0;<br />
* bleak_epsilon_2_2T_2E = 0;<br />
* bleak_epsilon_3_2T_2E = 0;<br />
* bleak_epsilon_4_2T_2E = 0;<br />
* bleak_epsilon_0_0E_0E = 0;<br />
* bleak_epsilon_1_0E_0E = 0;<br />
* bleak_epsilon_2_0E_0E = 0;<br />
* bleak_epsilon_3_0E_0E = 0;<br />
* bleak_epsilon_4_0E_0E = 0;<br />
* bleak_epsilon_0_0E_1E = 0;<br />
* bleak_epsilon_1_0E_1E = 0;<br />
* bleak_epsilon_2_0E_1E = 0;<br />
* bleak_epsilon_3_0E_1E = 0;<br />
* bleak_epsilon_4_0E_1E = 0;<br />
* bleak_epsilon_0_0E_2E = 0;<br />
* bleak_epsilon_1_0E_2E = 0;<br />
* bleak_epsilon_2_0E_2E = 0;<br />
* bleak_epsilon_3_0E_2E = 0;<br />
* bleak_epsilon_4_0E_2E = 0;<br />
* bleak_epsilon_0_1E_1E = 0;<br />
* bleak_epsilon_1_1E_1E = 0;<br />
* bleak_epsilon_2_1E_1E = 0;<br />
* bleak_epsilon_3_1E_1E = 0;<br />
* bleak_epsilon_4_1E_1E = 0;<br />
* bleak_epsilon_0_1E_2E = 0;<br />
* bleak_epsilon_1_1E_2E = 0;<br />
* bleak_epsilon_2_1E_2E = 0;<br />
* bleak_epsilon_3_1E_2E = 0;<br />
* bleak_epsilon_4_1E_2E = 0;<br />
* bleak_epsilon_0_2E_2E = 0;<br />
* bleak_epsilon_1_2E_2E = 0;<br />
* bleak_epsilon_2_2E_2E = 0;<br />
* bleak_epsilon_3_2E_2E = 0;<br />
* bleak_epsilon_4_2E_2E = 0;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* calib_100P = 1;<br />
* calib_143P = 1; <br />
* calib_217P = 1; <br />
* A_pol = 1;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT only - Plik lite'''<br />
This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range &#8467;=30-2508. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT</i> spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-&#8467; likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TT likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.<br />
<br />
'''TT EE TE - Plik lite'''<br />
This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range &#8467;=30-2508 for temperature and &#8467;=30-1996 for TE and EE. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT<i/>, <i>TE</i>, and <i>EE</i> spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TTTEEE likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TTTEEE, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the <i>EE</i>, and <i>TE</i> spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
''' Lensing likelihoods '''<br />
<br />
'''T only'''<br />
This file allows for the computation of the baseline lensing likelihood, using only the SMICA <i>T</i><br />
map-based lensing reconstruction. Only the lensing multipole range &#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of a model-dependent correction to the normalization and<br />
the "N1 bias." To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant "mean field" and "N0" contribution, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> CMB map;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i> spectrum is needed to compute the normalization and N1 corrections.<br />
<br />
'''T+P'''<br />
This file allows for the computation of the baseline lensing likelihood, using both the <br />
<i>T</i> and <i>P</i> SMICA map-based lensing reconstruction. Only the lensing multipole range&#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of model dependent correction to the normalization and<br />
the N1 bias. To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> and <i>P</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured outside a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> and <i>E</i> CMB maps;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T+P-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive), the <i>EE</i> and <i>TE</i> power spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i>, <i>EE</i>, and <i>TE</i> spectra are needed to compute the normalization and N1 corrections.<br />
<br />
'''Data sets - Extended data'''<br />
<br />
Four other data files are available.<br />
Those extend the baseline delivery by adding:<br />
* TE, EE and other joint high-&#8467 Plik likelihoods, ''COM_Likelihood_Data-extra-plik-HM-ext_R2.00.tar.gz'';<br />
* TT and TTTEEE unbinned high-&#8467 Plik likelihood, ''COM_Likelihood_Data-extra-plik-unbinned_R2.00.tar.gz'';<br />
* TT, TE, EE, and TTTEEE Plik likelihood using the detset cross-spectra instead of the half-mission one, and including empirical correlated noise correction for the TT spectra, ''COM_Likelihood_Data-extra-plik-DS_R2.00.tar.gz'';<br />
* extended &#8467 range lensing likelihood, ''COM_Likelihood_Data-extra-lensing-ext_R2.00.tar.gz''.<br />
<br />
Note that although these products are discussed in the Planck papers, they are not used for the baseline results.<br />
<br />
Each file contains a '''readme.md''' description of the content and the use of the different likelihood files.<br />
<br />
<br />
<br />
<!-- <br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the {{PlanckPapers|planck2013-p08|1|Power spectrum & Likelihood Paper}} (for the CMB based likelihood) and in the {{PlanckPapers|planck2013-p12|1|Lensing Paper}} (for the lensing likelihood) .<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The Commander likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 &plusmn; 0.2 and a_gs = 0.4 &plusmn; 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first-order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first-order renormalization procedure. This means that the code will need both the TT and &phi;&phi; power spectrum up to &#8467; = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between &#8467; = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
</span><br />
<span style="color:red">OUTSTANDING: description of likelihood masks </span><br />
'''Production process'''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each data set comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<sup>-6</sup> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander''<nowiki>:</nowiki><br />
* all Planck channel maps;<br />
* compact source catalogues;<br />
* common masks;<br />
* beam transfer functions for all channels.<br />
<br />
; ''lowlike''<nowiki>:</nowiki><br />
* WMAP9 likelihood data;<br />
* Low-<math>\ell</math> Commander map.<br />
<br />
; ''CAMspec''<nowiki>:</nowiki><br />
* 100-, 143- and 217-GHz detector and detsets maps;<br />
* 857GHz channel map;<br />
* compact source catalogue;<br />
* common masks (0,1 and 3);<br />
* beam transfer function and error eigenmodes and covariance for 100-, 143- and 217-GHz detectors and detsets;<br />
* theoretical templates for the tSZ and kSZ contributions;<br />
* color corrections for the CIB emission for the 143- and 217-GHz detectors and detsets;<br />
* fiducial CMB model (bootstrapped from WMAP7 best-fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz.<br />
<br />
; ''lensing''<nowiki>:</nowiki><br />
* the lensing map;<br />
* beam error eigenmodes and covariance for the 143- and 217-GHz channel maps;<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt''<nowiki>:</nowiki><br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here];<br />
* the tSZ and kSZ template are changed to match those of CAMspec.<br />
<br />
''' File names and Meta-data '''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta-data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
--><br />
<br />
'''Likelihood Masks'''<br />
<br />
'''General description'''<br />
<br />
We provide the masks for Temperature and Polarisation used to exclude the regions of strongest foreground emission in the CMB maps when computing the empirical spectra that we use to form the high-&#8467 likelihood. The masks are provided for each frequency between 100 and 217 GHz, masking the appropriate part of the Galactic Plane and, for temperature only, the relevant population of point sources. Note that to compute the empirical power spectrum of the maps, one should also take into account missing pixels in a particular map. This is not included in the masks we distribute.<br />
<br />
'''Production Process'''<br />
Complete production process for those masks is described in {{PlanckPapers|planck2014-a13}}.<br />
<br />
The temperature masks are the combination of a Galactic mask, a point source mask and (for 100Ghz and 217GHz) a CO mask. Extended objects, planets, etc are included in the point source mask. <br />
The polarization masks are simply the Galactic masks.<br />
<br />
The Galactic masks are obtained by thresholding a CMB corrected and <math>10^o</math> smoothed 353GHz map. The threshold is tuned so as to retain a given fraction of the sky, between 50% and 80%. Each mask is apodized by a <math>4^o.71</math> FWHM gaussian window function using the distance map. Special care is taken to smooth this distance map, in order to avoid strong caustics. The apodization down-weights an effective 10% of the sky. Following {{PlanckPapers|planck2014-a13}}, the Galactic masks are named by the effective unmasked sky area G70, G60, G50 and G41.<br />
<br />
The point source masks are different for each frequency. They are based on the 2015 Planck catalog and cut out all the sources detected at S/N = 5 or higher in each channel. Each source is masked with a circular aperture of size 3xFWHM of that channel (i.e. 3x9.′66 at 100GHz, 3x7.′22 at 143GHz, and 3x4.′90 at 217GHz). Note that we include in the point source masks all sources above our threshold, including possible galactic ones. The mask is further apodized with a gaussian window function with FWHM=30'. <br />
<br />
The CO masks is used only at 100GHz and 217GHz, since there is no (strong) CO line in the 147 GHz channel. They are based on the Type 3 CO map from the Planck2013 delivery. The CO map is smoothed to 120' and a threshold is applied to mask all regions above <math>1 K_{RJ} km s^{−1}</math>. The mask is further apodized to 30'.<br />
<br />
Mask combinations are performed by multiplying a galactic, a point source, and possibly a CO mask together.<br />
<br />
The Temperature masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter T and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: T66 = G70+Point source mask 100Ghz+CO mask<br />
* 143Ghz: T57 = G60+Point source mask 143Ghz<br />
* 217Ghz: T47 = G50+Point source mask 217Ghz+CO mask<br />
<br />
The Polarization masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter P and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: P70 = G70<br />
* 143Ghz: P50 = G50<br />
* 217Ghz: P41 = G41<br />
<br />
'''Inputs'''<br />
* Galactic masks: The SMICA CMB temperature map, the 353GHz temperature map.<br />
* Point source masks: The Planck 2015 catalog, the FWHM of each of the frequencies.<br />
* CO mask: the Type 3 CO map from the Planck 2013 delivery.<br />
<br />
''' File names and meta-data '''<br />
The masks are distributed in a single tar file ''COM_Likelihood_Masks_R2.00.tar.gz''.<br />
The files extract to 6 files<br />
* temperature_100.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 100Ghz, i.e. T66<br />
* temperature_143.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 143Ghz, i.e. T57<br />
* temperature_217.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 217Ghz, i.e. T47<br />
* polarization_100.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 100Ghz, i.e. P70<br />
* polarization_143.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 143Ghz, i.e. P50<br />
* polarization_217.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 217Ghz, i.e. P41<br />
<br />
<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #EEE8AA;width:80%"><br />
'''2013 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''General description'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles <math> \ell </math> = 2-2479. Over the multipole range <math> \ell </math> = 2–49, the power spectrum is derived from a component-separation algorithm, ''Commander'', applied to maps in the frequency range 30–353 GHz over 91% of the sky {{PlanckPapers|planck2013-p06}}. The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction. For multipoles greater than <math>\ell=50</math>, instead, the spectrum is derived from the ''CAMspec'' likelihood {{PlanckPapers|planck2013-p08}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds. Associated 1-sigma errors include beam and foreground uncertainties. Both ''Commander'' and ''CAMspec'' are described in more details in the sections below.<br />
<br />
[[File: mission_spectrum.png|thumb|center|700px|'''CMB spectrum. Logarithmic x-scale up to <math>\ell=50</math>, linear at higher <math>\ell</math>; all points with error bars. The red line is the Planck best-fit primordial power spectrum (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}).''']]<br />
<br />
'''Likelihood'''<br />
<br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the Power spectrum & Likelihood Paper {{PlanckPapers|planck2013-p08}} (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) {{PlanckPapers|planck2013-p12}}.<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The ''Commander'' likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 ± 0.2 and a_gs = 0.4 ± 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. This means that the code will need both the TT and $\phi\phi$ power spectrum up to <math>\ell</math> = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between <math>\ell</math> = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
<br />
'''Production process'''<br />
<br />
'''CMB spectra'''<br />
<br />
The <math>\ell</math> < 50 part of the Planck power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters {{PlanckPapers|planck2013-p06}}. The power spectrum at any multipole <math>\ell</math> is given as the maximum probability point for the posterior <math>C_\ell</math> distribution, marginalized over the other multipoles, and the error bars are 68% confidence level {{PlanckPapers|planck2013-p08}}. <br />
<br />
The <math>\ell</math> > 50 part of the CMB temperature power spectrum has been derived by the CamSpec likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of {{PlanckPapers|planck2013-p08}}. Frequency spectra are computed as noise weighted averages of the cross-spectra between single detector and sets of detector maps. Mask and multipole range choices for each frequency spectrum are summarized in Table 4 of {{PlanckPapers|planck2013-p08}}. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of {{PlanckPapers|planck2013-p08}} and Sec. 4 of {{PlanckPapers|planck2013-p11}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with unresolved foreground and beam uncertainties. Both spectrum and associated covariance matrix are given as uniformly weighted band averages in 74 bins. <br />
<br />
'''Likelihood'''<br />
<br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each dataset comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<math>^{-6}</math> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
; Low-l spectrum (<math>\ell < 50</math>):<br />
* frequency maps from 30–353 GHz<br />
* common mask {{PlanckPapers|planck2013-p06}}<br />
* compact sources catalog<br />
<br />
; High-l spectrum (<math>50 < \ell < 2500</math>): <br />
<br />
* 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 2 in {{PlanckPapers|planck2013-p08}})<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of {{PlanckPapers|planck2013-p11}})<br />
* Beam transfer function uncertainties {{PlanckPapers|planck2013-p03c}}<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander'' :<br />
* all Planck channels maps<br />
* compact source catalogs<br />
* common masks<br />
* beam transfer functions for all channels<br />
<br />
; ''lowlike'' :<br />
* WMAP9 likelihood data<br />
* Low-<math>\ell</math> Commander map<br />
<br />
; ''CAMspec'' :<br />
* 100, 143 and 217 GHz detector and detsets maps<br />
* 857GHz channel map<br />
* compact source catalog<br />
* common masks (0,1 & 3)<br />
* beam transfer function and error eigenmodes and covariance for 100, 143 and 217 GHz detectors & detsets<br />
* theoretical templates for the tSZ and kSZ contributions<br />
* color corrections for the CIB emission for the 143 and 217GHz detectors and detsets<br />
* fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz<br />
<br />
; ''lensing'' :<br />
* the lensing map<br />
* beam error eigenmodes and covariance for the 143 and 217GHz channel maps<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt'' :<br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]<br />
* the tSZ andkSZ template are changed to match those of CAMspec<br />
<br />
''' File names and Meta data '''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The CMB spectrum and its covariance matrix are distributed in a single FITS file named <br />
* ''{{PLASingleFile | fileType=cosmo | name=COM_PowerSpect_CMB_R1.10.fits | link=COM_PowerSpect_CMB_R1.10.fits}}'' <br />
<br />
which contains 3 extensions<br />
<br />
; LOW-ELL (BINTABLE)<br />
: with the low ell part of the spectrum, not binned, and for l=2-49. The table columns are<br />
# ''ELL'' (integer): multipole number<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERRUP'' (float): the upward uncertainty<br />
# ''ERRDOWN'' (float): the downward uncertainty<br />
<br />
; HIGH-ELL (BINTABLE)<br />
: with the high-ell part of the spectrum, binned into 74 bins covering <math>\langle l \rangle = 47-2419\ </math> in bins of width <math>l=31</math> (with the exception of the last 4 bins that are wider). The table columns are as follows:<br />
# ''ELL'' (integer): mean multipole number of bin<br />
# ''L_MIN'' (integer): lowest multipole of bin<br />
# ''L_MAX'' (integer): highest multipole of bin<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERR'' (float): the uncertainty<br />
<br />
; COV-MAT (IMAGE)<br />
: with the covariance matrix of the high-ell part of the spectrum in a 74x74 pixel image, i.e., covering the same bins as the ''HIGH-ELL'' table.<br />
<br />
The spectra give $D_\ell = \ell(\ell+1)C_\ell / 2\pi$ in units of $\mu\, K^2$, and the covariance matrix is in units of $\mu\, K^4$. The spectra are shown in the figure below, in blue and red for the low- and high-<math>\ell</math> parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.<br />
<br />
[[File: CMBspect.jpg|thumb|center|700px|'''CMB spectrum. Linear x-scale; error bars only at high <math>\ell</math>.''']]<br />
<br />
'''Likelihood'''<br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
<br />
</div><br />
</div><br />
<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
[[Category:Mission products|008]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=14380CMB spectrum & Likelihood Code2018-07-16T13:38:35Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:CMB spectra and likelihood code}}<br />
<br />
== 2018 CMB spectra==<br />
<br />
<br />
===General description===<br />
====TT====<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 86% of the sky ({{PlanckPapers|planck2016-l06}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood {{PlanckPapers|planck2016-l05}}, with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.51.48.png|thumb|600px|center]]<br />
<br />
====TE, EE, and EB, BB ====<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. In the multipole range 2 ≤ l ≤ 29, we plot the power spectra estimates from the SimAll likelihood (though only the EE spectrum is used in the baseline parameter analysis at l ≤ 29), see {{PlanckPapers|planck2016-l06}}). .<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.52.35.png|thumb|600px|center]]<br />
[[File:Screen Shot 2018-07-16 at 05.52.24.png|thumb|600px|center]]<br />
<br />
<br />
In the range &#8467; = 2-29, we also release the <i>BB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2016-l03}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
==== Theory ====<br />
<br />
We also provide best-fit LCDM CMB power spectra from the baseline Planck TT,TE,EE+lowE+lensing. The spectra must be divided by the best-fit Planck map-based calibration parameter squared, calPlanck**2, to be compared to the coadded CMB spectra. The best-fit calPlanck value can be found in the file "COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt".<br />
<br />
===Production process===<br />
The Plik high-multipole likelihood (described in detail in {{PlanckPapers|planck2016-l05}}) is a Gaussian approximation of the probability distributions of the <i>TT</i>, <i>EE</i>, and <i>TE</i> angular power spectra, with semi-analytic covariance matrices calculated assuming a fiducial cosmology. It includes multipoles in the range 30 to 2508 for TT and 30 to 1996 for <i>TE</i> and <i>EE</i> and is constructed from half-mission cross-spectra measured from the 100-, 143-, and 217-GHz HFI frequency maps. For more details see {{PlanckPapers|planck2016-l06}}.<br />
<br />
<br />
<br />
===Inputs===<br />
<br />
The T T likelihood uses four half-mission cross-spectra with different multipole cuts to avoid multipole regions where noise dominates due to the limited resolution of the beams and to en-sure foreground contamination is correctly handled by our fore-ground model: 100 × 100 ( &#8467; = 30–1197); 143 × 143 (&#8467; = 30– 1996); 143 × 217 (&#8467; = 30–2508); and 217 × 217 (&#8467; = 30–2508). The TE and EE likelihoods also include the 100 × 143 and 100 × 217 cross-spectra to improve the signal-to-noise ratio, and have different multipole cuts: 100 × 100 (&#8467; = 30–999); 100 × 143 (&#8467; = 30–999); 100 × 217 (&#8467; = 505–999); 143 × 143 (&#8467; = 30– 1996); 143 × 217 (&#8467; = 505–1996); and 217 × 217 (&#8467; = 505– 1996). <br />
<br />
=== File names and meta-data ===<br />
<br />
The CMB spectra and their uncertainties are distributed in ASCII text files named ''COM_PowerSpect_CMB_nn_R3.01.fits'', where nn stands for the type of spectrum the file contains:<br />
* COM_PowerSpect_CMB-EE-full_R3.01.txt<br />
* COM_PowerSpect_CMB-TE-full_R3.01.txt<br />
* COM_PowerSpect_CMB-TT-full_R3.01.txt<br />
* COM_PowerSpect_CMB-low-ell-BB-full_R3.01.txt<br />
* COM_PowerSpect_CMB-low-ell-EB-full_R3.01.txt<br />
<br />
In addition we provide one file containing all the parameters of the Plik runs which yielded the spectra. This file is named<br />
* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt<br />
<br />
The theoretical spectrum of the best-fit model itself is provided in a separate file named<br />
* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt<br />
<br />
The data file columns give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>, and the lower and upper 68% uncertainties.<br />
<br />
<br />
== 2018 Likelihood==<br />
<br />
The 2018 Likelihood code will be released at a later time.<br />
<br />
== Previous Releases: (2015) and (2013) CMB spectrum and Likelihood ==<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%"><br />
'''2015 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''2015 CMB spectra'''<br />
<br />
'''General description'''<br />
<br />
'''TT'''<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2014-a12}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP &Lambda;CDM run. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]<br />
<br />
'''TE, EE, and TB, EB, BB '''<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
'''Production process'''<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
'''Inputs'''<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
''' File names and meta-data '''<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
'''Likelihood'''<br />
<br />
The 2015 baseline likelihood release consists of a code package and a single data package. Four extended data packages are also available enabling exploration of alternatives to the baseline results.<br />
The code compiles to a library allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets. A data set permits the computation of a single likelihood among:<br />
* the high-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the low-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the CMB lensing reconstruction.<br />
By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.<br />
<br />
Only the baseline data package, ''COM_Likelihood_Data-baseline_R2.00.tar.gz'', will be fully described on this page. It contains six data sets, which are enough to compute all of the baseline Planck results that are discussed in {{PlanckPapers|planck2014-a14}}. In particular it allows for the computation of the CMB and lensing likelihood from either the Temperature data only, or the Temperature + Polarization combination.<br />
<br />
The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in {{PlanckPapers|planck2014-a13}} and {{PlanckPapers|planck2014-a17}}. Their full description is contained in the documentation included in each of the extended data packages.<br />
<br />
'''Library and tools'''<br />
<br />
'''Description'''<br />
The library consists of code written in C and Fortran 90. It can be called from both of<br />
those languages. Optionally, a python wrapper can be built as well. Scripts to<br />
simplify the linking of the library with other codes are part of the package, as<br />
well as some example codes that can be used to test the correct installation of<br />
the code and the integrity of the data packages. Optionally, a script is also available, allowing<br />
the user to modify the multipole range of the TT likelihoods and reproduce the hybridization<br />
test performed in the paper.<br />
A description of the tool, the API of the library, as well as different <br />
installation procedure are detailed in the ''readme.md'' file in the code package.<br />
<br />
'''File name'''<br />
The code can be extracted from <br />
''COM_Likelihood_Code-v2.0_R2.00.tar.bz2''.<br />
<br />
Please read the file ''readme.md'' for installation instructions.<br />
<br />
'''Data sets - Baseline data'''<br />
All of the released baseline data are distributed within a single file,<br />
''COM_Likelihood_Data-baseline_R2.00.tar.gz''.<br />
<br />
This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.<br />
<br />
Each data set is stored in its own directory. The directory structure follows similar rules<br />
for each data set, and stores data, template, and meta-data for each particular likelihood.<br />
<br />
As in 2013, the CMB likelihood is cut into low-&#8467; and high-&#8467; parts. Moreover, <br />
for each of those, we distribute both a T-only datafile and a joint T+P one. In the case <br />
of the high-&#8467; part, we also distribute two specific versions of the likelihood, <br />
that allow for estimate of T and T+P marginalized over the nuisance parameters.<br />
Combining both the low-&#8467; and high-&#8467; files, one can compute the likelihood over the<br />
range &#8467;=2-2508 in TT and &#8467;=2-1996 in TE and EE. A full description of the low-&#8467; <br />
and high-&#8467; likelihood is available in {{PlanckPapers|planck2014-a13}}.<br />
<br />
Similarly, for the case of lensing, we also distribute the likelihood using both<br />
the reconstruction based on the <i>T</i> map only, or on <i>T</i>+<i>P</i> maps. <br />
A full description of the lensing likelihood is available in {{PlanckPapers|planck2014-a17}}.<br />
<br />
All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that his parameter is explored in the Gaussian prior 1.0000&plusmn;0.0025.<br />
<br />
''' Low-&#8467; likelihoods '''<br />
<br />
'''TT only - commander'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=2-29.<br />
Using the optional tool in the code package, it can be modified to cover any multipole range <br />
up to &#8467;&lt;200. <br />
<br />
''' Production process'''<br />
The likelihood is based on the results of the Commander approach, which implements a <br />
Bayesian component separation method in pixel space, sampling the posterior distribution <br />
of the parameters of a model that describes both the CMB and the foreground emissions<br />
in a combination of the Planck maps, the WMAP map, and the 408-MHz survey. The samples<br />
of this exploration are used to infer the foreground marginalized low-&#8467; likelihood <br />
for any <i>TT</i> CMB spectrum. <br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
'''File name and usage'''<br />
The commander likelihood is distributed in <br />
''plc_2.0/low_l/commander/commander_rc2_v1.1_l2_29_B.clik''<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the vector really starts at &#8467;=0, although<br />
the first two entries are null.<br />
<br />
'''TEB '''<br />
This file allows for the computation of the CMB joint TT,EE, BB and TE likelihood <br />
in the range &#8467;=2-29. It should not be used with the low-&#8467; TT-only likelihood.<br />
<br />
''' Production process'''<br />
The file allows for the computation of the pixel based likelihood of <i>T</i>, <i>E</i>, and <i>B</i> <br />
maps. The <i>T</i> map is the best-fit map obtained from the commander algorithm, as described above, <br />
while the <i>E</i> and <i>B</i> maps are obtained from the 70GHz LFI full mission data, but excluding the second and fourth surveys. Foreground contamination is<br />
dealt with by marginalizing over templates based on the 30-GHz LFI and 353-GHz HFI maps.<br />
The covariance matrix comes from the Planck detector sensitivity modulated on the <br />
sky by the scanning strategy. The covariance matrix is further enlarged to account <br />
for the foreground template removal. <br />
To speed up the computation by about an order of magnitude, the problem is <br />
projected into <i>C</i><sub>&#8467;</sub> space using the Sherman-Morrison-Woodbury identity. Only the <br />
projected quantities are stored in the data package.<br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask {{PlanckPapers|planck2014-a12}}.<br />
<br />
<br />
'''File name and usage'''<br />
The low ell TEB likelihood is distributed in <br />
''plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive), followed by the <i>EE</i> (&#8467;=0 to 29), <br />
<i>BB</i> (&#8467;=0 to 29) and <i>TE</i> (&#8467;=0 to 29) spectra, and by an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the entries really start at &#8467;=0, although the<br />
&#8467;=0 and &#8467;=1 values will be null.<br />
<br />
''' High-&#8467; likelihoods '''<br />
<br />
'''TT only - Plik'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=30-2508.<br />
Using the optional tool in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>TT</i> cross-spectra. <br />
Only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission <i>T</i> maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by a vector of 16 nuisance parameters.<br />
Those are, in order:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217;<br />
* calib_100T, the relative calibration between the 100 and 143 spectra;<br />
* calib_217T, the relative calibration between the 217 and 143 spectra;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT+TE+EE - Plik'''<br />
This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range &#8467;=30-2508 for TT and &#8467;=30-1996 for TE and EE.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>T</i> and <i>E</i> cross-spectra. <br />
In temperature, only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used, while<br />
in <i>TE</i> and <i>EE</i> all of them are used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission T+P maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz and 353-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates;<br />
* best-fit CMB+foreground model for the beam-leakage template.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, plik TTTEEE likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik''.<br />
<br />
This file should not be used with any other TT-only high-&#8467; file.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed the <i>EE</i> and <i>TE</i> spectra (same range) and by a vector of 94 nuisance parameters.<br />
Those are, in g:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100TT;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143TT;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217TT;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217TT;<br />
* galf_EE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100EE;<br />
* galf_EE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143EE;<br />
* galf_EE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217EE;<br />
* galf_EE_A_143, the dust residual contamination at &#8467;=500 in 143&times;143EE;<br />
* galf_EE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217EE;<br />
* galf_EE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217EE;<br />
* galf_EE_index, the dust EE template slope, which should be set to -2.4;<br />
* galf_TE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100TE;<br />
* galf_TE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143TE;<br />
* galf_TE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217TE;<br />
* galf_TE_A_143, the dust residual contamination at &#8467;=500 in 143x143TE;<br />
* galf_TE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217TE;<br />
* galf_TE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217TE;<br />
* galf_TE_index, the dust EE template slope, which should be set to -2.4;<br />
* bleak_epsilon_0_0T_0E, beam-leakage parameter, espilon_0, 100&times;100 TE;<br />
* bleak_epsilon_1_0T_0E, beam-leakage parameter, espilon_1, 100&times;100 TE;<br />
* bleak_epsilon_2_0T_0E, beam-leakage parameter, espilon_2, 100&times;100 TE;<br />
* bleak_epsilon_3_0T_0E, beam-leakage parameter, espilon_3, 100&times;100 TE;<br />
* bleak_epsilon_4_0T_0E, beam-leakage parameter, espilon_4, 100&times;100 TE;<br />
* bleak_epsilon_0_0T_1E, beam-leakage parameter, espilon_0, 100&times;143 TE;<br />
* bleak_epsilon_1_0T_1E, beam-leakage parameter, espilon_1, 100&times;143 TE;<br />
* bleak_epsilon_2_0T_1E, beam-leakage parameter, espilon_2, 100&times;143 TE;<br />
* bleak_epsilon_3_0T_1E, beam-leakage parameter, espilon_3, 100&times;143 TE;<br />
* bleak_epsilon_4_0T_1E, beam-leakage parameter, espilon_4, 100&times;143 TE;<br />
* bleak_epsilon_0_0T_2E, beam-leakage parameter, espilon_0, 100&times;217 TE;<br />
* bleak_epsilon_1_0T_2E, beam-leakage parameter, espilon_1, 100&times;217 TE;<br />
* bleak_epsilon_2_0T_2E, beam-leakage parameter, espilon_2, 100&times;217 TE;<br />
* bleak_epsilon_3_0T_2E, beam-leakage parameter, espilon_3, 100&times;217 TE;<br />
* bleak_epsilon_4_0T_2E, beam-leakage parameter, espilon_4, 100&times;217 TE;<br />
* bleak_epsilon_0_1T_1E, beam-leakage parameter, espilon_0, 143&times;143 TE;<br />
* bleak_epsilon_1_1T_1E, beam-leakage parameter, espilon_1, 143&times;143 TE;<br />
* bleak_epsilon_2_1T_1E, beam-leakage parameter, espilon_2, 143&times;143 TE;<br />
* bleak_epsilon_3_1T_1E, beam-leakage parameter, espilon_3, 143&times;143 TE;<br />
* bleak_epsilon_4_1T_1E, beam-leakage parameter, espilon_4, 143&times;143 TE;<br />
* bleak_epsilon_0_1T_2E, beam-leakage parameter, espilon_0, 143&times;217 TE;<br />
* bleak_epsilon_1_1T_2E, beam-leakage parameter, espilon_1, 143&times;217 TE;<br />
* bleak_epsilon_2_1T_2E, beam-leakage parameter, espilon_2, 143&times;217 TE;<br />
* bleak_epsilon_3_1T_2E, beam-leakage parameter, espilon_3, 143&times;217 TE;<br />
* bleak_epsilon_4_1T_2E, beam-leakage parameter, espilon_4, 143&times;217 TE;<br />
* bleak_epsilon_0_2T_2E, beam-leakage parameter, espilon_0, 217&times;217 TE;<br />
* bleak_epsilon_1_2T_2E, beam-leakage parameter, espilon_1, 217&times;217 TE;<br />
* bleak_epsilon_2_2T_2E, beam-leakage parameter, espilon_2, 217&times;217 TE;<br />
* bleak_epsilon_3_2T_2E, beam-leakage parameter, espilon_3, 217&times;217 TE;<br />
* bleak_epsilon_4_2T_2E, beam-leakage parameter, espilon_4, 217&times;217 TE;<br />
* bleak_epsilon_0_0E_0E, beam-leakage parameter, espilon_0, 100&times;100 EE;<br />
* bleak_epsilon_1_0E_0E, beam-leakage parameter, espilon_1, 100&times;100 EE;<br />
* bleak_epsilon_2_0E_0E, beam-leakage parameter, espilon_2, 100&times;100 EE;<br />
* bleak_epsilon_3_0E_0E, beam-leakage parameter, espilon_3, 100&times;100 EE;<br />
* bleak_epsilon_4_0E_0E, beam-leakage parameter, espilon_4, 100&times;100 EE;<br />
* bleak_epsilon_0_0E_1E, beam-leakage parameter, espilon_0, 100&times;143 EE;<br />
* bleak_epsilon_1_0E_1E, beam-leakage parameter, espilon_1, 100&times;143 EE;<br />
* bleak_epsilon_2_0E_1E, beam-leakage parameter, espilon_2, 100&times;143 EE;<br />
* bleak_epsilon_3_0E_1E, beam-leakage parameter, espilon_3, 100&times;143 EE;<br />
* bleak_epsilon_4_0E_1E, beam-leakage parameter, espilon_4, 100&times;143 EE;<br />
* bleak_epsilon_0_0E_2E, beam-leakage parameter, espilon_0, 100&times;217 EE;<br />
* bleak_epsilon_1_0E_2E, beam-leakage parameter, espilon_1, 100&times;217 EE;<br />
* bleak_epsilon_2_0E_2E, beam-leakage parameter, espilon_2, 100&times;217 EE;<br />
* bleak_epsilon_3_0E_2E, beam-leakage parameter, espilon_3, 100&times;217 EE;<br />
* bleak_epsilon_4_0E_2E, beam-leakage parameter, espilon_4, 100&times;217 EE;<br />
* bleak_epsilon_0_1E_1E, beam-leakage parameter, espilon_0, 143&times;143 EE;<br />
* bleak_epsilon_1_1E_1E, beam-leakage parameter, espilon_1, 143&times;143 EE;<br />
* bleak_epsilon_2_1E_1E, beam-leakage parameter, espilon_2, 143&times;143 EE;<br />
* bleak_epsilon_3_1E_1E, beam-leakage parameter, espilon_3, 143&times;143 EE;<br />
* bleak_epsilon_4_1E_1E, beam-leakage parameter, espilon_4, 143&times;143 EE;<br />
* bleak_epsilon_0_1E_2E, beam-leakage parameter, espilon_0, 143&times;217 EE;<br />
* bleak_epsilon_1_1E_2E, beam-leakage parameter, espilon_1, 143&times;217 EE;<br />
* bleak_epsilon_2_1E_2E, beam-leakage parameter, espilon_2, 143&times;217 EE;<br />
* bleak_epsilon_3_1E_2E, beam-leakage parameter, espilon_3, 143&times;217 EE;<br />
* bleak_epsilon_4_1E_2E, beam-leakage parameter, espilon_4, 143&times;217 EE;<br />
* bleak_epsilon_0_2E_2E, beam-leakage parameter, espilon_0, 217&times;217 EE;<br />
* bleak_epsilon_1_2E_2E, beam-leakage parameter, espilon_1, 217&times;217 EE;<br />
* bleak_epsilon_2_2E_2E, beam-leakage parameter, espilon_2, 217&times;217 EE;<br />
* bleak_epsilon_3_2E_2E, beam-leakage parameter, espilon_3, 217&times;217 EE;<br />
* bleak_epsilon_4_2E_2E, beam-leakage parameter, espilon_4, 217&times;217 EE;<br />
* calib_100T, the relative calibration between 100 and 143 TT spectra;<br />
* calib_217T, the relative calibration between 217 and 143 TT spectra;<br />
* calib_100P, the calibration of the 100 EE spectra, which should be set to 1;<br />
* calib_143P, the calibration of the 143 EE spectra, which should be set to 1;<br />
* calib_217P, the calibration of the 217 EE spectra, which should be set to 1;<br />
* A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* galf_EE_A_100 = 0.060&plusmn;0.012;<br />
* galf_EE_A_100_143 = 0.050&plusmn;0.015;<br />
* galf_EE_A_100_217 = 0.110&plusmn;0.033;<br />
* galf_EE_A_143 = 0.10&plusmn;0.02;<br />
* galf_EE_A_143_217 = 0.240&plusmn;0.048;<br />
* galf_EE_A_217 = 0.72&plusmn;0.14;<br />
* galf_EE_index = -2.4;<br />
* galf_TE_A_100 = 0.140&plusmn;0.042;<br />
* galf_TE_A_100_143 = 0.120&plusmn;0.036;<br />
* galf_TE_A_100_217 = 0.30&plusmn;0.09;<br />
* galf_TE_A_143 = 0.240&plusmn;0.072;<br />
* galf_TE_A_143_217 = 0.60&plusmn;0.018;<br />
* galf_TE_A_217 = 1.80&plusmn;0.54;<br />
* galf_TE_index = -2.4;<br />
* bleak_epsilon_0_0T_0E = 0;<br />
* bleak_epsilon_1_0T_0E = 0;<br />
* bleak_epsilon_2_0T_0E = 0;<br />
* bleak_epsilon_3_0T_0E = 0;<br />
* bleak_epsilon_4_0T_0E = 0;<br />
* bleak_epsilon_0_0T_1E = 0;<br />
* bleak_epsilon_1_0T_1E = 0;<br />
* bleak_epsilon_2_0T_1E = 0;<br />
* bleak_epsilon_3_0T_1E = 0;<br />
* bleak_epsilon_4_0T_1E = 0;<br />
* bleak_epsilon_0_0T_2E = 0;<br />
* bleak_epsilon_1_0T_2E = 0;<br />
* bleak_epsilon_2_0T_2E = 0;<br />
* bleak_epsilon_3_0T_2E = 0;<br />
* bleak_epsilon_4_0T_2E = 0;<br />
* bleak_epsilon_0_1T_1E = 0;<br />
* bleak_epsilon_1_1T_1E = 0;<br />
* bleak_epsilon_2_1T_1E = 0;<br />
* bleak_epsilon_3_1T_1E = 0;<br />
* bleak_epsilon_4_1T_1E = 0;<br />
* bleak_epsilon_0_1T_2E = 0;<br />
* bleak_epsilon_1_1T_2E = 0;<br />
* bleak_epsilon_2_1T_2E = 0;<br />
* bleak_epsilon_3_1T_2E = 0;<br />
* bleak_epsilon_4_1T_2E = 0;<br />
* bleak_epsilon_0_2T_2E = 0;<br />
* bleak_epsilon_1_2T_2E = 0;<br />
* bleak_epsilon_2_2T_2E = 0;<br />
* bleak_epsilon_3_2T_2E = 0;<br />
* bleak_epsilon_4_2T_2E = 0;<br />
* bleak_epsilon_0_0E_0E = 0;<br />
* bleak_epsilon_1_0E_0E = 0;<br />
* bleak_epsilon_2_0E_0E = 0;<br />
* bleak_epsilon_3_0E_0E = 0;<br />
* bleak_epsilon_4_0E_0E = 0;<br />
* bleak_epsilon_0_0E_1E = 0;<br />
* bleak_epsilon_1_0E_1E = 0;<br />
* bleak_epsilon_2_0E_1E = 0;<br />
* bleak_epsilon_3_0E_1E = 0;<br />
* bleak_epsilon_4_0E_1E = 0;<br />
* bleak_epsilon_0_0E_2E = 0;<br />
* bleak_epsilon_1_0E_2E = 0;<br />
* bleak_epsilon_2_0E_2E = 0;<br />
* bleak_epsilon_3_0E_2E = 0;<br />
* bleak_epsilon_4_0E_2E = 0;<br />
* bleak_epsilon_0_1E_1E = 0;<br />
* bleak_epsilon_1_1E_1E = 0;<br />
* bleak_epsilon_2_1E_1E = 0;<br />
* bleak_epsilon_3_1E_1E = 0;<br />
* bleak_epsilon_4_1E_1E = 0;<br />
* bleak_epsilon_0_1E_2E = 0;<br />
* bleak_epsilon_1_1E_2E = 0;<br />
* bleak_epsilon_2_1E_2E = 0;<br />
* bleak_epsilon_3_1E_2E = 0;<br />
* bleak_epsilon_4_1E_2E = 0;<br />
* bleak_epsilon_0_2E_2E = 0;<br />
* bleak_epsilon_1_2E_2E = 0;<br />
* bleak_epsilon_2_2E_2E = 0;<br />
* bleak_epsilon_3_2E_2E = 0;<br />
* bleak_epsilon_4_2E_2E = 0;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* calib_100P = 1;<br />
* calib_143P = 1; <br />
* calib_217P = 1; <br />
* A_pol = 1;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT only - Plik lite'''<br />
This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range &#8467;=30-2508. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT</i> spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-&#8467; likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TT likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.<br />
<br />
'''TT EE TE - Plik lite'''<br />
This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range &#8467;=30-2508 for temperature and &#8467;=30-1996 for TE and EE. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT<i/>, <i>TE</i>, and <i>EE</i> spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TTTEEE likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TTTEEE, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the <i>EE</i>, and <i>TE</i> spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
''' Lensing likelihoods '''<br />
<br />
'''T only'''<br />
This file allows for the computation of the baseline lensing likelihood, using only the SMICA <i>T</i><br />
map-based lensing reconstruction. Only the lensing multipole range &#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of a model-dependent correction to the normalization and<br />
the "N1 bias." To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant "mean field" and "N0" contribution, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> CMB map;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i> spectrum is needed to compute the normalization and N1 corrections.<br />
<br />
'''T+P'''<br />
This file allows for the computation of the baseline lensing likelihood, using both the <br />
<i>T</i> and <i>P</i> SMICA map-based lensing reconstruction. Only the lensing multipole range&#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of model dependent correction to the normalization and<br />
the N1 bias. To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> and <i>P</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured outside a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> and <i>E</i> CMB maps;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T+P-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive), the <i>EE</i> and <i>TE</i> power spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i>, <i>EE</i>, and <i>TE</i> spectra are needed to compute the normalization and N1 corrections.<br />
<br />
'''Data sets - Extended data'''<br />
<br />
Four other data files are available.<br />
Those extend the baseline delivery by adding:<br />
* TE, EE and other joint high-&#8467 Plik likelihoods, ''COM_Likelihood_Data-extra-plik-HM-ext_R2.00.tar.gz'';<br />
* TT and TTTEEE unbinned high-&#8467 Plik likelihood, ''COM_Likelihood_Data-extra-plik-unbinned_R2.00.tar.gz'';<br />
* TT, TE, EE, and TTTEEE Plik likelihood using the detset cross-spectra instead of the half-mission one, and including empirical correlated noise correction for the TT spectra, ''COM_Likelihood_Data-extra-plik-DS_R2.00.tar.gz'';<br />
* extended &#8467 range lensing likelihood, ''COM_Likelihood_Data-extra-lensing-ext_R2.00.tar.gz''.<br />
<br />
Note that although these products are discussed in the Planck papers, they are not used for the baseline results.<br />
<br />
Each file contains a '''readme.md''' description of the content and the use of the different likelihood files.<br />
<br />
<br />
<br />
<!-- <br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the {{PlanckPapers|planck2013-p08|1|Power spectrum & Likelihood Paper}} (for the CMB based likelihood) and in the {{PlanckPapers|planck2013-p12|1|Lensing Paper}} (for the lensing likelihood) .<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The Commander likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 &plusmn; 0.2 and a_gs = 0.4 &plusmn; 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first-order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first-order renormalization procedure. This means that the code will need both the TT and &phi;&phi; power spectrum up to &#8467; = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between &#8467; = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
</span><br />
<span style="color:red">OUTSTANDING: description of likelihood masks </span><br />
'''Production process'''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each data set comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<sup>-6</sup> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander''<nowiki>:</nowiki><br />
* all Planck channel maps;<br />
* compact source catalogues;<br />
* common masks;<br />
* beam transfer functions for all channels.<br />
<br />
; ''lowlike''<nowiki>:</nowiki><br />
* WMAP9 likelihood data;<br />
* Low-<math>\ell</math> Commander map.<br />
<br />
; ''CAMspec''<nowiki>:</nowiki><br />
* 100-, 143- and 217-GHz detector and detsets maps;<br />
* 857GHz channel map;<br />
* compact source catalogue;<br />
* common masks (0,1 and 3);<br />
* beam transfer function and error eigenmodes and covariance for 100-, 143- and 217-GHz detectors and detsets;<br />
* theoretical templates for the tSZ and kSZ contributions;<br />
* color corrections for the CIB emission for the 143- and 217-GHz detectors and detsets;<br />
* fiducial CMB model (bootstrapped from WMAP7 best-fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz.<br />
<br />
; ''lensing''<nowiki>:</nowiki><br />
* the lensing map;<br />
* beam error eigenmodes and covariance for the 143- and 217-GHz channel maps;<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt''<nowiki>:</nowiki><br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here];<br />
* the tSZ and kSZ template are changed to match those of CAMspec.<br />
<br />
''' File names and Meta-data '''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta-data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
--><br />
<br />
'''Likelihood Masks'''<br />
<br />
'''General description'''<br />
<br />
We provide the masks for Temperature and Polarisation used to exclude the regions of strongest foreground emission in the CMB maps when computing the empirical spectra that we use to form the high-&#8467 likelihood. The masks are provided for each frequency between 100 and 217 GHz, masking the appropriate part of the Galactic Plane and, for temperature only, the relevant population of point sources. Note that to compute the empirical power spectrum of the maps, one should also take into account missing pixels in a particular map. This is not included in the masks we distribute.<br />
<br />
'''Production Process'''<br />
Complete production process for those masks is described in {{PlanckPapers|planck2014-a13}}.<br />
<br />
The temperature masks are the combination of a Galactic mask, a point source mask and (for 100Ghz and 217GHz) a CO mask. Extended objects, planets, etc are included in the point source mask. <br />
The polarization masks are simply the Galactic masks.<br />
<br />
The Galactic masks are obtained by thresholding a CMB corrected and <math>10^o</math> smoothed 353GHz map. The threshold is tuned so as to retain a given fraction of the sky, between 50% and 80%. Each mask is apodized by a <math>4^o.71</math> FWHM gaussian window function using the distance map. Special care is taken to smooth this distance map, in order to avoid strong caustics. The apodization down-weights an effective 10% of the sky. Following {{PlanckPapers|planck2014-a13}}, the Galactic masks are named by the effective unmasked sky area G70, G60, G50 and G41.<br />
<br />
The point source masks are different for each frequency. They are based on the 2015 Planck catalog and cut out all the sources detected at S/N = 5 or higher in each channel. Each source is masked with a circular aperture of size 3xFWHM of that channel (i.e. 3x9.′66 at 100GHz, 3x7.′22 at 143GHz, and 3x4.′90 at 217GHz). Note that we include in the point source masks all sources above our threshold, including possible galactic ones. The mask is further apodized with a gaussian window function with FWHM=30'. <br />
<br />
The CO masks is used only at 100GHz and 217GHz, since there is no (strong) CO line in the 147 GHz channel. They are based on the Type 3 CO map from the Planck2013 delivery. The CO map is smoothed to 120' and a threshold is applied to mask all regions above <math>1 K_{RJ} km s^{−1}</math>. The mask is further apodized to 30'.<br />
<br />
Mask combinations are performed by multiplying a galactic, a point source, and possibly a CO mask together.<br />
<br />
The Temperature masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter T and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: T66 = G70+Point source mask 100Ghz+CO mask<br />
* 143Ghz: T57 = G60+Point source mask 143Ghz<br />
* 217Ghz: T47 = G50+Point source mask 217Ghz+CO mask<br />
<br />
The Polarization masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter P and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: P70 = G70<br />
* 143Ghz: P50 = G50<br />
* 217Ghz: P41 = G41<br />
<br />
'''Inputs'''<br />
* Galactic masks: The SMICA CMB temperature map, the 353GHz temperature map.<br />
* Point source masks: The Planck 2015 catalog, the FWHM of each of the frequencies.<br />
* CO mask: the Type 3 CO map from the Planck 2013 delivery.<br />
<br />
''' File names and meta-data '''<br />
The masks are distributed in a single tar file ''COM_Likelihood_Masks_R2.00.tar.gz''.<br />
The files extract to 6 files<br />
* temperature_100.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 100Ghz, i.e. T66<br />
* temperature_143.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 143Ghz, i.e. T57<br />
* temperature_217.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 217Ghz, i.e. T47<br />
* polarization_100.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 100Ghz, i.e. P70<br />
* polarization_143.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 143Ghz, i.e. P50<br />
* polarization_217.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 217Ghz, i.e. P41<br />
<br />
<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #EEE8AA;width:80%"><br />
'''2013 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''General description'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles <math> \ell </math> = 2-2479. Over the multipole range <math> \ell </math> = 2–49, the power spectrum is derived from a component-separation algorithm, ''Commander'', applied to maps in the frequency range 30–353 GHz over 91% of the sky {{PlanckPapers|planck2013-p06}}. The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction. For multipoles greater than <math>\ell=50</math>, instead, the spectrum is derived from the ''CAMspec'' likelihood {{PlanckPapers|planck2013-p08}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds. Associated 1-sigma errors include beam and foreground uncertainties. Both ''Commander'' and ''CAMspec'' are described in more details in the sections below.<br />
<br />
[[File: mission_spectrum.png|thumb|center|700px|'''CMB spectrum. Logarithmic x-scale up to <math>\ell=50</math>, linear at higher <math>\ell</math>; all points with error bars. The red line is the Planck best-fit primordial power spectrum (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}).''']]<br />
<br />
'''Likelihood'''<br />
<br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the Power spectrum & Likelihood Paper {{PlanckPapers|planck2013-p08}} (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) {{PlanckPapers|planck2013-p12}}.<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The ''Commander'' likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 ± 0.2 and a_gs = 0.4 ± 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. This means that the code will need both the TT and $\phi\phi$ power spectrum up to <math>\ell</math> = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between <math>\ell</math> = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
<br />
'''Production process'''<br />
<br />
'''CMB spectra'''<br />
<br />
The <math>\ell</math> < 50 part of the Planck power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters {{PlanckPapers|planck2013-p06}}. The power spectrum at any multipole <math>\ell</math> is given as the maximum probability point for the posterior <math>C_\ell</math> distribution, marginalized over the other multipoles, and the error bars are 68% confidence level {{PlanckPapers|planck2013-p08}}. <br />
<br />
The <math>\ell</math> > 50 part of the CMB temperature power spectrum has been derived by the CamSpec likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of {{PlanckPapers|planck2013-p08}}. Frequency spectra are computed as noise weighted averages of the cross-spectra between single detector and sets of detector maps. Mask and multipole range choices for each frequency spectrum are summarized in Table 4 of {{PlanckPapers|planck2013-p08}}. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of {{PlanckPapers|planck2013-p08}} and Sec. 4 of {{PlanckPapers|planck2013-p11}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with unresolved foreground and beam uncertainties. Both spectrum and associated covariance matrix are given as uniformly weighted band averages in 74 bins. <br />
<br />
'''Likelihood'''<br />
<br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each dataset comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<math>^{-6}</math> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
; Low-l spectrum (<math>\ell < 50</math>):<br />
* frequency maps from 30–353 GHz<br />
* common mask {{PlanckPapers|planck2013-p06}}<br />
* compact sources catalog<br />
<br />
; High-l spectrum (<math>50 < \ell < 2500</math>): <br />
<br />
* 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 2 in {{PlanckPapers|planck2013-p08}})<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of {{PlanckPapers|planck2013-p11}})<br />
* Beam transfer function uncertainties {{PlanckPapers|planck2013-p03c}}<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander'' :<br />
* all Planck channels maps<br />
* compact source catalogs<br />
* common masks<br />
* beam transfer functions for all channels<br />
<br />
; ''lowlike'' :<br />
* WMAP9 likelihood data<br />
* Low-<math>\ell</math> Commander map<br />
<br />
; ''CAMspec'' :<br />
* 100, 143 and 217 GHz detector and detsets maps<br />
* 857GHz channel map<br />
* compact source catalog<br />
* common masks (0,1 & 3)<br />
* beam transfer function and error eigenmodes and covariance for 100, 143 and 217 GHz detectors & detsets<br />
* theoretical templates for the tSZ and kSZ contributions<br />
* color corrections for the CIB emission for the 143 and 217GHz detectors and detsets<br />
* fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz<br />
<br />
; ''lensing'' :<br />
* the lensing map<br />
* beam error eigenmodes and covariance for the 143 and 217GHz channel maps<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt'' :<br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]<br />
* the tSZ andkSZ template are changed to match those of CAMspec<br />
<br />
''' File names and Meta data '''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The CMB spectrum and its covariance matrix are distributed in a single FITS file named <br />
* ''{{PLASingleFile | fileType=cosmo | name=COM_PowerSpect_CMB_R1.10.fits | link=COM_PowerSpect_CMB_R1.10.fits}}'' <br />
<br />
which contains 3 extensions<br />
<br />
; LOW-ELL (BINTABLE)<br />
: with the low ell part of the spectrum, not binned, and for l=2-49. The table columns are<br />
# ''ELL'' (integer): multipole number<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERRUP'' (float): the upward uncertainty<br />
# ''ERRDOWN'' (float): the downward uncertainty<br />
<br />
; HIGH-ELL (BINTABLE)<br />
: with the high-ell part of the spectrum, binned into 74 bins covering <math>\langle l \rangle = 47-2419\ </math> in bins of width <math>l=31</math> (with the exception of the last 4 bins that are wider). The table columns are as follows:<br />
# ''ELL'' (integer): mean multipole number of bin<br />
# ''L_MIN'' (integer): lowest multipole of bin<br />
# ''L_MAX'' (integer): highest multipole of bin<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERR'' (float): the uncertainty<br />
<br />
; COV-MAT (IMAGE)<br />
: with the covariance matrix of the high-ell part of the spectrum in a 74x74 pixel image, i.e., covering the same bins as the ''HIGH-ELL'' table.<br />
<br />
The spectra give $D_\ell = \ell(\ell+1)C_\ell / 2\pi$ in units of $\mu\, K^2$, and the covariance matrix is in units of $\mu\, K^4$. The spectra are shown in the figure below, in blue and red for the low- and high-<math>\ell</math> parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.<br />
<br />
[[File: CMBspect.jpg|thumb|center|700px|'''CMB spectrum. Linear x-scale; error bars only at high <math>\ell</math>.''']]<br />
<br />
'''Likelihood'''<br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
<br />
</div><br />
</div><br />
<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
[[Category:Mission products|008]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=14379CMB spectrum & Likelihood Code2018-07-16T13:33:49Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:CMB spectra and likelihood code}}<br />
<br />
== 2018 CMB spectra==<br />
<br />
<br />
===General description===<br />
====TT====<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 86% of the sky ({{PlanckPapers|planck2016-l06}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood {{PlanckPapers|planck2016-l05}}, with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.51.48.png|thumb|600px|center]]<br />
<br />
====TE, EE, and EB, BB ====<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. In the multipole range 2 ≤ l ≤ 29, we plot the power spectra estimates from the SimAll likelihood (though only the EE spectrum is used in the baseline parameter analysis at l ≤ 29), see {{PlanckPapers|planck2016-l06}}). .<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.52.35.png|thumb|600px|center]]<br />
[[File:Screen Shot 2018-07-16 at 05.52.24.png|thumb|600px|center]]<br />
<br />
<br />
In the range &#8467; = 2-29, we also release the <i>BB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2016-l03}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
==== Theory ====<br />
<br />
We also provide best-fit LCDM CMB power spectra from the baseline Planck TT,TE,EE+lowE+lensing. The spectra must be divided by the best-fit Planck map-based calibration parameter squared, calPlanck**2, to be compared to the coadded CMB spectra. The best-fit calPlanck value can be found in the file "COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt".<br />
<br />
===Production process===<br />
The Plik high-multipole likelihood (described in detail in {{PlanckPapers|planck2016-l05}}) is a Gaussian approximation of the probability distributions of the <i>TT</i>, <i>EE</i>, and <i>TE</i> angular power spectra, with semi-analytic covariance matrices calculated assuming a fiducial cosmology. It includes multipoles in the range 30 to 2508 for TT and 30 to 1996 for <i>TE</i> and <i>EE</i> and is constructed from half-mission cross-spectra measured from the 100-, 143-, and 217-GHz HFI frequency maps. For more details see {{PlanckPapers|planck2016-l06}}.<br />
<br />
<br />
<br />
===Inputs===<br />
<br />
The T T likelihood uses four half-mission cross-spectra with different multipole cuts to avoid multipole regions where noise dominates due to the limited resolution of the beams and to en-sure foreground contamination is correctly handled by our fore-ground model: 100 × 100 ( &#8467; = 30–1197); 143 × 143 (&#8467; = 30– 1996); 143 × 217 (&#8467; = 30–2508); and 217 × 217 (&#8467; = 30–2508). The TE and EE likelihoods also include the 100 × 143 and 100 × 217 cross-spectra to improve the signal-to-noise ratio, and have different multipole cuts: 100 × 100 (&#8467; = 30–999); 100 × 143 (&#8467; = 30–999); 100 × 217 (&#8467; = 505–999); 143 × 143 (&#8467; = 30– 1996); 143 × 217 (&#8467; = 505–1996); and 217 × 217 (&#8467; = 505– 1996). <br />
<br />
=== File names and meta-data ===<br />
<br />
The CMB spectra and their uncertainties are distributed in ASCII text files named ''COM_PowerSpect_CMB_nn_R3.01.fits'', where nn stands for the type of spectrum the file contains:<br />
* COM_PowerSpect_CMB-EE-full_R3.01.txt<br />
* COM_PowerSpect_CMB-TE-full_R3.01.txt<br />
* COM_PowerSpect_CMB-TT-full_R3.01.txt<br />
* COM_PowerSpect_CMB-low-ell-BB-full_R3.01.txt<br />
* COM_PowerSpect_CMB-low-ell-EB-full_R3.01.txt<br />
<br />
In addition we provide one file containing all the parameters of the Plik runs which yielded the spectra. This file is named<br />
* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt<br />
<br />
The theoretical spectrum of the best-fit model itself is provided in a separate file named<br />
* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt<br />
<br />
<br />
<br />
a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
== 2018 Likelihood==<br />
<br />
The 2018 Likelihood code will be released at a later time.<br />
<br />
== Previous Releases: (2015) and (2013) CMB spectrum and Likelihood ==<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%"><br />
'''2015 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''2015 CMB spectra'''<br />
<br />
'''General description'''<br />
<br />
'''TT'''<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2014-a12}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP &Lambda;CDM run. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]<br />
<br />
'''TE, EE, and TB, EB, BB '''<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
'''Production process'''<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
'''Inputs'''<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
''' File names and meta-data '''<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
'''Likelihood'''<br />
<br />
The 2015 baseline likelihood release consists of a code package and a single data package. Four extended data packages are also available enabling exploration of alternatives to the baseline results.<br />
The code compiles to a library allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets. A data set permits the computation of a single likelihood among:<br />
* the high-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the low-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the CMB lensing reconstruction.<br />
By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.<br />
<br />
Only the baseline data package, ''COM_Likelihood_Data-baseline_R2.00.tar.gz'', will be fully described on this page. It contains six data sets, which are enough to compute all of the baseline Planck results that are discussed in {{PlanckPapers|planck2014-a14}}. In particular it allows for the computation of the CMB and lensing likelihood from either the Temperature data only, or the Temperature + Polarization combination.<br />
<br />
The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in {{PlanckPapers|planck2014-a13}} and {{PlanckPapers|planck2014-a17}}. Their full description is contained in the documentation included in each of the extended data packages.<br />
<br />
'''Library and tools'''<br />
<br />
'''Description'''<br />
The library consists of code written in C and Fortran 90. It can be called from both of<br />
those languages. Optionally, a python wrapper can be built as well. Scripts to<br />
simplify the linking of the library with other codes are part of the package, as<br />
well as some example codes that can be used to test the correct installation of<br />
the code and the integrity of the data packages. Optionally, a script is also available, allowing<br />
the user to modify the multipole range of the TT likelihoods and reproduce the hybridization<br />
test performed in the paper.<br />
A description of the tool, the API of the library, as well as different <br />
installation procedure are detailed in the ''readme.md'' file in the code package.<br />
<br />
'''File name'''<br />
The code can be extracted from <br />
''COM_Likelihood_Code-v2.0_R2.00.tar.bz2''.<br />
<br />
Please read the file ''readme.md'' for installation instructions.<br />
<br />
'''Data sets - Baseline data'''<br />
All of the released baseline data are distributed within a single file,<br />
''COM_Likelihood_Data-baseline_R2.00.tar.gz''.<br />
<br />
This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.<br />
<br />
Each data set is stored in its own directory. The directory structure follows similar rules<br />
for each data set, and stores data, template, and meta-data for each particular likelihood.<br />
<br />
As in 2013, the CMB likelihood is cut into low-&#8467; and high-&#8467; parts. Moreover, <br />
for each of those, we distribute both a T-only datafile and a joint T+P one. In the case <br />
of the high-&#8467; part, we also distribute two specific versions of the likelihood, <br />
that allow for estimate of T and T+P marginalized over the nuisance parameters.<br />
Combining both the low-&#8467; and high-&#8467; files, one can compute the likelihood over the<br />
range &#8467;=2-2508 in TT and &#8467;=2-1996 in TE and EE. A full description of the low-&#8467; <br />
and high-&#8467; likelihood is available in {{PlanckPapers|planck2014-a13}}.<br />
<br />
Similarly, for the case of lensing, we also distribute the likelihood using both<br />
the reconstruction based on the <i>T</i> map only, or on <i>T</i>+<i>P</i> maps. <br />
A full description of the lensing likelihood is available in {{PlanckPapers|planck2014-a17}}.<br />
<br />
All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that his parameter is explored in the Gaussian prior 1.0000&plusmn;0.0025.<br />
<br />
''' Low-&#8467; likelihoods '''<br />
<br />
'''TT only - commander'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=2-29.<br />
Using the optional tool in the code package, it can be modified to cover any multipole range <br />
up to &#8467;&lt;200. <br />
<br />
''' Production process'''<br />
The likelihood is based on the results of the Commander approach, which implements a <br />
Bayesian component separation method in pixel space, sampling the posterior distribution <br />
of the parameters of a model that describes both the CMB and the foreground emissions<br />
in a combination of the Planck maps, the WMAP map, and the 408-MHz survey. The samples<br />
of this exploration are used to infer the foreground marginalized low-&#8467; likelihood <br />
for any <i>TT</i> CMB spectrum. <br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
'''File name and usage'''<br />
The commander likelihood is distributed in <br />
''plc_2.0/low_l/commander/commander_rc2_v1.1_l2_29_B.clik''<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the vector really starts at &#8467;=0, although<br />
the first two entries are null.<br />
<br />
'''TEB '''<br />
This file allows for the computation of the CMB joint TT,EE, BB and TE likelihood <br />
in the range &#8467;=2-29. It should not be used with the low-&#8467; TT-only likelihood.<br />
<br />
''' Production process'''<br />
The file allows for the computation of the pixel based likelihood of <i>T</i>, <i>E</i>, and <i>B</i> <br />
maps. The <i>T</i> map is the best-fit map obtained from the commander algorithm, as described above, <br />
while the <i>E</i> and <i>B</i> maps are obtained from the 70GHz LFI full mission data, but excluding the second and fourth surveys. Foreground contamination is<br />
dealt with by marginalizing over templates based on the 30-GHz LFI and 353-GHz HFI maps.<br />
The covariance matrix comes from the Planck detector sensitivity modulated on the <br />
sky by the scanning strategy. The covariance matrix is further enlarged to account <br />
for the foreground template removal. <br />
To speed up the computation by about an order of magnitude, the problem is <br />
projected into <i>C</i><sub>&#8467;</sub> space using the Sherman-Morrison-Woodbury identity. Only the <br />
projected quantities are stored in the data package.<br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask {{PlanckPapers|planck2014-a12}}.<br />
<br />
<br />
'''File name and usage'''<br />
The low ell TEB likelihood is distributed in <br />
''plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive), followed by the <i>EE</i> (&#8467;=0 to 29), <br />
<i>BB</i> (&#8467;=0 to 29) and <i>TE</i> (&#8467;=0 to 29) spectra, and by an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the entries really start at &#8467;=0, although the<br />
&#8467;=0 and &#8467;=1 values will be null.<br />
<br />
''' High-&#8467; likelihoods '''<br />
<br />
'''TT only - Plik'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=30-2508.<br />
Using the optional tool in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>TT</i> cross-spectra. <br />
Only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission <i>T</i> maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by a vector of 16 nuisance parameters.<br />
Those are, in order:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217;<br />
* calib_100T, the relative calibration between the 100 and 143 spectra;<br />
* calib_217T, the relative calibration between the 217 and 143 spectra;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT+TE+EE - Plik'''<br />
This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range &#8467;=30-2508 for TT and &#8467;=30-1996 for TE and EE.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>T</i> and <i>E</i> cross-spectra. <br />
In temperature, only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used, while<br />
in <i>TE</i> and <i>EE</i> all of them are used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission T+P maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz and 353-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates;<br />
* best-fit CMB+foreground model for the beam-leakage template.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, plik TTTEEE likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik''.<br />
<br />
This file should not be used with any other TT-only high-&#8467; file.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed the <i>EE</i> and <i>TE</i> spectra (same range) and by a vector of 94 nuisance parameters.<br />
Those are, in g:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100TT;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143TT;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217TT;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217TT;<br />
* galf_EE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100EE;<br />
* galf_EE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143EE;<br />
* galf_EE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217EE;<br />
* galf_EE_A_143, the dust residual contamination at &#8467;=500 in 143&times;143EE;<br />
* galf_EE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217EE;<br />
* galf_EE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217EE;<br />
* galf_EE_index, the dust EE template slope, which should be set to -2.4;<br />
* galf_TE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100TE;<br />
* galf_TE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143TE;<br />
* galf_TE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217TE;<br />
* galf_TE_A_143, the dust residual contamination at &#8467;=500 in 143x143TE;<br />
* galf_TE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217TE;<br />
* galf_TE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217TE;<br />
* galf_TE_index, the dust EE template slope, which should be set to -2.4;<br />
* bleak_epsilon_0_0T_0E, beam-leakage parameter, espilon_0, 100&times;100 TE;<br />
* bleak_epsilon_1_0T_0E, beam-leakage parameter, espilon_1, 100&times;100 TE;<br />
* bleak_epsilon_2_0T_0E, beam-leakage parameter, espilon_2, 100&times;100 TE;<br />
* bleak_epsilon_3_0T_0E, beam-leakage parameter, espilon_3, 100&times;100 TE;<br />
* bleak_epsilon_4_0T_0E, beam-leakage parameter, espilon_4, 100&times;100 TE;<br />
* bleak_epsilon_0_0T_1E, beam-leakage parameter, espilon_0, 100&times;143 TE;<br />
* bleak_epsilon_1_0T_1E, beam-leakage parameter, espilon_1, 100&times;143 TE;<br />
* bleak_epsilon_2_0T_1E, beam-leakage parameter, espilon_2, 100&times;143 TE;<br />
* bleak_epsilon_3_0T_1E, beam-leakage parameter, espilon_3, 100&times;143 TE;<br />
* bleak_epsilon_4_0T_1E, beam-leakage parameter, espilon_4, 100&times;143 TE;<br />
* bleak_epsilon_0_0T_2E, beam-leakage parameter, espilon_0, 100&times;217 TE;<br />
* bleak_epsilon_1_0T_2E, beam-leakage parameter, espilon_1, 100&times;217 TE;<br />
* bleak_epsilon_2_0T_2E, beam-leakage parameter, espilon_2, 100&times;217 TE;<br />
* bleak_epsilon_3_0T_2E, beam-leakage parameter, espilon_3, 100&times;217 TE;<br />
* bleak_epsilon_4_0T_2E, beam-leakage parameter, espilon_4, 100&times;217 TE;<br />
* bleak_epsilon_0_1T_1E, beam-leakage parameter, espilon_0, 143&times;143 TE;<br />
* bleak_epsilon_1_1T_1E, beam-leakage parameter, espilon_1, 143&times;143 TE;<br />
* bleak_epsilon_2_1T_1E, beam-leakage parameter, espilon_2, 143&times;143 TE;<br />
* bleak_epsilon_3_1T_1E, beam-leakage parameter, espilon_3, 143&times;143 TE;<br />
* bleak_epsilon_4_1T_1E, beam-leakage parameter, espilon_4, 143&times;143 TE;<br />
* bleak_epsilon_0_1T_2E, beam-leakage parameter, espilon_0, 143&times;217 TE;<br />
* bleak_epsilon_1_1T_2E, beam-leakage parameter, espilon_1, 143&times;217 TE;<br />
* bleak_epsilon_2_1T_2E, beam-leakage parameter, espilon_2, 143&times;217 TE;<br />
* bleak_epsilon_3_1T_2E, beam-leakage parameter, espilon_3, 143&times;217 TE;<br />
* bleak_epsilon_4_1T_2E, beam-leakage parameter, espilon_4, 143&times;217 TE;<br />
* bleak_epsilon_0_2T_2E, beam-leakage parameter, espilon_0, 217&times;217 TE;<br />
* bleak_epsilon_1_2T_2E, beam-leakage parameter, espilon_1, 217&times;217 TE;<br />
* bleak_epsilon_2_2T_2E, beam-leakage parameter, espilon_2, 217&times;217 TE;<br />
* bleak_epsilon_3_2T_2E, beam-leakage parameter, espilon_3, 217&times;217 TE;<br />
* bleak_epsilon_4_2T_2E, beam-leakage parameter, espilon_4, 217&times;217 TE;<br />
* bleak_epsilon_0_0E_0E, beam-leakage parameter, espilon_0, 100&times;100 EE;<br />
* bleak_epsilon_1_0E_0E, beam-leakage parameter, espilon_1, 100&times;100 EE;<br />
* bleak_epsilon_2_0E_0E, beam-leakage parameter, espilon_2, 100&times;100 EE;<br />
* bleak_epsilon_3_0E_0E, beam-leakage parameter, espilon_3, 100&times;100 EE;<br />
* bleak_epsilon_4_0E_0E, beam-leakage parameter, espilon_4, 100&times;100 EE;<br />
* bleak_epsilon_0_0E_1E, beam-leakage parameter, espilon_0, 100&times;143 EE;<br />
* bleak_epsilon_1_0E_1E, beam-leakage parameter, espilon_1, 100&times;143 EE;<br />
* bleak_epsilon_2_0E_1E, beam-leakage parameter, espilon_2, 100&times;143 EE;<br />
* bleak_epsilon_3_0E_1E, beam-leakage parameter, espilon_3, 100&times;143 EE;<br />
* bleak_epsilon_4_0E_1E, beam-leakage parameter, espilon_4, 100&times;143 EE;<br />
* bleak_epsilon_0_0E_2E, beam-leakage parameter, espilon_0, 100&times;217 EE;<br />
* bleak_epsilon_1_0E_2E, beam-leakage parameter, espilon_1, 100&times;217 EE;<br />
* bleak_epsilon_2_0E_2E, beam-leakage parameter, espilon_2, 100&times;217 EE;<br />
* bleak_epsilon_3_0E_2E, beam-leakage parameter, espilon_3, 100&times;217 EE;<br />
* bleak_epsilon_4_0E_2E, beam-leakage parameter, espilon_4, 100&times;217 EE;<br />
* bleak_epsilon_0_1E_1E, beam-leakage parameter, espilon_0, 143&times;143 EE;<br />
* bleak_epsilon_1_1E_1E, beam-leakage parameter, espilon_1, 143&times;143 EE;<br />
* bleak_epsilon_2_1E_1E, beam-leakage parameter, espilon_2, 143&times;143 EE;<br />
* bleak_epsilon_3_1E_1E, beam-leakage parameter, espilon_3, 143&times;143 EE;<br />
* bleak_epsilon_4_1E_1E, beam-leakage parameter, espilon_4, 143&times;143 EE;<br />
* bleak_epsilon_0_1E_2E, beam-leakage parameter, espilon_0, 143&times;217 EE;<br />
* bleak_epsilon_1_1E_2E, beam-leakage parameter, espilon_1, 143&times;217 EE;<br />
* bleak_epsilon_2_1E_2E, beam-leakage parameter, espilon_2, 143&times;217 EE;<br />
* bleak_epsilon_3_1E_2E, beam-leakage parameter, espilon_3, 143&times;217 EE;<br />
* bleak_epsilon_4_1E_2E, beam-leakage parameter, espilon_4, 143&times;217 EE;<br />
* bleak_epsilon_0_2E_2E, beam-leakage parameter, espilon_0, 217&times;217 EE;<br />
* bleak_epsilon_1_2E_2E, beam-leakage parameter, espilon_1, 217&times;217 EE;<br />
* bleak_epsilon_2_2E_2E, beam-leakage parameter, espilon_2, 217&times;217 EE;<br />
* bleak_epsilon_3_2E_2E, beam-leakage parameter, espilon_3, 217&times;217 EE;<br />
* bleak_epsilon_4_2E_2E, beam-leakage parameter, espilon_4, 217&times;217 EE;<br />
* calib_100T, the relative calibration between 100 and 143 TT spectra;<br />
* calib_217T, the relative calibration between 217 and 143 TT spectra;<br />
* calib_100P, the calibration of the 100 EE spectra, which should be set to 1;<br />
* calib_143P, the calibration of the 143 EE spectra, which should be set to 1;<br />
* calib_217P, the calibration of the 217 EE spectra, which should be set to 1;<br />
* A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* galf_EE_A_100 = 0.060&plusmn;0.012;<br />
* galf_EE_A_100_143 = 0.050&plusmn;0.015;<br />
* galf_EE_A_100_217 = 0.110&plusmn;0.033;<br />
* galf_EE_A_143 = 0.10&plusmn;0.02;<br />
* galf_EE_A_143_217 = 0.240&plusmn;0.048;<br />
* galf_EE_A_217 = 0.72&plusmn;0.14;<br />
* galf_EE_index = -2.4;<br />
* galf_TE_A_100 = 0.140&plusmn;0.042;<br />
* galf_TE_A_100_143 = 0.120&plusmn;0.036;<br />
* galf_TE_A_100_217 = 0.30&plusmn;0.09;<br />
* galf_TE_A_143 = 0.240&plusmn;0.072;<br />
* galf_TE_A_143_217 = 0.60&plusmn;0.018;<br />
* galf_TE_A_217 = 1.80&plusmn;0.54;<br />
* galf_TE_index = -2.4;<br />
* bleak_epsilon_0_0T_0E = 0;<br />
* bleak_epsilon_1_0T_0E = 0;<br />
* bleak_epsilon_2_0T_0E = 0;<br />
* bleak_epsilon_3_0T_0E = 0;<br />
* bleak_epsilon_4_0T_0E = 0;<br />
* bleak_epsilon_0_0T_1E = 0;<br />
* bleak_epsilon_1_0T_1E = 0;<br />
* bleak_epsilon_2_0T_1E = 0;<br />
* bleak_epsilon_3_0T_1E = 0;<br />
* bleak_epsilon_4_0T_1E = 0;<br />
* bleak_epsilon_0_0T_2E = 0;<br />
* bleak_epsilon_1_0T_2E = 0;<br />
* bleak_epsilon_2_0T_2E = 0;<br />
* bleak_epsilon_3_0T_2E = 0;<br />
* bleak_epsilon_4_0T_2E = 0;<br />
* bleak_epsilon_0_1T_1E = 0;<br />
* bleak_epsilon_1_1T_1E = 0;<br />
* bleak_epsilon_2_1T_1E = 0;<br />
* bleak_epsilon_3_1T_1E = 0;<br />
* bleak_epsilon_4_1T_1E = 0;<br />
* bleak_epsilon_0_1T_2E = 0;<br />
* bleak_epsilon_1_1T_2E = 0;<br />
* bleak_epsilon_2_1T_2E = 0;<br />
* bleak_epsilon_3_1T_2E = 0;<br />
* bleak_epsilon_4_1T_2E = 0;<br />
* bleak_epsilon_0_2T_2E = 0;<br />
* bleak_epsilon_1_2T_2E = 0;<br />
* bleak_epsilon_2_2T_2E = 0;<br />
* bleak_epsilon_3_2T_2E = 0;<br />
* bleak_epsilon_4_2T_2E = 0;<br />
* bleak_epsilon_0_0E_0E = 0;<br />
* bleak_epsilon_1_0E_0E = 0;<br />
* bleak_epsilon_2_0E_0E = 0;<br />
* bleak_epsilon_3_0E_0E = 0;<br />
* bleak_epsilon_4_0E_0E = 0;<br />
* bleak_epsilon_0_0E_1E = 0;<br />
* bleak_epsilon_1_0E_1E = 0;<br />
* bleak_epsilon_2_0E_1E = 0;<br />
* bleak_epsilon_3_0E_1E = 0;<br />
* bleak_epsilon_4_0E_1E = 0;<br />
* bleak_epsilon_0_0E_2E = 0;<br />
* bleak_epsilon_1_0E_2E = 0;<br />
* bleak_epsilon_2_0E_2E = 0;<br />
* bleak_epsilon_3_0E_2E = 0;<br />
* bleak_epsilon_4_0E_2E = 0;<br />
* bleak_epsilon_0_1E_1E = 0;<br />
* bleak_epsilon_1_1E_1E = 0;<br />
* bleak_epsilon_2_1E_1E = 0;<br />
* bleak_epsilon_3_1E_1E = 0;<br />
* bleak_epsilon_4_1E_1E = 0;<br />
* bleak_epsilon_0_1E_2E = 0;<br />
* bleak_epsilon_1_1E_2E = 0;<br />
* bleak_epsilon_2_1E_2E = 0;<br />
* bleak_epsilon_3_1E_2E = 0;<br />
* bleak_epsilon_4_1E_2E = 0;<br />
* bleak_epsilon_0_2E_2E = 0;<br />
* bleak_epsilon_1_2E_2E = 0;<br />
* bleak_epsilon_2_2E_2E = 0;<br />
* bleak_epsilon_3_2E_2E = 0;<br />
* bleak_epsilon_4_2E_2E = 0;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* calib_100P = 1;<br />
* calib_143P = 1; <br />
* calib_217P = 1; <br />
* A_pol = 1;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT only - Plik lite'''<br />
This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range &#8467;=30-2508. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT</i> spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-&#8467; likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TT likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.<br />
<br />
'''TT EE TE - Plik lite'''<br />
This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range &#8467;=30-2508 for temperature and &#8467;=30-1996 for TE and EE. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT<i/>, <i>TE</i>, and <i>EE</i> spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TTTEEE likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TTTEEE, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the <i>EE</i>, and <i>TE</i> spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
''' Lensing likelihoods '''<br />
<br />
'''T only'''<br />
This file allows for the computation of the baseline lensing likelihood, using only the SMICA <i>T</i><br />
map-based lensing reconstruction. Only the lensing multipole range &#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of a model-dependent correction to the normalization and<br />
the "N1 bias." To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant "mean field" and "N0" contribution, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> CMB map;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i> spectrum is needed to compute the normalization and N1 corrections.<br />
<br />
'''T+P'''<br />
This file allows for the computation of the baseline lensing likelihood, using both the <br />
<i>T</i> and <i>P</i> SMICA map-based lensing reconstruction. Only the lensing multipole range&#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of model dependent correction to the normalization and<br />
the N1 bias. To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> and <i>P</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured outside a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> and <i>E</i> CMB maps;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T+P-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive), the <i>EE</i> and <i>TE</i> power spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i>, <i>EE</i>, and <i>TE</i> spectra are needed to compute the normalization and N1 corrections.<br />
<br />
'''Data sets - Extended data'''<br />
<br />
Four other data files are available.<br />
Those extend the baseline delivery by adding:<br />
* TE, EE and other joint high-&#8467 Plik likelihoods, ''COM_Likelihood_Data-extra-plik-HM-ext_R2.00.tar.gz'';<br />
* TT and TTTEEE unbinned high-&#8467 Plik likelihood, ''COM_Likelihood_Data-extra-plik-unbinned_R2.00.tar.gz'';<br />
* TT, TE, EE, and TTTEEE Plik likelihood using the detset cross-spectra instead of the half-mission one, and including empirical correlated noise correction for the TT spectra, ''COM_Likelihood_Data-extra-plik-DS_R2.00.tar.gz'';<br />
* extended &#8467 range lensing likelihood, ''COM_Likelihood_Data-extra-lensing-ext_R2.00.tar.gz''.<br />
<br />
Note that although these products are discussed in the Planck papers, they are not used for the baseline results.<br />
<br />
Each file contains a '''readme.md''' description of the content and the use of the different likelihood files.<br />
<br />
<br />
<br />
<!-- <br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the {{PlanckPapers|planck2013-p08|1|Power spectrum & Likelihood Paper}} (for the CMB based likelihood) and in the {{PlanckPapers|planck2013-p12|1|Lensing Paper}} (for the lensing likelihood) .<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The Commander likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 &plusmn; 0.2 and a_gs = 0.4 &plusmn; 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first-order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first-order renormalization procedure. This means that the code will need both the TT and &phi;&phi; power spectrum up to &#8467; = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between &#8467; = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
</span><br />
<span style="color:red">OUTSTANDING: description of likelihood masks </span><br />
'''Production process'''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each data set comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<sup>-6</sup> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander''<nowiki>:</nowiki><br />
* all Planck channel maps;<br />
* compact source catalogues;<br />
* common masks;<br />
* beam transfer functions for all channels.<br />
<br />
; ''lowlike''<nowiki>:</nowiki><br />
* WMAP9 likelihood data;<br />
* Low-<math>\ell</math> Commander map.<br />
<br />
; ''CAMspec''<nowiki>:</nowiki><br />
* 100-, 143- and 217-GHz detector and detsets maps;<br />
* 857GHz channel map;<br />
* compact source catalogue;<br />
* common masks (0,1 and 3);<br />
* beam transfer function and error eigenmodes and covariance for 100-, 143- and 217-GHz detectors and detsets;<br />
* theoretical templates for the tSZ and kSZ contributions;<br />
* color corrections for the CIB emission for the 143- and 217-GHz detectors and detsets;<br />
* fiducial CMB model (bootstrapped from WMAP7 best-fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz.<br />
<br />
; ''lensing''<nowiki>:</nowiki><br />
* the lensing map;<br />
* beam error eigenmodes and covariance for the 143- and 217-GHz channel maps;<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt''<nowiki>:</nowiki><br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here];<br />
* the tSZ and kSZ template are changed to match those of CAMspec.<br />
<br />
''' File names and Meta-data '''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta-data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
--><br />
<br />
'''Likelihood Masks'''<br />
<br />
'''General description'''<br />
<br />
We provide the masks for Temperature and Polarisation used to exclude the regions of strongest foreground emission in the CMB maps when computing the empirical spectra that we use to form the high-&#8467 likelihood. The masks are provided for each frequency between 100 and 217 GHz, masking the appropriate part of the Galactic Plane and, for temperature only, the relevant population of point sources. Note that to compute the empirical power spectrum of the maps, one should also take into account missing pixels in a particular map. This is not included in the masks we distribute.<br />
<br />
'''Production Process'''<br />
Complete production process for those masks is described in {{PlanckPapers|planck2014-a13}}.<br />
<br />
The temperature masks are the combination of a Galactic mask, a point source mask and (for 100Ghz and 217GHz) a CO mask. Extended objects, planets, etc are included in the point source mask. <br />
The polarization masks are simply the Galactic masks.<br />
<br />
The Galactic masks are obtained by thresholding a CMB corrected and <math>10^o</math> smoothed 353GHz map. The threshold is tuned so as to retain a given fraction of the sky, between 50% and 80%. Each mask is apodized by a <math>4^o.71</math> FWHM gaussian window function using the distance map. Special care is taken to smooth this distance map, in order to avoid strong caustics. The apodization down-weights an effective 10% of the sky. Following {{PlanckPapers|planck2014-a13}}, the Galactic masks are named by the effective unmasked sky area G70, G60, G50 and G41.<br />
<br />
The point source masks are different for each frequency. They are based on the 2015 Planck catalog and cut out all the sources detected at S/N = 5 or higher in each channel. Each source is masked with a circular aperture of size 3xFWHM of that channel (i.e. 3x9.′66 at 100GHz, 3x7.′22 at 143GHz, and 3x4.′90 at 217GHz). Note that we include in the point source masks all sources above our threshold, including possible galactic ones. The mask is further apodized with a gaussian window function with FWHM=30'. <br />
<br />
The CO masks is used only at 100GHz and 217GHz, since there is no (strong) CO line in the 147 GHz channel. They are based on the Type 3 CO map from the Planck2013 delivery. The CO map is smoothed to 120' and a threshold is applied to mask all regions above <math>1 K_{RJ} km s^{−1}</math>. The mask is further apodized to 30'.<br />
<br />
Mask combinations are performed by multiplying a galactic, a point source, and possibly a CO mask together.<br />
<br />
The Temperature masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter T and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: T66 = G70+Point source mask 100Ghz+CO mask<br />
* 143Ghz: T57 = G60+Point source mask 143Ghz<br />
* 217Ghz: T47 = G50+Point source mask 217Ghz+CO mask<br />
<br />
The Polarization masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter P and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: P70 = G70<br />
* 143Ghz: P50 = G50<br />
* 217Ghz: P41 = G41<br />
<br />
'''Inputs'''<br />
* Galactic masks: The SMICA CMB temperature map, the 353GHz temperature map.<br />
* Point source masks: The Planck 2015 catalog, the FWHM of each of the frequencies.<br />
* CO mask: the Type 3 CO map from the Planck 2013 delivery.<br />
<br />
''' File names and meta-data '''<br />
The masks are distributed in a single tar file ''COM_Likelihood_Masks_R2.00.tar.gz''.<br />
The files extract to 6 files<br />
* temperature_100.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 100Ghz, i.e. T66<br />
* temperature_143.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 143Ghz, i.e. T57<br />
* temperature_217.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 217Ghz, i.e. T47<br />
* polarization_100.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 100Ghz, i.e. P70<br />
* polarization_143.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 143Ghz, i.e. P50<br />
* polarization_217.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 217Ghz, i.e. P41<br />
<br />
<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #EEE8AA;width:80%"><br />
'''2013 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''General description'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles <math> \ell </math> = 2-2479. Over the multipole range <math> \ell </math> = 2–49, the power spectrum is derived from a component-separation algorithm, ''Commander'', applied to maps in the frequency range 30–353 GHz over 91% of the sky {{PlanckPapers|planck2013-p06}}. The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction. For multipoles greater than <math>\ell=50</math>, instead, the spectrum is derived from the ''CAMspec'' likelihood {{PlanckPapers|planck2013-p08}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds. Associated 1-sigma errors include beam and foreground uncertainties. Both ''Commander'' and ''CAMspec'' are described in more details in the sections below.<br />
<br />
[[File: mission_spectrum.png|thumb|center|700px|'''CMB spectrum. Logarithmic x-scale up to <math>\ell=50</math>, linear at higher <math>\ell</math>; all points with error bars. The red line is the Planck best-fit primordial power spectrum (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}).''']]<br />
<br />
'''Likelihood'''<br />
<br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the Power spectrum & Likelihood Paper {{PlanckPapers|planck2013-p08}} (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) {{PlanckPapers|planck2013-p12}}.<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The ''Commander'' likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 ± 0.2 and a_gs = 0.4 ± 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. This means that the code will need both the TT and $\phi\phi$ power spectrum up to <math>\ell</math> = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between <math>\ell</math> = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
<br />
'''Production process'''<br />
<br />
'''CMB spectra'''<br />
<br />
The <math>\ell</math> < 50 part of the Planck power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters {{PlanckPapers|planck2013-p06}}. The power spectrum at any multipole <math>\ell</math> is given as the maximum probability point for the posterior <math>C_\ell</math> distribution, marginalized over the other multipoles, and the error bars are 68% confidence level {{PlanckPapers|planck2013-p08}}. <br />
<br />
The <math>\ell</math> > 50 part of the CMB temperature power spectrum has been derived by the CamSpec likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of {{PlanckPapers|planck2013-p08}}. Frequency spectra are computed as noise weighted averages of the cross-spectra between single detector and sets of detector maps. Mask and multipole range choices for each frequency spectrum are summarized in Table 4 of {{PlanckPapers|planck2013-p08}}. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of {{PlanckPapers|planck2013-p08}} and Sec. 4 of {{PlanckPapers|planck2013-p11}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with unresolved foreground and beam uncertainties. Both spectrum and associated covariance matrix are given as uniformly weighted band averages in 74 bins. <br />
<br />
'''Likelihood'''<br />
<br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each dataset comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<math>^{-6}</math> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
; Low-l spectrum (<math>\ell < 50</math>):<br />
* frequency maps from 30–353 GHz<br />
* common mask {{PlanckPapers|planck2013-p06}}<br />
* compact sources catalog<br />
<br />
; High-l spectrum (<math>50 < \ell < 2500</math>): <br />
<br />
* 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 2 in {{PlanckPapers|planck2013-p08}})<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of {{PlanckPapers|planck2013-p11}})<br />
* Beam transfer function uncertainties {{PlanckPapers|planck2013-p03c}}<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander'' :<br />
* all Planck channels maps<br />
* compact source catalogs<br />
* common masks<br />
* beam transfer functions for all channels<br />
<br />
; ''lowlike'' :<br />
* WMAP9 likelihood data<br />
* Low-<math>\ell</math> Commander map<br />
<br />
; ''CAMspec'' :<br />
* 100, 143 and 217 GHz detector and detsets maps<br />
* 857GHz channel map<br />
* compact source catalog<br />
* common masks (0,1 & 3)<br />
* beam transfer function and error eigenmodes and covariance for 100, 143 and 217 GHz detectors & detsets<br />
* theoretical templates for the tSZ and kSZ contributions<br />
* color corrections for the CIB emission for the 143 and 217GHz detectors and detsets<br />
* fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz<br />
<br />
; ''lensing'' :<br />
* the lensing map<br />
* beam error eigenmodes and covariance for the 143 and 217GHz channel maps<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt'' :<br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]<br />
* the tSZ andkSZ template are changed to match those of CAMspec<br />
<br />
''' File names and Meta data '''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The CMB spectrum and its covariance matrix are distributed in a single FITS file named <br />
* ''{{PLASingleFile | fileType=cosmo | name=COM_PowerSpect_CMB_R1.10.fits | link=COM_PowerSpect_CMB_R1.10.fits}}'' <br />
<br />
which contains 3 extensions<br />
<br />
; LOW-ELL (BINTABLE)<br />
: with the low ell part of the spectrum, not binned, and for l=2-49. The table columns are<br />
# ''ELL'' (integer): multipole number<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERRUP'' (float): the upward uncertainty<br />
# ''ERRDOWN'' (float): the downward uncertainty<br />
<br />
; HIGH-ELL (BINTABLE)<br />
: with the high-ell part of the spectrum, binned into 74 bins covering <math>\langle l \rangle = 47-2419\ </math> in bins of width <math>l=31</math> (with the exception of the last 4 bins that are wider). The table columns are as follows:<br />
# ''ELL'' (integer): mean multipole number of bin<br />
# ''L_MIN'' (integer): lowest multipole of bin<br />
# ''L_MAX'' (integer): highest multipole of bin<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERR'' (float): the uncertainty<br />
<br />
; COV-MAT (IMAGE)<br />
: with the covariance matrix of the high-ell part of the spectrum in a 74x74 pixel image, i.e., covering the same bins as the ''HIGH-ELL'' table.<br />
<br />
The spectra give $D_\ell = \ell(\ell+1)C_\ell / 2\pi$ in units of $\mu\, K^2$, and the covariance matrix is in units of $\mu\, K^4$. The spectra are shown in the figure below, in blue and red for the low- and high-<math>\ell</math> parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.<br />
<br />
[[File: CMBspect.jpg|thumb|center|700px|'''CMB spectrum. Linear x-scale; error bars only at high <math>\ell</math>.''']]<br />
<br />
'''Likelihood'''<br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
<br />
</div><br />
</div><br />
<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
[[Category:Mission products|008]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=14378CMB spectrum & Likelihood Code2018-07-16T13:22:42Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:CMB spectra and likelihood code}}<br />
<br />
== 2018 CMB spectra==<br />
<br />
<br />
===General description===<br />
====TT====<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 86% of the sky ({{PlanckPapers|planck2016-l06}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood {{PlanckPapers|planck2016-l05}}, with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.51.48.png|thumb|600px|center]]<br />
<br />
====TE, EE, and EB, BB ====<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. In the multipole range 2 ≤ l ≤ 29, we plot the power spectra estimates from the SimAll likelihood (though only the EE spectrum is used in the baseline parameter analysis at l ≤ 29), see {{PlanckPapers|planck2016-l06}}). .<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.52.35.png|thumb|600px|center]]<br />
[[File:Screen Shot 2018-07-16 at 05.52.24.png|thumb|600px|center]]<br />
<br />
<br />
In the range &#8467; = 2-29, we also release the <i>BB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2016-l03}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
==== Theory ====<br />
<br />
We also provide best-fit LCDM CMB power spectra from the baseline Planck TT,TE,EE+lowE+lensing. The spectra must be divided by the best-fit Planck map-based calibration parameter squared, calPlanck**2, to be compared to the coadded CMB spectra. The best-fit calPlanck value can be found in the file "COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt".<br />
<br />
===Production process===<br />
The Plik high-multipole likelihood (described in detail in {{PlanckPapers|planck2016-l05}}) is a Gaussian approximation of the probability distributions of the <i>TT</i>, <i>EE</i>, and <i>TE</i> angular power spectra, with semi-analytic covariance matrices calculated assuming a fiducial cosmology. It includes multipoles in the range 30 to 2508 for TT and 30 to 1996 for <i>TE</i> and <i>EE</i> and is constructed from half-mission cross-spectra measured from the 100-, 143-, and 217-GHz HFI frequency maps. For more details see {{PlanckPapers|planck2016-l06}}.<br />
<br />
<br />
<br />
===Inputs===<br />
<br />
The T T likelihood uses four half-mission cross-spectra with different multipole cuts to avoid multipole regions where noise dominates due to the limited resolution of the beams and to en-sure foreground contamination is correctly handled by our fore-ground model: 100 × 100 ( &#8467; = l = 30–1197); 143 × 143 (l = 30– 1996); 143 × 217 (l = 30–2508); and 217 × 217 (l = 30–2508). The TE and EE likelihoods also include the 100 × 143 and 100 × 217 cross-spectra to improve the signal-to-noise ratio, and have different multipole cuts: 100 × 100 (l = 30–999); 100 × 143 (l = 30–999); 100 × 217 (l = 505–999); 143 × 143 (l = 30– 1996); 143 × 217 (l = 505–1996); and 217 × 217 (l = 505– 1996). <br />
<br />
=== File names and meta-data ===<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
== 2018 Likelihood==<br />
<br />
The 2018 Likelihood code will be released at a later time.<br />
<br />
== Previous Releases: (2015) and (2013) CMB spectrum and Likelihood ==<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%"><br />
'''2015 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''2015 CMB spectra'''<br />
<br />
'''General description'''<br />
<br />
'''TT'''<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2014-a12}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP &Lambda;CDM run. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]<br />
<br />
'''TE, EE, and TB, EB, BB '''<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
'''Production process'''<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
'''Inputs'''<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
''' File names and meta-data '''<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
'''Likelihood'''<br />
<br />
The 2015 baseline likelihood release consists of a code package and a single data package. Four extended data packages are also available enabling exploration of alternatives to the baseline results.<br />
The code compiles to a library allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets. A data set permits the computation of a single likelihood among:<br />
* the high-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the low-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the CMB lensing reconstruction.<br />
By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.<br />
<br />
Only the baseline data package, ''COM_Likelihood_Data-baseline_R2.00.tar.gz'', will be fully described on this page. It contains six data sets, which are enough to compute all of the baseline Planck results that are discussed in {{PlanckPapers|planck2014-a14}}. In particular it allows for the computation of the CMB and lensing likelihood from either the Temperature data only, or the Temperature + Polarization combination.<br />
<br />
The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in {{PlanckPapers|planck2014-a13}} and {{PlanckPapers|planck2014-a17}}. Their full description is contained in the documentation included in each of the extended data packages.<br />
<br />
'''Library and tools'''<br />
<br />
'''Description'''<br />
The library consists of code written in C and Fortran 90. It can be called from both of<br />
those languages. Optionally, a python wrapper can be built as well. Scripts to<br />
simplify the linking of the library with other codes are part of the package, as<br />
well as some example codes that can be used to test the correct installation of<br />
the code and the integrity of the data packages. Optionally, a script is also available, allowing<br />
the user to modify the multipole range of the TT likelihoods and reproduce the hybridization<br />
test performed in the paper.<br />
A description of the tool, the API of the library, as well as different <br />
installation procedure are detailed in the ''readme.md'' file in the code package.<br />
<br />
'''File name'''<br />
The code can be extracted from <br />
''COM_Likelihood_Code-v2.0_R2.00.tar.bz2''.<br />
<br />
Please read the file ''readme.md'' for installation instructions.<br />
<br />
'''Data sets - Baseline data'''<br />
All of the released baseline data are distributed within a single file,<br />
''COM_Likelihood_Data-baseline_R2.00.tar.gz''.<br />
<br />
This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.<br />
<br />
Each data set is stored in its own directory. The directory structure follows similar rules<br />
for each data set, and stores data, template, and meta-data for each particular likelihood.<br />
<br />
As in 2013, the CMB likelihood is cut into low-&#8467; and high-&#8467; parts. Moreover, <br />
for each of those, we distribute both a T-only datafile and a joint T+P one. In the case <br />
of the high-&#8467; part, we also distribute two specific versions of the likelihood, <br />
that allow for estimate of T and T+P marginalized over the nuisance parameters.<br />
Combining both the low-&#8467; and high-&#8467; files, one can compute the likelihood over the<br />
range &#8467;=2-2508 in TT and &#8467;=2-1996 in TE and EE. A full description of the low-&#8467; <br />
and high-&#8467; likelihood is available in {{PlanckPapers|planck2014-a13}}.<br />
<br />
Similarly, for the case of lensing, we also distribute the likelihood using both<br />
the reconstruction based on the <i>T</i> map only, or on <i>T</i>+<i>P</i> maps. <br />
A full description of the lensing likelihood is available in {{PlanckPapers|planck2014-a17}}.<br />
<br />
All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that his parameter is explored in the Gaussian prior 1.0000&plusmn;0.0025.<br />
<br />
''' Low-&#8467; likelihoods '''<br />
<br />
'''TT only - commander'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=2-29.<br />
Using the optional tool in the code package, it can be modified to cover any multipole range <br />
up to &#8467;&lt;200. <br />
<br />
''' Production process'''<br />
The likelihood is based on the results of the Commander approach, which implements a <br />
Bayesian component separation method in pixel space, sampling the posterior distribution <br />
of the parameters of a model that describes both the CMB and the foreground emissions<br />
in a combination of the Planck maps, the WMAP map, and the 408-MHz survey. The samples<br />
of this exploration are used to infer the foreground marginalized low-&#8467; likelihood <br />
for any <i>TT</i> CMB spectrum. <br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
'''File name and usage'''<br />
The commander likelihood is distributed in <br />
''plc_2.0/low_l/commander/commander_rc2_v1.1_l2_29_B.clik''<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the vector really starts at &#8467;=0, although<br />
the first two entries are null.<br />
<br />
'''TEB '''<br />
This file allows for the computation of the CMB joint TT,EE, BB and TE likelihood <br />
in the range &#8467;=2-29. It should not be used with the low-&#8467; TT-only likelihood.<br />
<br />
''' Production process'''<br />
The file allows for the computation of the pixel based likelihood of <i>T</i>, <i>E</i>, and <i>B</i> <br />
maps. The <i>T</i> map is the best-fit map obtained from the commander algorithm, as described above, <br />
while the <i>E</i> and <i>B</i> maps are obtained from the 70GHz LFI full mission data, but excluding the second and fourth surveys. Foreground contamination is<br />
dealt with by marginalizing over templates based on the 30-GHz LFI and 353-GHz HFI maps.<br />
The covariance matrix comes from the Planck detector sensitivity modulated on the <br />
sky by the scanning strategy. The covariance matrix is further enlarged to account <br />
for the foreground template removal. <br />
To speed up the computation by about an order of magnitude, the problem is <br />
projected into <i>C</i><sub>&#8467;</sub> space using the Sherman-Morrison-Woodbury identity. Only the <br />
projected quantities are stored in the data package.<br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask {{PlanckPapers|planck2014-a12}}.<br />
<br />
<br />
'''File name and usage'''<br />
The low ell TEB likelihood is distributed in <br />
''plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive), followed by the <i>EE</i> (&#8467;=0 to 29), <br />
<i>BB</i> (&#8467;=0 to 29) and <i>TE</i> (&#8467;=0 to 29) spectra, and by an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the entries really start at &#8467;=0, although the<br />
&#8467;=0 and &#8467;=1 values will be null.<br />
<br />
''' High-&#8467; likelihoods '''<br />
<br />
'''TT only - Plik'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=30-2508.<br />
Using the optional tool in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>TT</i> cross-spectra. <br />
Only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission <i>T</i> maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by a vector of 16 nuisance parameters.<br />
Those are, in order:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217;<br />
* calib_100T, the relative calibration between the 100 and 143 spectra;<br />
* calib_217T, the relative calibration between the 217 and 143 spectra;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT+TE+EE - Plik'''<br />
This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range &#8467;=30-2508 for TT and &#8467;=30-1996 for TE and EE.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>T</i> and <i>E</i> cross-spectra. <br />
In temperature, only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used, while<br />
in <i>TE</i> and <i>EE</i> all of them are used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission T+P maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz and 353-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates;<br />
* best-fit CMB+foreground model for the beam-leakage template.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, plik TTTEEE likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik''.<br />
<br />
This file should not be used with any other TT-only high-&#8467; file.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed the <i>EE</i> and <i>TE</i> spectra (same range) and by a vector of 94 nuisance parameters.<br />
Those are, in g:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100TT;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143TT;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217TT;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217TT;<br />
* galf_EE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100EE;<br />
* galf_EE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143EE;<br />
* galf_EE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217EE;<br />
* galf_EE_A_143, the dust residual contamination at &#8467;=500 in 143&times;143EE;<br />
* galf_EE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217EE;<br />
* galf_EE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217EE;<br />
* galf_EE_index, the dust EE template slope, which should be set to -2.4;<br />
* galf_TE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100TE;<br />
* galf_TE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143TE;<br />
* galf_TE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217TE;<br />
* galf_TE_A_143, the dust residual contamination at &#8467;=500 in 143x143TE;<br />
* galf_TE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217TE;<br />
* galf_TE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217TE;<br />
* galf_TE_index, the dust EE template slope, which should be set to -2.4;<br />
* bleak_epsilon_0_0T_0E, beam-leakage parameter, espilon_0, 100&times;100 TE;<br />
* bleak_epsilon_1_0T_0E, beam-leakage parameter, espilon_1, 100&times;100 TE;<br />
* bleak_epsilon_2_0T_0E, beam-leakage parameter, espilon_2, 100&times;100 TE;<br />
* bleak_epsilon_3_0T_0E, beam-leakage parameter, espilon_3, 100&times;100 TE;<br />
* bleak_epsilon_4_0T_0E, beam-leakage parameter, espilon_4, 100&times;100 TE;<br />
* bleak_epsilon_0_0T_1E, beam-leakage parameter, espilon_0, 100&times;143 TE;<br />
* bleak_epsilon_1_0T_1E, beam-leakage parameter, espilon_1, 100&times;143 TE;<br />
* bleak_epsilon_2_0T_1E, beam-leakage parameter, espilon_2, 100&times;143 TE;<br />
* bleak_epsilon_3_0T_1E, beam-leakage parameter, espilon_3, 100&times;143 TE;<br />
* bleak_epsilon_4_0T_1E, beam-leakage parameter, espilon_4, 100&times;143 TE;<br />
* bleak_epsilon_0_0T_2E, beam-leakage parameter, espilon_0, 100&times;217 TE;<br />
* bleak_epsilon_1_0T_2E, beam-leakage parameter, espilon_1, 100&times;217 TE;<br />
* bleak_epsilon_2_0T_2E, beam-leakage parameter, espilon_2, 100&times;217 TE;<br />
* bleak_epsilon_3_0T_2E, beam-leakage parameter, espilon_3, 100&times;217 TE;<br />
* bleak_epsilon_4_0T_2E, beam-leakage parameter, espilon_4, 100&times;217 TE;<br />
* bleak_epsilon_0_1T_1E, beam-leakage parameter, espilon_0, 143&times;143 TE;<br />
* bleak_epsilon_1_1T_1E, beam-leakage parameter, espilon_1, 143&times;143 TE;<br />
* bleak_epsilon_2_1T_1E, beam-leakage parameter, espilon_2, 143&times;143 TE;<br />
* bleak_epsilon_3_1T_1E, beam-leakage parameter, espilon_3, 143&times;143 TE;<br />
* bleak_epsilon_4_1T_1E, beam-leakage parameter, espilon_4, 143&times;143 TE;<br />
* bleak_epsilon_0_1T_2E, beam-leakage parameter, espilon_0, 143&times;217 TE;<br />
* bleak_epsilon_1_1T_2E, beam-leakage parameter, espilon_1, 143&times;217 TE;<br />
* bleak_epsilon_2_1T_2E, beam-leakage parameter, espilon_2, 143&times;217 TE;<br />
* bleak_epsilon_3_1T_2E, beam-leakage parameter, espilon_3, 143&times;217 TE;<br />
* bleak_epsilon_4_1T_2E, beam-leakage parameter, espilon_4, 143&times;217 TE;<br />
* bleak_epsilon_0_2T_2E, beam-leakage parameter, espilon_0, 217&times;217 TE;<br />
* bleak_epsilon_1_2T_2E, beam-leakage parameter, espilon_1, 217&times;217 TE;<br />
* bleak_epsilon_2_2T_2E, beam-leakage parameter, espilon_2, 217&times;217 TE;<br />
* bleak_epsilon_3_2T_2E, beam-leakage parameter, espilon_3, 217&times;217 TE;<br />
* bleak_epsilon_4_2T_2E, beam-leakage parameter, espilon_4, 217&times;217 TE;<br />
* bleak_epsilon_0_0E_0E, beam-leakage parameter, espilon_0, 100&times;100 EE;<br />
* bleak_epsilon_1_0E_0E, beam-leakage parameter, espilon_1, 100&times;100 EE;<br />
* bleak_epsilon_2_0E_0E, beam-leakage parameter, espilon_2, 100&times;100 EE;<br />
* bleak_epsilon_3_0E_0E, beam-leakage parameter, espilon_3, 100&times;100 EE;<br />
* bleak_epsilon_4_0E_0E, beam-leakage parameter, espilon_4, 100&times;100 EE;<br />
* bleak_epsilon_0_0E_1E, beam-leakage parameter, espilon_0, 100&times;143 EE;<br />
* bleak_epsilon_1_0E_1E, beam-leakage parameter, espilon_1, 100&times;143 EE;<br />
* bleak_epsilon_2_0E_1E, beam-leakage parameter, espilon_2, 100&times;143 EE;<br />
* bleak_epsilon_3_0E_1E, beam-leakage parameter, espilon_3, 100&times;143 EE;<br />
* bleak_epsilon_4_0E_1E, beam-leakage parameter, espilon_4, 100&times;143 EE;<br />
* bleak_epsilon_0_0E_2E, beam-leakage parameter, espilon_0, 100&times;217 EE;<br />
* bleak_epsilon_1_0E_2E, beam-leakage parameter, espilon_1, 100&times;217 EE;<br />
* bleak_epsilon_2_0E_2E, beam-leakage parameter, espilon_2, 100&times;217 EE;<br />
* bleak_epsilon_3_0E_2E, beam-leakage parameter, espilon_3, 100&times;217 EE;<br />
* bleak_epsilon_4_0E_2E, beam-leakage parameter, espilon_4, 100&times;217 EE;<br />
* bleak_epsilon_0_1E_1E, beam-leakage parameter, espilon_0, 143&times;143 EE;<br />
* bleak_epsilon_1_1E_1E, beam-leakage parameter, espilon_1, 143&times;143 EE;<br />
* bleak_epsilon_2_1E_1E, beam-leakage parameter, espilon_2, 143&times;143 EE;<br />
* bleak_epsilon_3_1E_1E, beam-leakage parameter, espilon_3, 143&times;143 EE;<br />
* bleak_epsilon_4_1E_1E, beam-leakage parameter, espilon_4, 143&times;143 EE;<br />
* bleak_epsilon_0_1E_2E, beam-leakage parameter, espilon_0, 143&times;217 EE;<br />
* bleak_epsilon_1_1E_2E, beam-leakage parameter, espilon_1, 143&times;217 EE;<br />
* bleak_epsilon_2_1E_2E, beam-leakage parameter, espilon_2, 143&times;217 EE;<br />
* bleak_epsilon_3_1E_2E, beam-leakage parameter, espilon_3, 143&times;217 EE;<br />
* bleak_epsilon_4_1E_2E, beam-leakage parameter, espilon_4, 143&times;217 EE;<br />
* bleak_epsilon_0_2E_2E, beam-leakage parameter, espilon_0, 217&times;217 EE;<br />
* bleak_epsilon_1_2E_2E, beam-leakage parameter, espilon_1, 217&times;217 EE;<br />
* bleak_epsilon_2_2E_2E, beam-leakage parameter, espilon_2, 217&times;217 EE;<br />
* bleak_epsilon_3_2E_2E, beam-leakage parameter, espilon_3, 217&times;217 EE;<br />
* bleak_epsilon_4_2E_2E, beam-leakage parameter, espilon_4, 217&times;217 EE;<br />
* calib_100T, the relative calibration between 100 and 143 TT spectra;<br />
* calib_217T, the relative calibration between 217 and 143 TT spectra;<br />
* calib_100P, the calibration of the 100 EE spectra, which should be set to 1;<br />
* calib_143P, the calibration of the 143 EE spectra, which should be set to 1;<br />
* calib_217P, the calibration of the 217 EE spectra, which should be set to 1;<br />
* A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* galf_EE_A_100 = 0.060&plusmn;0.012;<br />
* galf_EE_A_100_143 = 0.050&plusmn;0.015;<br />
* galf_EE_A_100_217 = 0.110&plusmn;0.033;<br />
* galf_EE_A_143 = 0.10&plusmn;0.02;<br />
* galf_EE_A_143_217 = 0.240&plusmn;0.048;<br />
* galf_EE_A_217 = 0.72&plusmn;0.14;<br />
* galf_EE_index = -2.4;<br />
* galf_TE_A_100 = 0.140&plusmn;0.042;<br />
* galf_TE_A_100_143 = 0.120&plusmn;0.036;<br />
* galf_TE_A_100_217 = 0.30&plusmn;0.09;<br />
* galf_TE_A_143 = 0.240&plusmn;0.072;<br />
* galf_TE_A_143_217 = 0.60&plusmn;0.018;<br />
* galf_TE_A_217 = 1.80&plusmn;0.54;<br />
* galf_TE_index = -2.4;<br />
* bleak_epsilon_0_0T_0E = 0;<br />
* bleak_epsilon_1_0T_0E = 0;<br />
* bleak_epsilon_2_0T_0E = 0;<br />
* bleak_epsilon_3_0T_0E = 0;<br />
* bleak_epsilon_4_0T_0E = 0;<br />
* bleak_epsilon_0_0T_1E = 0;<br />
* bleak_epsilon_1_0T_1E = 0;<br />
* bleak_epsilon_2_0T_1E = 0;<br />
* bleak_epsilon_3_0T_1E = 0;<br />
* bleak_epsilon_4_0T_1E = 0;<br />
* bleak_epsilon_0_0T_2E = 0;<br />
* bleak_epsilon_1_0T_2E = 0;<br />
* bleak_epsilon_2_0T_2E = 0;<br />
* bleak_epsilon_3_0T_2E = 0;<br />
* bleak_epsilon_4_0T_2E = 0;<br />
* bleak_epsilon_0_1T_1E = 0;<br />
* bleak_epsilon_1_1T_1E = 0;<br />
* bleak_epsilon_2_1T_1E = 0;<br />
* bleak_epsilon_3_1T_1E = 0;<br />
* bleak_epsilon_4_1T_1E = 0;<br />
* bleak_epsilon_0_1T_2E = 0;<br />
* bleak_epsilon_1_1T_2E = 0;<br />
* bleak_epsilon_2_1T_2E = 0;<br />
* bleak_epsilon_3_1T_2E = 0;<br />
* bleak_epsilon_4_1T_2E = 0;<br />
* bleak_epsilon_0_2T_2E = 0;<br />
* bleak_epsilon_1_2T_2E = 0;<br />
* bleak_epsilon_2_2T_2E = 0;<br />
* bleak_epsilon_3_2T_2E = 0;<br />
* bleak_epsilon_4_2T_2E = 0;<br />
* bleak_epsilon_0_0E_0E = 0;<br />
* bleak_epsilon_1_0E_0E = 0;<br />
* bleak_epsilon_2_0E_0E = 0;<br />
* bleak_epsilon_3_0E_0E = 0;<br />
* bleak_epsilon_4_0E_0E = 0;<br />
* bleak_epsilon_0_0E_1E = 0;<br />
* bleak_epsilon_1_0E_1E = 0;<br />
* bleak_epsilon_2_0E_1E = 0;<br />
* bleak_epsilon_3_0E_1E = 0;<br />
* bleak_epsilon_4_0E_1E = 0;<br />
* bleak_epsilon_0_0E_2E = 0;<br />
* bleak_epsilon_1_0E_2E = 0;<br />
* bleak_epsilon_2_0E_2E = 0;<br />
* bleak_epsilon_3_0E_2E = 0;<br />
* bleak_epsilon_4_0E_2E = 0;<br />
* bleak_epsilon_0_1E_1E = 0;<br />
* bleak_epsilon_1_1E_1E = 0;<br />
* bleak_epsilon_2_1E_1E = 0;<br />
* bleak_epsilon_3_1E_1E = 0;<br />
* bleak_epsilon_4_1E_1E = 0;<br />
* bleak_epsilon_0_1E_2E = 0;<br />
* bleak_epsilon_1_1E_2E = 0;<br />
* bleak_epsilon_2_1E_2E = 0;<br />
* bleak_epsilon_3_1E_2E = 0;<br />
* bleak_epsilon_4_1E_2E = 0;<br />
* bleak_epsilon_0_2E_2E = 0;<br />
* bleak_epsilon_1_2E_2E = 0;<br />
* bleak_epsilon_2_2E_2E = 0;<br />
* bleak_epsilon_3_2E_2E = 0;<br />
* bleak_epsilon_4_2E_2E = 0;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* calib_100P = 1;<br />
* calib_143P = 1; <br />
* calib_217P = 1; <br />
* A_pol = 1;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT only - Plik lite'''<br />
This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range &#8467;=30-2508. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT</i> spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-&#8467; likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TT likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.<br />
<br />
'''TT EE TE - Plik lite'''<br />
This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range &#8467;=30-2508 for temperature and &#8467;=30-1996 for TE and EE. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT<i/>, <i>TE</i>, and <i>EE</i> spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TTTEEE likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TTTEEE, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the <i>EE</i>, and <i>TE</i> spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
''' Lensing likelihoods '''<br />
<br />
'''T only'''<br />
This file allows for the computation of the baseline lensing likelihood, using only the SMICA <i>T</i><br />
map-based lensing reconstruction. Only the lensing multipole range &#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of a model-dependent correction to the normalization and<br />
the "N1 bias." To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant "mean field" and "N0" contribution, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> CMB map;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i> spectrum is needed to compute the normalization and N1 corrections.<br />
<br />
'''T+P'''<br />
This file allows for the computation of the baseline lensing likelihood, using both the <br />
<i>T</i> and <i>P</i> SMICA map-based lensing reconstruction. Only the lensing multipole range&#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of model dependent correction to the normalization and<br />
the N1 bias. To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> and <i>P</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured outside a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> and <i>E</i> CMB maps;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T+P-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive), the <i>EE</i> and <i>TE</i> power spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i>, <i>EE</i>, and <i>TE</i> spectra are needed to compute the normalization and N1 corrections.<br />
<br />
'''Data sets - Extended data'''<br />
<br />
Four other data files are available.<br />
Those extend the baseline delivery by adding:<br />
* TE, EE and other joint high-&#8467 Plik likelihoods, ''COM_Likelihood_Data-extra-plik-HM-ext_R2.00.tar.gz'';<br />
* TT and TTTEEE unbinned high-&#8467 Plik likelihood, ''COM_Likelihood_Data-extra-plik-unbinned_R2.00.tar.gz'';<br />
* TT, TE, EE, and TTTEEE Plik likelihood using the detset cross-spectra instead of the half-mission one, and including empirical correlated noise correction for the TT spectra, ''COM_Likelihood_Data-extra-plik-DS_R2.00.tar.gz'';<br />
* extended &#8467 range lensing likelihood, ''COM_Likelihood_Data-extra-lensing-ext_R2.00.tar.gz''.<br />
<br />
Note that although these products are discussed in the Planck papers, they are not used for the baseline results.<br />
<br />
Each file contains a '''readme.md''' description of the content and the use of the different likelihood files.<br />
<br />
<br />
<br />
<!-- <br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the {{PlanckPapers|planck2013-p08|1|Power spectrum & Likelihood Paper}} (for the CMB based likelihood) and in the {{PlanckPapers|planck2013-p12|1|Lensing Paper}} (for the lensing likelihood) .<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The Commander likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 &plusmn; 0.2 and a_gs = 0.4 &plusmn; 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first-order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first-order renormalization procedure. This means that the code will need both the TT and &phi;&phi; power spectrum up to &#8467; = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between &#8467; = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
</span><br />
<span style="color:red">OUTSTANDING: description of likelihood masks </span><br />
'''Production process'''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each data set comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<sup>-6</sup> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander''<nowiki>:</nowiki><br />
* all Planck channel maps;<br />
* compact source catalogues;<br />
* common masks;<br />
* beam transfer functions for all channels.<br />
<br />
; ''lowlike''<nowiki>:</nowiki><br />
* WMAP9 likelihood data;<br />
* Low-<math>\ell</math> Commander map.<br />
<br />
; ''CAMspec''<nowiki>:</nowiki><br />
* 100-, 143- and 217-GHz detector and detsets maps;<br />
* 857GHz channel map;<br />
* compact source catalogue;<br />
* common masks (0,1 and 3);<br />
* beam transfer function and error eigenmodes and covariance for 100-, 143- and 217-GHz detectors and detsets;<br />
* theoretical templates for the tSZ and kSZ contributions;<br />
* color corrections for the CIB emission for the 143- and 217-GHz detectors and detsets;<br />
* fiducial CMB model (bootstrapped from WMAP7 best-fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz.<br />
<br />
; ''lensing''<nowiki>:</nowiki><br />
* the lensing map;<br />
* beam error eigenmodes and covariance for the 143- and 217-GHz channel maps;<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt''<nowiki>:</nowiki><br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here];<br />
* the tSZ and kSZ template are changed to match those of CAMspec.<br />
<br />
''' File names and Meta-data '''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta-data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
--><br />
<br />
'''Likelihood Masks'''<br />
<br />
'''General description'''<br />
<br />
We provide the masks for Temperature and Polarisation used to exclude the regions of strongest foreground emission in the CMB maps when computing the empirical spectra that we use to form the high-&#8467 likelihood. The masks are provided for each frequency between 100 and 217 GHz, masking the appropriate part of the Galactic Plane and, for temperature only, the relevant population of point sources. Note that to compute the empirical power spectrum of the maps, one should also take into account missing pixels in a particular map. This is not included in the masks we distribute.<br />
<br />
'''Production Process'''<br />
Complete production process for those masks is described in {{PlanckPapers|planck2014-a13}}.<br />
<br />
The temperature masks are the combination of a Galactic mask, a point source mask and (for 100Ghz and 217GHz) a CO mask. Extended objects, planets, etc are included in the point source mask. <br />
The polarization masks are simply the Galactic masks.<br />
<br />
The Galactic masks are obtained by thresholding a CMB corrected and <math>10^o</math> smoothed 353GHz map. The threshold is tuned so as to retain a given fraction of the sky, between 50% and 80%. Each mask is apodized by a <math>4^o.71</math> FWHM gaussian window function using the distance map. Special care is taken to smooth this distance map, in order to avoid strong caustics. The apodization down-weights an effective 10% of the sky. Following {{PlanckPapers|planck2014-a13}}, the Galactic masks are named by the effective unmasked sky area G70, G60, G50 and G41.<br />
<br />
The point source masks are different for each frequency. They are based on the 2015 Planck catalog and cut out all the sources detected at S/N = 5 or higher in each channel. Each source is masked with a circular aperture of size 3xFWHM of that channel (i.e. 3x9.′66 at 100GHz, 3x7.′22 at 143GHz, and 3x4.′90 at 217GHz). Note that we include in the point source masks all sources above our threshold, including possible galactic ones. The mask is further apodized with a gaussian window function with FWHM=30'. <br />
<br />
The CO masks is used only at 100GHz and 217GHz, since there is no (strong) CO line in the 147 GHz channel. They are based on the Type 3 CO map from the Planck2013 delivery. The CO map is smoothed to 120' and a threshold is applied to mask all regions above <math>1 K_{RJ} km s^{−1}</math>. The mask is further apodized to 30'.<br />
<br />
Mask combinations are performed by multiplying a galactic, a point source, and possibly a CO mask together.<br />
<br />
The Temperature masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter T and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: T66 = G70+Point source mask 100Ghz+CO mask<br />
* 143Ghz: T57 = G60+Point source mask 143Ghz<br />
* 217Ghz: T47 = G50+Point source mask 217Ghz+CO mask<br />
<br />
The Polarization masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter P and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: P70 = G70<br />
* 143Ghz: P50 = G50<br />
* 217Ghz: P41 = G41<br />
<br />
'''Inputs'''<br />
* Galactic masks: The SMICA CMB temperature map, the 353GHz temperature map.<br />
* Point source masks: The Planck 2015 catalog, the FWHM of each of the frequencies.<br />
* CO mask: the Type 3 CO map from the Planck 2013 delivery.<br />
<br />
''' File names and meta-data '''<br />
The masks are distributed in a single tar file ''COM_Likelihood_Masks_R2.00.tar.gz''.<br />
The files extract to 6 files<br />
* temperature_100.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 100Ghz, i.e. T66<br />
* temperature_143.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 143Ghz, i.e. T57<br />
* temperature_217.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 217Ghz, i.e. T47<br />
* polarization_100.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 100Ghz, i.e. P70<br />
* polarization_143.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 143Ghz, i.e. P50<br />
* polarization_217.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 217Ghz, i.e. P41<br />
<br />
<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #EEE8AA;width:80%"><br />
'''2013 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''General description'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles <math> \ell </math> = 2-2479. Over the multipole range <math> \ell </math> = 2–49, the power spectrum is derived from a component-separation algorithm, ''Commander'', applied to maps in the frequency range 30–353 GHz over 91% of the sky {{PlanckPapers|planck2013-p06}}. The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction. For multipoles greater than <math>\ell=50</math>, instead, the spectrum is derived from the ''CAMspec'' likelihood {{PlanckPapers|planck2013-p08}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds. Associated 1-sigma errors include beam and foreground uncertainties. Both ''Commander'' and ''CAMspec'' are described in more details in the sections below.<br />
<br />
[[File: mission_spectrum.png|thumb|center|700px|'''CMB spectrum. Logarithmic x-scale up to <math>\ell=50</math>, linear at higher <math>\ell</math>; all points with error bars. The red line is the Planck best-fit primordial power spectrum (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}).''']]<br />
<br />
'''Likelihood'''<br />
<br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the Power spectrum & Likelihood Paper {{PlanckPapers|planck2013-p08}} (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) {{PlanckPapers|planck2013-p12}}.<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The ''Commander'' likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 ± 0.2 and a_gs = 0.4 ± 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. This means that the code will need both the TT and $\phi\phi$ power spectrum up to <math>\ell</math> = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between <math>\ell</math> = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
<br />
'''Production process'''<br />
<br />
'''CMB spectra'''<br />
<br />
The <math>\ell</math> < 50 part of the Planck power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters {{PlanckPapers|planck2013-p06}}. The power spectrum at any multipole <math>\ell</math> is given as the maximum probability point for the posterior <math>C_\ell</math> distribution, marginalized over the other multipoles, and the error bars are 68% confidence level {{PlanckPapers|planck2013-p08}}. <br />
<br />
The <math>\ell</math> > 50 part of the CMB temperature power spectrum has been derived by the CamSpec likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of {{PlanckPapers|planck2013-p08}}. Frequency spectra are computed as noise weighted averages of the cross-spectra between single detector and sets of detector maps. Mask and multipole range choices for each frequency spectrum are summarized in Table 4 of {{PlanckPapers|planck2013-p08}}. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of {{PlanckPapers|planck2013-p08}} and Sec. 4 of {{PlanckPapers|planck2013-p11}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with unresolved foreground and beam uncertainties. Both spectrum and associated covariance matrix are given as uniformly weighted band averages in 74 bins. <br />
<br />
'''Likelihood'''<br />
<br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each dataset comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<math>^{-6}</math> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
; Low-l spectrum (<math>\ell < 50</math>):<br />
* frequency maps from 30–353 GHz<br />
* common mask {{PlanckPapers|planck2013-p06}}<br />
* compact sources catalog<br />
<br />
; High-l spectrum (<math>50 < \ell < 2500</math>): <br />
<br />
* 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 2 in {{PlanckPapers|planck2013-p08}})<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of {{PlanckPapers|planck2013-p11}})<br />
* Beam transfer function uncertainties {{PlanckPapers|planck2013-p03c}}<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander'' :<br />
* all Planck channels maps<br />
* compact source catalogs<br />
* common masks<br />
* beam transfer functions for all channels<br />
<br />
; ''lowlike'' :<br />
* WMAP9 likelihood data<br />
* Low-<math>\ell</math> Commander map<br />
<br />
; ''CAMspec'' :<br />
* 100, 143 and 217 GHz detector and detsets maps<br />
* 857GHz channel map<br />
* compact source catalog<br />
* common masks (0,1 & 3)<br />
* beam transfer function and error eigenmodes and covariance for 100, 143 and 217 GHz detectors & detsets<br />
* theoretical templates for the tSZ and kSZ contributions<br />
* color corrections for the CIB emission for the 143 and 217GHz detectors and detsets<br />
* fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz<br />
<br />
; ''lensing'' :<br />
* the lensing map<br />
* beam error eigenmodes and covariance for the 143 and 217GHz channel maps<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt'' :<br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]<br />
* the tSZ andkSZ template are changed to match those of CAMspec<br />
<br />
''' File names and Meta data '''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The CMB spectrum and its covariance matrix are distributed in a single FITS file named <br />
* ''{{PLASingleFile | fileType=cosmo | name=COM_PowerSpect_CMB_R1.10.fits | link=COM_PowerSpect_CMB_R1.10.fits}}'' <br />
<br />
which contains 3 extensions<br />
<br />
; LOW-ELL (BINTABLE)<br />
: with the low ell part of the spectrum, not binned, and for l=2-49. The table columns are<br />
# ''ELL'' (integer): multipole number<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERRUP'' (float): the upward uncertainty<br />
# ''ERRDOWN'' (float): the downward uncertainty<br />
<br />
; HIGH-ELL (BINTABLE)<br />
: with the high-ell part of the spectrum, binned into 74 bins covering <math>\langle l \rangle = 47-2419\ </math> in bins of width <math>l=31</math> (with the exception of the last 4 bins that are wider). The table columns are as follows:<br />
# ''ELL'' (integer): mean multipole number of bin<br />
# ''L_MIN'' (integer): lowest multipole of bin<br />
# ''L_MAX'' (integer): highest multipole of bin<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERR'' (float): the uncertainty<br />
<br />
; COV-MAT (IMAGE)<br />
: with the covariance matrix of the high-ell part of the spectrum in a 74x74 pixel image, i.e., covering the same bins as the ''HIGH-ELL'' table.<br />
<br />
The spectra give $D_\ell = \ell(\ell+1)C_\ell / 2\pi$ in units of $\mu\, K^2$, and the covariance matrix is in units of $\mu\, K^4$. The spectra are shown in the figure below, in blue and red for the low- and high-<math>\ell</math> parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.<br />
<br />
[[File: CMBspect.jpg|thumb|center|700px|'''CMB spectrum. Linear x-scale; error bars only at high <math>\ell</math>.''']]<br />
<br />
'''Likelihood'''<br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
<br />
</div><br />
</div><br />
<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
[[Category:Mission products|008]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=14377CMB spectrum & Likelihood Code2018-07-16T13:13:49Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:CMB spectra and likelihood code}}<br />
<br />
== 2018 CMB spectra==<br />
<br />
<br />
===General description===<br />
====TT====<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 86% of the sky ({{PlanckPapers|planck2016-l06}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood {{PlanckPapers|planck2016-l05}}, with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.51.48.png|thumb|600px|center]]<br />
<br />
====TE, EE, and EB, BB ====<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. In the multipole range 2 ≤ l ≤ 29, we plot the power spectra estimates from the SimAll likelihood (though only the EE spectrum is used in the baseline parameter analysis at l ≤ 29), see {{PlanckPapers|planck2016-l06}}). .<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.52.35.png|thumb|600px|center]]<br />
[[File:Screen Shot 2018-07-16 at 05.52.24.png|thumb|600px|center]]<br />
<br />
<br />
In the range &#8467; = 2-29, we also release the <i>BB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2016-l03}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
==== Theory ====<br />
<br />
We also provide best-fit LCDM CMB power spectra from the baseline Planck TT,TE,EE+lowE+lensing. The spectra must be divided by the best-fit Planck map-based calibration parameter squared, calPlanck**2, to be compared to the coadded CMB spectra. The best-fit calPlanck value can be found in the file "COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt".<br />
<br />
===Production process===<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2016-l06}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2016-l05}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
===Inputs===<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
=== File names and meta-data ===<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
== 2018 Likelihood==<br />
<br />
The 2018 Likelihood code will be released at a later time.<br />
<br />
== Previous Releases: (2015) and (2013) CMB spectrum and Likelihood ==<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%"><br />
'''2015 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''2015 CMB spectra'''<br />
<br />
'''General description'''<br />
<br />
'''TT'''<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2014-a12}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP &Lambda;CDM run. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]<br />
<br />
'''TE, EE, and TB, EB, BB '''<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
'''Production process'''<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
'''Inputs'''<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
''' File names and meta-data '''<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
'''Likelihood'''<br />
<br />
The 2015 baseline likelihood release consists of a code package and a single data package. Four extended data packages are also available enabling exploration of alternatives to the baseline results.<br />
The code compiles to a library allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets. A data set permits the computation of a single likelihood among:<br />
* the high-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the low-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the CMB lensing reconstruction.<br />
By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.<br />
<br />
Only the baseline data package, ''COM_Likelihood_Data-baseline_R2.00.tar.gz'', will be fully described on this page. It contains six data sets, which are enough to compute all of the baseline Planck results that are discussed in {{PlanckPapers|planck2014-a14}}. In particular it allows for the computation of the CMB and lensing likelihood from either the Temperature data only, or the Temperature + Polarization combination.<br />
<br />
The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in {{PlanckPapers|planck2014-a13}} and {{PlanckPapers|planck2014-a17}}. Their full description is contained in the documentation included in each of the extended data packages.<br />
<br />
'''Library and tools'''<br />
<br />
'''Description'''<br />
The library consists of code written in C and Fortran 90. It can be called from both of<br />
those languages. Optionally, a python wrapper can be built as well. Scripts to<br />
simplify the linking of the library with other codes are part of the package, as<br />
well as some example codes that can be used to test the correct installation of<br />
the code and the integrity of the data packages. Optionally, a script is also available, allowing<br />
the user to modify the multipole range of the TT likelihoods and reproduce the hybridization<br />
test performed in the paper.<br />
A description of the tool, the API of the library, as well as different <br />
installation procedure are detailed in the ''readme.md'' file in the code package.<br />
<br />
'''File name'''<br />
The code can be extracted from <br />
''COM_Likelihood_Code-v2.0_R2.00.tar.bz2''.<br />
<br />
Please read the file ''readme.md'' for installation instructions.<br />
<br />
'''Data sets - Baseline data'''<br />
All of the released baseline data are distributed within a single file,<br />
''COM_Likelihood_Data-baseline_R2.00.tar.gz''.<br />
<br />
This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.<br />
<br />
Each data set is stored in its own directory. The directory structure follows similar rules<br />
for each data set, and stores data, template, and meta-data for each particular likelihood.<br />
<br />
As in 2013, the CMB likelihood is cut into low-&#8467; and high-&#8467; parts. Moreover, <br />
for each of those, we distribute both a T-only datafile and a joint T+P one. In the case <br />
of the high-&#8467; part, we also distribute two specific versions of the likelihood, <br />
that allow for estimate of T and T+P marginalized over the nuisance parameters.<br />
Combining both the low-&#8467; and high-&#8467; files, one can compute the likelihood over the<br />
range &#8467;=2-2508 in TT and &#8467;=2-1996 in TE and EE. A full description of the low-&#8467; <br />
and high-&#8467; likelihood is available in {{PlanckPapers|planck2014-a13}}.<br />
<br />
Similarly, for the case of lensing, we also distribute the likelihood using both<br />
the reconstruction based on the <i>T</i> map only, or on <i>T</i>+<i>P</i> maps. <br />
A full description of the lensing likelihood is available in {{PlanckPapers|planck2014-a17}}.<br />
<br />
All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that his parameter is explored in the Gaussian prior 1.0000&plusmn;0.0025.<br />
<br />
''' Low-&#8467; likelihoods '''<br />
<br />
'''TT only - commander'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=2-29.<br />
Using the optional tool in the code package, it can be modified to cover any multipole range <br />
up to &#8467;&lt;200. <br />
<br />
''' Production process'''<br />
The likelihood is based on the results of the Commander approach, which implements a <br />
Bayesian component separation method in pixel space, sampling the posterior distribution <br />
of the parameters of a model that describes both the CMB and the foreground emissions<br />
in a combination of the Planck maps, the WMAP map, and the 408-MHz survey. The samples<br />
of this exploration are used to infer the foreground marginalized low-&#8467; likelihood <br />
for any <i>TT</i> CMB spectrum. <br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
'''File name and usage'''<br />
The commander likelihood is distributed in <br />
''plc_2.0/low_l/commander/commander_rc2_v1.1_l2_29_B.clik''<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the vector really starts at &#8467;=0, although<br />
the first two entries are null.<br />
<br />
'''TEB '''<br />
This file allows for the computation of the CMB joint TT,EE, BB and TE likelihood <br />
in the range &#8467;=2-29. It should not be used with the low-&#8467; TT-only likelihood.<br />
<br />
''' Production process'''<br />
The file allows for the computation of the pixel based likelihood of <i>T</i>, <i>E</i>, and <i>B</i> <br />
maps. The <i>T</i> map is the best-fit map obtained from the commander algorithm, as described above, <br />
while the <i>E</i> and <i>B</i> maps are obtained from the 70GHz LFI full mission data, but excluding the second and fourth surveys. Foreground contamination is<br />
dealt with by marginalizing over templates based on the 30-GHz LFI and 353-GHz HFI maps.<br />
The covariance matrix comes from the Planck detector sensitivity modulated on the <br />
sky by the scanning strategy. The covariance matrix is further enlarged to account <br />
for the foreground template removal. <br />
To speed up the computation by about an order of magnitude, the problem is <br />
projected into <i>C</i><sub>&#8467;</sub> space using the Sherman-Morrison-Woodbury identity. Only the <br />
projected quantities are stored in the data package.<br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask {{PlanckPapers|planck2014-a12}}.<br />
<br />
<br />
'''File name and usage'''<br />
The low ell TEB likelihood is distributed in <br />
''plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive), followed by the <i>EE</i> (&#8467;=0 to 29), <br />
<i>BB</i> (&#8467;=0 to 29) and <i>TE</i> (&#8467;=0 to 29) spectra, and by an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the entries really start at &#8467;=0, although the<br />
&#8467;=0 and &#8467;=1 values will be null.<br />
<br />
''' High-&#8467; likelihoods '''<br />
<br />
'''TT only - Plik'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=30-2508.<br />
Using the optional tool in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>TT</i> cross-spectra. <br />
Only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission <i>T</i> maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by a vector of 16 nuisance parameters.<br />
Those are, in order:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217;<br />
* calib_100T, the relative calibration between the 100 and 143 spectra;<br />
* calib_217T, the relative calibration between the 217 and 143 spectra;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT+TE+EE - Plik'''<br />
This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range &#8467;=30-2508 for TT and &#8467;=30-1996 for TE and EE.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>T</i> and <i>E</i> cross-spectra. <br />
In temperature, only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used, while<br />
in <i>TE</i> and <i>EE</i> all of them are used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission T+P maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz and 353-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates;<br />
* best-fit CMB+foreground model for the beam-leakage template.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, plik TTTEEE likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik''.<br />
<br />
This file should not be used with any other TT-only high-&#8467; file.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed the <i>EE</i> and <i>TE</i> spectra (same range) and by a vector of 94 nuisance parameters.<br />
Those are, in g:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100TT;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143TT;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217TT;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217TT;<br />
* galf_EE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100EE;<br />
* galf_EE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143EE;<br />
* galf_EE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217EE;<br />
* galf_EE_A_143, the dust residual contamination at &#8467;=500 in 143&times;143EE;<br />
* galf_EE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217EE;<br />
* galf_EE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217EE;<br />
* galf_EE_index, the dust EE template slope, which should be set to -2.4;<br />
* galf_TE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100TE;<br />
* galf_TE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143TE;<br />
* galf_TE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217TE;<br />
* galf_TE_A_143, the dust residual contamination at &#8467;=500 in 143x143TE;<br />
* galf_TE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217TE;<br />
* galf_TE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217TE;<br />
* galf_TE_index, the dust EE template slope, which should be set to -2.4;<br />
* bleak_epsilon_0_0T_0E, beam-leakage parameter, espilon_0, 100&times;100 TE;<br />
* bleak_epsilon_1_0T_0E, beam-leakage parameter, espilon_1, 100&times;100 TE;<br />
* bleak_epsilon_2_0T_0E, beam-leakage parameter, espilon_2, 100&times;100 TE;<br />
* bleak_epsilon_3_0T_0E, beam-leakage parameter, espilon_3, 100&times;100 TE;<br />
* bleak_epsilon_4_0T_0E, beam-leakage parameter, espilon_4, 100&times;100 TE;<br />
* bleak_epsilon_0_0T_1E, beam-leakage parameter, espilon_0, 100&times;143 TE;<br />
* bleak_epsilon_1_0T_1E, beam-leakage parameter, espilon_1, 100&times;143 TE;<br />
* bleak_epsilon_2_0T_1E, beam-leakage parameter, espilon_2, 100&times;143 TE;<br />
* bleak_epsilon_3_0T_1E, beam-leakage parameter, espilon_3, 100&times;143 TE;<br />
* bleak_epsilon_4_0T_1E, beam-leakage parameter, espilon_4, 100&times;143 TE;<br />
* bleak_epsilon_0_0T_2E, beam-leakage parameter, espilon_0, 100&times;217 TE;<br />
* bleak_epsilon_1_0T_2E, beam-leakage parameter, espilon_1, 100&times;217 TE;<br />
* bleak_epsilon_2_0T_2E, beam-leakage parameter, espilon_2, 100&times;217 TE;<br />
* bleak_epsilon_3_0T_2E, beam-leakage parameter, espilon_3, 100&times;217 TE;<br />
* bleak_epsilon_4_0T_2E, beam-leakage parameter, espilon_4, 100&times;217 TE;<br />
* bleak_epsilon_0_1T_1E, beam-leakage parameter, espilon_0, 143&times;143 TE;<br />
* bleak_epsilon_1_1T_1E, beam-leakage parameter, espilon_1, 143&times;143 TE;<br />
* bleak_epsilon_2_1T_1E, beam-leakage parameter, espilon_2, 143&times;143 TE;<br />
* bleak_epsilon_3_1T_1E, beam-leakage parameter, espilon_3, 143&times;143 TE;<br />
* bleak_epsilon_4_1T_1E, beam-leakage parameter, espilon_4, 143&times;143 TE;<br />
* bleak_epsilon_0_1T_2E, beam-leakage parameter, espilon_0, 143&times;217 TE;<br />
* bleak_epsilon_1_1T_2E, beam-leakage parameter, espilon_1, 143&times;217 TE;<br />
* bleak_epsilon_2_1T_2E, beam-leakage parameter, espilon_2, 143&times;217 TE;<br />
* bleak_epsilon_3_1T_2E, beam-leakage parameter, espilon_3, 143&times;217 TE;<br />
* bleak_epsilon_4_1T_2E, beam-leakage parameter, espilon_4, 143&times;217 TE;<br />
* bleak_epsilon_0_2T_2E, beam-leakage parameter, espilon_0, 217&times;217 TE;<br />
* bleak_epsilon_1_2T_2E, beam-leakage parameter, espilon_1, 217&times;217 TE;<br />
* bleak_epsilon_2_2T_2E, beam-leakage parameter, espilon_2, 217&times;217 TE;<br />
* bleak_epsilon_3_2T_2E, beam-leakage parameter, espilon_3, 217&times;217 TE;<br />
* bleak_epsilon_4_2T_2E, beam-leakage parameter, espilon_4, 217&times;217 TE;<br />
* bleak_epsilon_0_0E_0E, beam-leakage parameter, espilon_0, 100&times;100 EE;<br />
* bleak_epsilon_1_0E_0E, beam-leakage parameter, espilon_1, 100&times;100 EE;<br />
* bleak_epsilon_2_0E_0E, beam-leakage parameter, espilon_2, 100&times;100 EE;<br />
* bleak_epsilon_3_0E_0E, beam-leakage parameter, espilon_3, 100&times;100 EE;<br />
* bleak_epsilon_4_0E_0E, beam-leakage parameter, espilon_4, 100&times;100 EE;<br />
* bleak_epsilon_0_0E_1E, beam-leakage parameter, espilon_0, 100&times;143 EE;<br />
* bleak_epsilon_1_0E_1E, beam-leakage parameter, espilon_1, 100&times;143 EE;<br />
* bleak_epsilon_2_0E_1E, beam-leakage parameter, espilon_2, 100&times;143 EE;<br />
* bleak_epsilon_3_0E_1E, beam-leakage parameter, espilon_3, 100&times;143 EE;<br />
* bleak_epsilon_4_0E_1E, beam-leakage parameter, espilon_4, 100&times;143 EE;<br />
* bleak_epsilon_0_0E_2E, beam-leakage parameter, espilon_0, 100&times;217 EE;<br />
* bleak_epsilon_1_0E_2E, beam-leakage parameter, espilon_1, 100&times;217 EE;<br />
* bleak_epsilon_2_0E_2E, beam-leakage parameter, espilon_2, 100&times;217 EE;<br />
* bleak_epsilon_3_0E_2E, beam-leakage parameter, espilon_3, 100&times;217 EE;<br />
* bleak_epsilon_4_0E_2E, beam-leakage parameter, espilon_4, 100&times;217 EE;<br />
* bleak_epsilon_0_1E_1E, beam-leakage parameter, espilon_0, 143&times;143 EE;<br />
* bleak_epsilon_1_1E_1E, beam-leakage parameter, espilon_1, 143&times;143 EE;<br />
* bleak_epsilon_2_1E_1E, beam-leakage parameter, espilon_2, 143&times;143 EE;<br />
* bleak_epsilon_3_1E_1E, beam-leakage parameter, espilon_3, 143&times;143 EE;<br />
* bleak_epsilon_4_1E_1E, beam-leakage parameter, espilon_4, 143&times;143 EE;<br />
* bleak_epsilon_0_1E_2E, beam-leakage parameter, espilon_0, 143&times;217 EE;<br />
* bleak_epsilon_1_1E_2E, beam-leakage parameter, espilon_1, 143&times;217 EE;<br />
* bleak_epsilon_2_1E_2E, beam-leakage parameter, espilon_2, 143&times;217 EE;<br />
* bleak_epsilon_3_1E_2E, beam-leakage parameter, espilon_3, 143&times;217 EE;<br />
* bleak_epsilon_4_1E_2E, beam-leakage parameter, espilon_4, 143&times;217 EE;<br />
* bleak_epsilon_0_2E_2E, beam-leakage parameter, espilon_0, 217&times;217 EE;<br />
* bleak_epsilon_1_2E_2E, beam-leakage parameter, espilon_1, 217&times;217 EE;<br />
* bleak_epsilon_2_2E_2E, beam-leakage parameter, espilon_2, 217&times;217 EE;<br />
* bleak_epsilon_3_2E_2E, beam-leakage parameter, espilon_3, 217&times;217 EE;<br />
* bleak_epsilon_4_2E_2E, beam-leakage parameter, espilon_4, 217&times;217 EE;<br />
* calib_100T, the relative calibration between 100 and 143 TT spectra;<br />
* calib_217T, the relative calibration between 217 and 143 TT spectra;<br />
* calib_100P, the calibration of the 100 EE spectra, which should be set to 1;<br />
* calib_143P, the calibration of the 143 EE spectra, which should be set to 1;<br />
* calib_217P, the calibration of the 217 EE spectra, which should be set to 1;<br />
* A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* galf_EE_A_100 = 0.060&plusmn;0.012;<br />
* galf_EE_A_100_143 = 0.050&plusmn;0.015;<br />
* galf_EE_A_100_217 = 0.110&plusmn;0.033;<br />
* galf_EE_A_143 = 0.10&plusmn;0.02;<br />
* galf_EE_A_143_217 = 0.240&plusmn;0.048;<br />
* galf_EE_A_217 = 0.72&plusmn;0.14;<br />
* galf_EE_index = -2.4;<br />
* galf_TE_A_100 = 0.140&plusmn;0.042;<br />
* galf_TE_A_100_143 = 0.120&plusmn;0.036;<br />
* galf_TE_A_100_217 = 0.30&plusmn;0.09;<br />
* galf_TE_A_143 = 0.240&plusmn;0.072;<br />
* galf_TE_A_143_217 = 0.60&plusmn;0.018;<br />
* galf_TE_A_217 = 1.80&plusmn;0.54;<br />
* galf_TE_index = -2.4;<br />
* bleak_epsilon_0_0T_0E = 0;<br />
* bleak_epsilon_1_0T_0E = 0;<br />
* bleak_epsilon_2_0T_0E = 0;<br />
* bleak_epsilon_3_0T_0E = 0;<br />
* bleak_epsilon_4_0T_0E = 0;<br />
* bleak_epsilon_0_0T_1E = 0;<br />
* bleak_epsilon_1_0T_1E = 0;<br />
* bleak_epsilon_2_0T_1E = 0;<br />
* bleak_epsilon_3_0T_1E = 0;<br />
* bleak_epsilon_4_0T_1E = 0;<br />
* bleak_epsilon_0_0T_2E = 0;<br />
* bleak_epsilon_1_0T_2E = 0;<br />
* bleak_epsilon_2_0T_2E = 0;<br />
* bleak_epsilon_3_0T_2E = 0;<br />
* bleak_epsilon_4_0T_2E = 0;<br />
* bleak_epsilon_0_1T_1E = 0;<br />
* bleak_epsilon_1_1T_1E = 0;<br />
* bleak_epsilon_2_1T_1E = 0;<br />
* bleak_epsilon_3_1T_1E = 0;<br />
* bleak_epsilon_4_1T_1E = 0;<br />
* bleak_epsilon_0_1T_2E = 0;<br />
* bleak_epsilon_1_1T_2E = 0;<br />
* bleak_epsilon_2_1T_2E = 0;<br />
* bleak_epsilon_3_1T_2E = 0;<br />
* bleak_epsilon_4_1T_2E = 0;<br />
* bleak_epsilon_0_2T_2E = 0;<br />
* bleak_epsilon_1_2T_2E = 0;<br />
* bleak_epsilon_2_2T_2E = 0;<br />
* bleak_epsilon_3_2T_2E = 0;<br />
* bleak_epsilon_4_2T_2E = 0;<br />
* bleak_epsilon_0_0E_0E = 0;<br />
* bleak_epsilon_1_0E_0E = 0;<br />
* bleak_epsilon_2_0E_0E = 0;<br />
* bleak_epsilon_3_0E_0E = 0;<br />
* bleak_epsilon_4_0E_0E = 0;<br />
* bleak_epsilon_0_0E_1E = 0;<br />
* bleak_epsilon_1_0E_1E = 0;<br />
* bleak_epsilon_2_0E_1E = 0;<br />
* bleak_epsilon_3_0E_1E = 0;<br />
* bleak_epsilon_4_0E_1E = 0;<br />
* bleak_epsilon_0_0E_2E = 0;<br />
* bleak_epsilon_1_0E_2E = 0;<br />
* bleak_epsilon_2_0E_2E = 0;<br />
* bleak_epsilon_3_0E_2E = 0;<br />
* bleak_epsilon_4_0E_2E = 0;<br />
* bleak_epsilon_0_1E_1E = 0;<br />
* bleak_epsilon_1_1E_1E = 0;<br />
* bleak_epsilon_2_1E_1E = 0;<br />
* bleak_epsilon_3_1E_1E = 0;<br />
* bleak_epsilon_4_1E_1E = 0;<br />
* bleak_epsilon_0_1E_2E = 0;<br />
* bleak_epsilon_1_1E_2E = 0;<br />
* bleak_epsilon_2_1E_2E = 0;<br />
* bleak_epsilon_3_1E_2E = 0;<br />
* bleak_epsilon_4_1E_2E = 0;<br />
* bleak_epsilon_0_2E_2E = 0;<br />
* bleak_epsilon_1_2E_2E = 0;<br />
* bleak_epsilon_2_2E_2E = 0;<br />
* bleak_epsilon_3_2E_2E = 0;<br />
* bleak_epsilon_4_2E_2E = 0;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* calib_100P = 1;<br />
* calib_143P = 1; <br />
* calib_217P = 1; <br />
* A_pol = 1;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT only - Plik lite'''<br />
This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range &#8467;=30-2508. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT</i> spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-&#8467; likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TT likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.<br />
<br />
'''TT EE TE - Plik lite'''<br />
This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range &#8467;=30-2508 for temperature and &#8467;=30-1996 for TE and EE. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT<i/>, <i>TE</i>, and <i>EE</i> spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TTTEEE likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TTTEEE, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the <i>EE</i>, and <i>TE</i> spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
''' Lensing likelihoods '''<br />
<br />
'''T only'''<br />
This file allows for the computation of the baseline lensing likelihood, using only the SMICA <i>T</i><br />
map-based lensing reconstruction. Only the lensing multipole range &#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of a model-dependent correction to the normalization and<br />
the "N1 bias." To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant "mean field" and "N0" contribution, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> CMB map;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i> spectrum is needed to compute the normalization and N1 corrections.<br />
<br />
'''T+P'''<br />
This file allows for the computation of the baseline lensing likelihood, using both the <br />
<i>T</i> and <i>P</i> SMICA map-based lensing reconstruction. Only the lensing multipole range&#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of model dependent correction to the normalization and<br />
the N1 bias. To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> and <i>P</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured outside a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> and <i>E</i> CMB maps;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T+P-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive), the <i>EE</i> and <i>TE</i> power spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i>, <i>EE</i>, and <i>TE</i> spectra are needed to compute the normalization and N1 corrections.<br />
<br />
'''Data sets - Extended data'''<br />
<br />
Four other data files are available.<br />
Those extend the baseline delivery by adding:<br />
* TE, EE and other joint high-&#8467 Plik likelihoods, ''COM_Likelihood_Data-extra-plik-HM-ext_R2.00.tar.gz'';<br />
* TT and TTTEEE unbinned high-&#8467 Plik likelihood, ''COM_Likelihood_Data-extra-plik-unbinned_R2.00.tar.gz'';<br />
* TT, TE, EE, and TTTEEE Plik likelihood using the detset cross-spectra instead of the half-mission one, and including empirical correlated noise correction for the TT spectra, ''COM_Likelihood_Data-extra-plik-DS_R2.00.tar.gz'';<br />
* extended &#8467 range lensing likelihood, ''COM_Likelihood_Data-extra-lensing-ext_R2.00.tar.gz''.<br />
<br />
Note that although these products are discussed in the Planck papers, they are not used for the baseline results.<br />
<br />
Each file contains a '''readme.md''' description of the content and the use of the different likelihood files.<br />
<br />
<br />
<br />
<!-- <br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the {{PlanckPapers|planck2013-p08|1|Power spectrum & Likelihood Paper}} (for the CMB based likelihood) and in the {{PlanckPapers|planck2013-p12|1|Lensing Paper}} (for the lensing likelihood) .<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The Commander likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 &plusmn; 0.2 and a_gs = 0.4 &plusmn; 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first-order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first-order renormalization procedure. This means that the code will need both the TT and &phi;&phi; power spectrum up to &#8467; = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between &#8467; = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
</span><br />
<span style="color:red">OUTSTANDING: description of likelihood masks </span><br />
'''Production process'''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each data set comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<sup>-6</sup> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander''<nowiki>:</nowiki><br />
* all Planck channel maps;<br />
* compact source catalogues;<br />
* common masks;<br />
* beam transfer functions for all channels.<br />
<br />
; ''lowlike''<nowiki>:</nowiki><br />
* WMAP9 likelihood data;<br />
* Low-<math>\ell</math> Commander map.<br />
<br />
; ''CAMspec''<nowiki>:</nowiki><br />
* 100-, 143- and 217-GHz detector and detsets maps;<br />
* 857GHz channel map;<br />
* compact source catalogue;<br />
* common masks (0,1 and 3);<br />
* beam transfer function and error eigenmodes and covariance for 100-, 143- and 217-GHz detectors and detsets;<br />
* theoretical templates for the tSZ and kSZ contributions;<br />
* color corrections for the CIB emission for the 143- and 217-GHz detectors and detsets;<br />
* fiducial CMB model (bootstrapped from WMAP7 best-fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz.<br />
<br />
; ''lensing''<nowiki>:</nowiki><br />
* the lensing map;<br />
* beam error eigenmodes and covariance for the 143- and 217-GHz channel maps;<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt''<nowiki>:</nowiki><br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here];<br />
* the tSZ and kSZ template are changed to match those of CAMspec.<br />
<br />
''' File names and Meta-data '''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta-data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
--><br />
<br />
'''Likelihood Masks'''<br />
<br />
'''General description'''<br />
<br />
We provide the masks for Temperature and Polarisation used to exclude the regions of strongest foreground emission in the CMB maps when computing the empirical spectra that we use to form the high-&#8467 likelihood. The masks are provided for each frequency between 100 and 217 GHz, masking the appropriate part of the Galactic Plane and, for temperature only, the relevant population of point sources. Note that to compute the empirical power spectrum of the maps, one should also take into account missing pixels in a particular map. This is not included in the masks we distribute.<br />
<br />
'''Production Process'''<br />
Complete production process for those masks is described in {{PlanckPapers|planck2014-a13}}.<br />
<br />
The temperature masks are the combination of a Galactic mask, a point source mask and (for 100Ghz and 217GHz) a CO mask. Extended objects, planets, etc are included in the point source mask. <br />
The polarization masks are simply the Galactic masks.<br />
<br />
The Galactic masks are obtained by thresholding a CMB corrected and <math>10^o</math> smoothed 353GHz map. The threshold is tuned so as to retain a given fraction of the sky, between 50% and 80%. Each mask is apodized by a <math>4^o.71</math> FWHM gaussian window function using the distance map. Special care is taken to smooth this distance map, in order to avoid strong caustics. The apodization down-weights an effective 10% of the sky. Following {{PlanckPapers|planck2014-a13}}, the Galactic masks are named by the effective unmasked sky area G70, G60, G50 and G41.<br />
<br />
The point source masks are different for each frequency. They are based on the 2015 Planck catalog and cut out all the sources detected at S/N = 5 or higher in each channel. Each source is masked with a circular aperture of size 3xFWHM of that channel (i.e. 3x9.′66 at 100GHz, 3x7.′22 at 143GHz, and 3x4.′90 at 217GHz). Note that we include in the point source masks all sources above our threshold, including possible galactic ones. The mask is further apodized with a gaussian window function with FWHM=30'. <br />
<br />
The CO masks is used only at 100GHz and 217GHz, since there is no (strong) CO line in the 147 GHz channel. They are based on the Type 3 CO map from the Planck2013 delivery. The CO map is smoothed to 120' and a threshold is applied to mask all regions above <math>1 K_{RJ} km s^{−1}</math>. The mask is further apodized to 30'.<br />
<br />
Mask combinations are performed by multiplying a galactic, a point source, and possibly a CO mask together.<br />
<br />
The Temperature masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter T and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: T66 = G70+Point source mask 100Ghz+CO mask<br />
* 143Ghz: T57 = G60+Point source mask 143Ghz<br />
* 217Ghz: T47 = G50+Point source mask 217Ghz+CO mask<br />
<br />
The Polarization masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter P and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: P70 = G70<br />
* 143Ghz: P50 = G50<br />
* 217Ghz: P41 = G41<br />
<br />
'''Inputs'''<br />
* Galactic masks: The SMICA CMB temperature map, the 353GHz temperature map.<br />
* Point source masks: The Planck 2015 catalog, the FWHM of each of the frequencies.<br />
* CO mask: the Type 3 CO map from the Planck 2013 delivery.<br />
<br />
''' File names and meta-data '''<br />
The masks are distributed in a single tar file ''COM_Likelihood_Masks_R2.00.tar.gz''.<br />
The files extract to 6 files<br />
* temperature_100.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 100Ghz, i.e. T66<br />
* temperature_143.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 143Ghz, i.e. T57<br />
* temperature_217.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 217Ghz, i.e. T47<br />
* polarization_100.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 100Ghz, i.e. P70<br />
* polarization_143.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 143Ghz, i.e. P50<br />
* polarization_217.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 217Ghz, i.e. P41<br />
<br />
<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #EEE8AA;width:80%"><br />
'''2013 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''General description'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles <math> \ell </math> = 2-2479. Over the multipole range <math> \ell </math> = 2–49, the power spectrum is derived from a component-separation algorithm, ''Commander'', applied to maps in the frequency range 30–353 GHz over 91% of the sky {{PlanckPapers|planck2013-p06}}. The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction. For multipoles greater than <math>\ell=50</math>, instead, the spectrum is derived from the ''CAMspec'' likelihood {{PlanckPapers|planck2013-p08}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds. Associated 1-sigma errors include beam and foreground uncertainties. Both ''Commander'' and ''CAMspec'' are described in more details in the sections below.<br />
<br />
[[File: mission_spectrum.png|thumb|center|700px|'''CMB spectrum. Logarithmic x-scale up to <math>\ell=50</math>, linear at higher <math>\ell</math>; all points with error bars. The red line is the Planck best-fit primordial power spectrum (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}).''']]<br />
<br />
'''Likelihood'''<br />
<br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the Power spectrum & Likelihood Paper {{PlanckPapers|planck2013-p08}} (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) {{PlanckPapers|planck2013-p12}}.<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The ''Commander'' likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 ± 0.2 and a_gs = 0.4 ± 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. This means that the code will need both the TT and $\phi\phi$ power spectrum up to <math>\ell</math> = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between <math>\ell</math> = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
<br />
'''Production process'''<br />
<br />
'''CMB spectra'''<br />
<br />
The <math>\ell</math> < 50 part of the Planck power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters {{PlanckPapers|planck2013-p06}}. The power spectrum at any multipole <math>\ell</math> is given as the maximum probability point for the posterior <math>C_\ell</math> distribution, marginalized over the other multipoles, and the error bars are 68% confidence level {{PlanckPapers|planck2013-p08}}. <br />
<br />
The <math>\ell</math> > 50 part of the CMB temperature power spectrum has been derived by the CamSpec likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of {{PlanckPapers|planck2013-p08}}. Frequency spectra are computed as noise weighted averages of the cross-spectra between single detector and sets of detector maps. Mask and multipole range choices for each frequency spectrum are summarized in Table 4 of {{PlanckPapers|planck2013-p08}}. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of {{PlanckPapers|planck2013-p08}} and Sec. 4 of {{PlanckPapers|planck2013-p11}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with unresolved foreground and beam uncertainties. Both spectrum and associated covariance matrix are given as uniformly weighted band averages in 74 bins. <br />
<br />
'''Likelihood'''<br />
<br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each dataset comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<math>^{-6}</math> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
; Low-l spectrum (<math>\ell < 50</math>):<br />
* frequency maps from 30–353 GHz<br />
* common mask {{PlanckPapers|planck2013-p06}}<br />
* compact sources catalog<br />
<br />
; High-l spectrum (<math>50 < \ell < 2500</math>): <br />
<br />
* 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 2 in {{PlanckPapers|planck2013-p08}})<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of {{PlanckPapers|planck2013-p11}})<br />
* Beam transfer function uncertainties {{PlanckPapers|planck2013-p03c}}<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander'' :<br />
* all Planck channels maps<br />
* compact source catalogs<br />
* common masks<br />
* beam transfer functions for all channels<br />
<br />
; ''lowlike'' :<br />
* WMAP9 likelihood data<br />
* Low-<math>\ell</math> Commander map<br />
<br />
; ''CAMspec'' :<br />
* 100, 143 and 217 GHz detector and detsets maps<br />
* 857GHz channel map<br />
* compact source catalog<br />
* common masks (0,1 & 3)<br />
* beam transfer function and error eigenmodes and covariance for 100, 143 and 217 GHz detectors & detsets<br />
* theoretical templates for the tSZ and kSZ contributions<br />
* color corrections for the CIB emission for the 143 and 217GHz detectors and detsets<br />
* fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz<br />
<br />
; ''lensing'' :<br />
* the lensing map<br />
* beam error eigenmodes and covariance for the 143 and 217GHz channel maps<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt'' :<br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]<br />
* the tSZ andkSZ template are changed to match those of CAMspec<br />
<br />
''' File names and Meta data '''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The CMB spectrum and its covariance matrix are distributed in a single FITS file named <br />
* ''{{PLASingleFile | fileType=cosmo | name=COM_PowerSpect_CMB_R1.10.fits | link=COM_PowerSpect_CMB_R1.10.fits}}'' <br />
<br />
which contains 3 extensions<br />
<br />
; LOW-ELL (BINTABLE)<br />
: with the low ell part of the spectrum, not binned, and for l=2-49. The table columns are<br />
# ''ELL'' (integer): multipole number<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERRUP'' (float): the upward uncertainty<br />
# ''ERRDOWN'' (float): the downward uncertainty<br />
<br />
; HIGH-ELL (BINTABLE)<br />
: with the high-ell part of the spectrum, binned into 74 bins covering <math>\langle l \rangle = 47-2419\ </math> in bins of width <math>l=31</math> (with the exception of the last 4 bins that are wider). The table columns are as follows:<br />
# ''ELL'' (integer): mean multipole number of bin<br />
# ''L_MIN'' (integer): lowest multipole of bin<br />
# ''L_MAX'' (integer): highest multipole of bin<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERR'' (float): the uncertainty<br />
<br />
; COV-MAT (IMAGE)<br />
: with the covariance matrix of the high-ell part of the spectrum in a 74x74 pixel image, i.e., covering the same bins as the ''HIGH-ELL'' table.<br />
<br />
The spectra give $D_\ell = \ell(\ell+1)C_\ell / 2\pi$ in units of $\mu\, K^2$, and the covariance matrix is in units of $\mu\, K^4$. The spectra are shown in the figure below, in blue and red for the low- and high-<math>\ell</math> parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.<br />
<br />
[[File: CMBspect.jpg|thumb|center|700px|'''CMB spectrum. Linear x-scale; error bars only at high <math>\ell</math>.''']]<br />
<br />
'''Likelihood'''<br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
<br />
</div><br />
</div><br />
<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
[[Category:Mission products|008]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=14376CMB spectrum & Likelihood Code2018-07-16T13:06:27Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:CMB spectra and likelihood code}}<br />
<br />
== 2018 CMB spectra==<br />
<br />
<br />
===General description===<br />
====TT====<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 86% of the sky ({{PlanckPapers|planck2016-l06}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood {{PlanckPapers|planck2016-l05}}, with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.51.48.png|thumb|600px|center]]<br />
<br />
====TE, EE, and TB, EB, BB ====<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. In the multipole range 2 ≤ l ≤ 29, we plot the power spectra estimates from the SimAll likelihood (though only the EE spectrum is used in the baseline parameter analysis at l ≤ 29), see {{PlanckPapers|planck2016-l06}}). .<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.52.35.png|thumb|600px|center]]<br />
[[File:Screen Shot 2018-07-16 at 05.52.24.png|thumb|600px|center]]<br />
<br />
<br />
In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
===Production process===<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
===Inputs===<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
=== File names and meta-data ===<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
== 2018 Likelihood==<br />
<br />
The 2018 Likelihood code will be released at a later time.<br />
<br />
== Previous Releases: (2015) and (2013) CMB spectrum and Likelihood ==<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%"><br />
'''2015 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''2015 CMB spectra'''<br />
<br />
'''General description'''<br />
<br />
'''TT'''<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2014-a12}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP &Lambda;CDM run. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]<br />
<br />
'''TE, EE, and TB, EB, BB '''<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
'''Production process'''<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
'''Inputs'''<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
''' File names and meta-data '''<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
'''Likelihood'''<br />
<br />
The 2015 baseline likelihood release consists of a code package and a single data package. Four extended data packages are also available enabling exploration of alternatives to the baseline results.<br />
The code compiles to a library allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets. A data set permits the computation of a single likelihood among:<br />
* the high-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the low-&#8467; temperature and polarization CMB (jointly or separately);<br />
* the CMB lensing reconstruction.<br />
By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.<br />
<br />
Only the baseline data package, ''COM_Likelihood_Data-baseline_R2.00.tar.gz'', will be fully described on this page. It contains six data sets, which are enough to compute all of the baseline Planck results that are discussed in {{PlanckPapers|planck2014-a14}}. In particular it allows for the computation of the CMB and lensing likelihood from either the Temperature data only, or the Temperature + Polarization combination.<br />
<br />
The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in {{PlanckPapers|planck2014-a13}} and {{PlanckPapers|planck2014-a17}}. Their full description is contained in the documentation included in each of the extended data packages.<br />
<br />
'''Library and tools'''<br />
<br />
'''Description'''<br />
The library consists of code written in C and Fortran 90. It can be called from both of<br />
those languages. Optionally, a python wrapper can be built as well. Scripts to<br />
simplify the linking of the library with other codes are part of the package, as<br />
well as some example codes that can be used to test the correct installation of<br />
the code and the integrity of the data packages. Optionally, a script is also available, allowing<br />
the user to modify the multipole range of the TT likelihoods and reproduce the hybridization<br />
test performed in the paper.<br />
A description of the tool, the API of the library, as well as different <br />
installation procedure are detailed in the ''readme.md'' file in the code package.<br />
<br />
'''File name'''<br />
The code can be extracted from <br />
''COM_Likelihood_Code-v2.0_R2.00.tar.bz2''.<br />
<br />
Please read the file ''readme.md'' for installation instructions.<br />
<br />
'''Data sets - Baseline data'''<br />
All of the released baseline data are distributed within a single file,<br />
''COM_Likelihood_Data-baseline_R2.00.tar.gz''.<br />
<br />
This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.<br />
<br />
Each data set is stored in its own directory. The directory structure follows similar rules<br />
for each data set, and stores data, template, and meta-data for each particular likelihood.<br />
<br />
As in 2013, the CMB likelihood is cut into low-&#8467; and high-&#8467; parts. Moreover, <br />
for each of those, we distribute both a T-only datafile and a joint T+P one. In the case <br />
of the high-&#8467; part, we also distribute two specific versions of the likelihood, <br />
that allow for estimate of T and T+P marginalized over the nuisance parameters.<br />
Combining both the low-&#8467; and high-&#8467; files, one can compute the likelihood over the<br />
range &#8467;=2-2508 in TT and &#8467;=2-1996 in TE and EE. A full description of the low-&#8467; <br />
and high-&#8467; likelihood is available in {{PlanckPapers|planck2014-a13}}.<br />
<br />
Similarly, for the case of lensing, we also distribute the likelihood using both<br />
the reconstruction based on the <i>T</i> map only, or on <i>T</i>+<i>P</i> maps. <br />
A full description of the lensing likelihood is available in {{PlanckPapers|planck2014-a17}}.<br />
<br />
All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that his parameter is explored in the Gaussian prior 1.0000&plusmn;0.0025.<br />
<br />
''' Low-&#8467; likelihoods '''<br />
<br />
'''TT only - commander'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=2-29.<br />
Using the optional tool in the code package, it can be modified to cover any multipole range <br />
up to &#8467;&lt;200. <br />
<br />
''' Production process'''<br />
The likelihood is based on the results of the Commander approach, which implements a <br />
Bayesian component separation method in pixel space, sampling the posterior distribution <br />
of the parameters of a model that describes both the CMB and the foreground emissions<br />
in a combination of the Planck maps, the WMAP map, and the 408-MHz survey. The samples<br />
of this exploration are used to infer the foreground marginalized low-&#8467; likelihood <br />
for any <i>TT</i> CMB spectrum. <br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
'''File name and usage'''<br />
The commander likelihood is distributed in <br />
''plc_2.0/low_l/commander/commander_rc2_v1.1_l2_29_B.clik''<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the vector really starts at &#8467;=0, although<br />
the first two entries are null.<br />
<br />
'''TEB '''<br />
This file allows for the computation of the CMB joint TT,EE, BB and TE likelihood <br />
in the range &#8467;=2-29. It should not be used with the low-&#8467; TT-only likelihood.<br />
<br />
''' Production process'''<br />
The file allows for the computation of the pixel based likelihood of <i>T</i>, <i>E</i>, and <i>B</i> <br />
maps. The <i>T</i> map is the best-fit map obtained from the commander algorithm, as described above, <br />
while the <i>E</i> and <i>B</i> maps are obtained from the 70GHz LFI full mission data, but excluding the second and fourth surveys. Foreground contamination is<br />
dealt with by marginalizing over templates based on the 30-GHz LFI and 353-GHz HFI maps.<br />
The covariance matrix comes from the Planck detector sensitivity modulated on the <br />
sky by the scanning strategy. The covariance matrix is further enlarged to account <br />
for the foreground template removal. <br />
To speed up the computation by about an order of magnitude, the problem is <br />
projected into <i>C</i><sub>&#8467;</sub> space using the Sherman-Morrison-Woodbury identity. Only the <br />
projected quantities are stored in the data package.<br />
<br />
''' Inputs: '''<br />
* Planck 30- and 44-GHz frequency maps;<br />
* Planck 70- to 857-GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask {{PlanckPapers|planck2014-a12}}.<br />
<br />
<br />
'''File name and usage'''<br />
The low ell TEB likelihood is distributed in <br />
''plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive), followed by the <i>EE</i> (&#8467;=0 to 29), <br />
<i>BB</i> (&#8467;=0 to 29) and <i>TE</i> (&#8467;=0 to 29) spectra, and by an extra nuisance parameter <br />
consisting of the overall Planck calibration. Note that the entries really start at &#8467;=0, although the<br />
&#8467;=0 and &#8467;=1 values will be null.<br />
<br />
''' High-&#8467; likelihoods '''<br />
<br />
'''TT only - Plik'''<br />
This file allows for the computation of the CMB TT likelihood in the range &#8467;=30-2508.<br />
Using the optional tool in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>TT</i> cross-spectra. <br />
Only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission <i>T</i> maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by a vector of 16 nuisance parameters.<br />
Those are, in order:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217;<br />
* calib_100T, the relative calibration between the 100 and 143 spectra;<br />
* calib_217T, the relative calibration between the 217 and 143 spectra;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT+TE+EE - Plik'''<br />
This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range &#8467;=30-2508 for TT and &#8467;=30-1996 for TE and EE.<br />
<br />
''' Production process'''<br />
The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>T</i> and <i>E</i> cross-spectra. <br />
In temperature, only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used, while<br />
in <i>TE</i> and <i>EE</i> all of them are used. Masks and multipole <br />
ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.<br />
Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.<br />
The file also contains<br />
templates for the residual foreground contamination of each spectrum. The templates are needed<br />
to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is <br />
computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.<br />
The covariance matrix is computed for a fiducial <br />
cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.<br />
<br />
''' Inputs: '''<br />
* Planck 100-, 143-, and 217-GHz half-mission T+P maps;<br />
* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;<br />
* Planck 545-GHz and 353-GHz maps for the dust residual contamination template;<br />
* CIB, tSZ, kSZ, and CIB&times;SZ templates;<br />
* best-fit CMB+foreground model for the beam-leakage template.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, plik TTTEEE likelihood is distributed in <br />
''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik''.<br />
<br />
This file should not be used with any other TT-only high-&#8467; file.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed the <i>EE</i> and <i>TE</i> spectra (same range) and by a vector of 94 nuisance parameters.<br />
Those are, in g:<br />
* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;<br />
* cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;<br />
* xi_sz_cib, the SZ&times;CIB cross-correlation;<br />
* A_sz, the tSZ contamination at 143GHz;<br />
* ps_A_100_100, the point source contribution in 100&times;100;<br />
* ps_A_143_143, the point source contribution in 143&times;143;<br />
* ps_A_143_217, the point source contribution in 143&times;217;<br />
* ps_A_217_217, the point source contribution in 217&times;217;<br />
* ksz_norm, the kSZ contamination;<br />
* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100TT;<br />
* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143TT;<br />
* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217TT;<br />
* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217TT;<br />
* galf_EE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100EE;<br />
* galf_EE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143EE;<br />
* galf_EE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217EE;<br />
* galf_EE_A_143, the dust residual contamination at &#8467;=500 in 143&times;143EE;<br />
* galf_EE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217EE;<br />
* galf_EE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217EE;<br />
* galf_EE_index, the dust EE template slope, which should be set to -2.4;<br />
* galf_TE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100TE;<br />
* galf_TE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143TE;<br />
* galf_TE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217TE;<br />
* galf_TE_A_143, the dust residual contamination at &#8467;=500 in 143x143TE;<br />
* galf_TE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217TE;<br />
* galf_TE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217TE;<br />
* galf_TE_index, the dust EE template slope, which should be set to -2.4;<br />
* bleak_epsilon_0_0T_0E, beam-leakage parameter, espilon_0, 100&times;100 TE;<br />
* bleak_epsilon_1_0T_0E, beam-leakage parameter, espilon_1, 100&times;100 TE;<br />
* bleak_epsilon_2_0T_0E, beam-leakage parameter, espilon_2, 100&times;100 TE;<br />
* bleak_epsilon_3_0T_0E, beam-leakage parameter, espilon_3, 100&times;100 TE;<br />
* bleak_epsilon_4_0T_0E, beam-leakage parameter, espilon_4, 100&times;100 TE;<br />
* bleak_epsilon_0_0T_1E, beam-leakage parameter, espilon_0, 100&times;143 TE;<br />
* bleak_epsilon_1_0T_1E, beam-leakage parameter, espilon_1, 100&times;143 TE;<br />
* bleak_epsilon_2_0T_1E, beam-leakage parameter, espilon_2, 100&times;143 TE;<br />
* bleak_epsilon_3_0T_1E, beam-leakage parameter, espilon_3, 100&times;143 TE;<br />
* bleak_epsilon_4_0T_1E, beam-leakage parameter, espilon_4, 100&times;143 TE;<br />
* bleak_epsilon_0_0T_2E, beam-leakage parameter, espilon_0, 100&times;217 TE;<br />
* bleak_epsilon_1_0T_2E, beam-leakage parameter, espilon_1, 100&times;217 TE;<br />
* bleak_epsilon_2_0T_2E, beam-leakage parameter, espilon_2, 100&times;217 TE;<br />
* bleak_epsilon_3_0T_2E, beam-leakage parameter, espilon_3, 100&times;217 TE;<br />
* bleak_epsilon_4_0T_2E, beam-leakage parameter, espilon_4, 100&times;217 TE;<br />
* bleak_epsilon_0_1T_1E, beam-leakage parameter, espilon_0, 143&times;143 TE;<br />
* bleak_epsilon_1_1T_1E, beam-leakage parameter, espilon_1, 143&times;143 TE;<br />
* bleak_epsilon_2_1T_1E, beam-leakage parameter, espilon_2, 143&times;143 TE;<br />
* bleak_epsilon_3_1T_1E, beam-leakage parameter, espilon_3, 143&times;143 TE;<br />
* bleak_epsilon_4_1T_1E, beam-leakage parameter, espilon_4, 143&times;143 TE;<br />
* bleak_epsilon_0_1T_2E, beam-leakage parameter, espilon_0, 143&times;217 TE;<br />
* bleak_epsilon_1_1T_2E, beam-leakage parameter, espilon_1, 143&times;217 TE;<br />
* bleak_epsilon_2_1T_2E, beam-leakage parameter, espilon_2, 143&times;217 TE;<br />
* bleak_epsilon_3_1T_2E, beam-leakage parameter, espilon_3, 143&times;217 TE;<br />
* bleak_epsilon_4_1T_2E, beam-leakage parameter, espilon_4, 143&times;217 TE;<br />
* bleak_epsilon_0_2T_2E, beam-leakage parameter, espilon_0, 217&times;217 TE;<br />
* bleak_epsilon_1_2T_2E, beam-leakage parameter, espilon_1, 217&times;217 TE;<br />
* bleak_epsilon_2_2T_2E, beam-leakage parameter, espilon_2, 217&times;217 TE;<br />
* bleak_epsilon_3_2T_2E, beam-leakage parameter, espilon_3, 217&times;217 TE;<br />
* bleak_epsilon_4_2T_2E, beam-leakage parameter, espilon_4, 217&times;217 TE;<br />
* bleak_epsilon_0_0E_0E, beam-leakage parameter, espilon_0, 100&times;100 EE;<br />
* bleak_epsilon_1_0E_0E, beam-leakage parameter, espilon_1, 100&times;100 EE;<br />
* bleak_epsilon_2_0E_0E, beam-leakage parameter, espilon_2, 100&times;100 EE;<br />
* bleak_epsilon_3_0E_0E, beam-leakage parameter, espilon_3, 100&times;100 EE;<br />
* bleak_epsilon_4_0E_0E, beam-leakage parameter, espilon_4, 100&times;100 EE;<br />
* bleak_epsilon_0_0E_1E, beam-leakage parameter, espilon_0, 100&times;143 EE;<br />
* bleak_epsilon_1_0E_1E, beam-leakage parameter, espilon_1, 100&times;143 EE;<br />
* bleak_epsilon_2_0E_1E, beam-leakage parameter, espilon_2, 100&times;143 EE;<br />
* bleak_epsilon_3_0E_1E, beam-leakage parameter, espilon_3, 100&times;143 EE;<br />
* bleak_epsilon_4_0E_1E, beam-leakage parameter, espilon_4, 100&times;143 EE;<br />
* bleak_epsilon_0_0E_2E, beam-leakage parameter, espilon_0, 100&times;217 EE;<br />
* bleak_epsilon_1_0E_2E, beam-leakage parameter, espilon_1, 100&times;217 EE;<br />
* bleak_epsilon_2_0E_2E, beam-leakage parameter, espilon_2, 100&times;217 EE;<br />
* bleak_epsilon_3_0E_2E, beam-leakage parameter, espilon_3, 100&times;217 EE;<br />
* bleak_epsilon_4_0E_2E, beam-leakage parameter, espilon_4, 100&times;217 EE;<br />
* bleak_epsilon_0_1E_1E, beam-leakage parameter, espilon_0, 143&times;143 EE;<br />
* bleak_epsilon_1_1E_1E, beam-leakage parameter, espilon_1, 143&times;143 EE;<br />
* bleak_epsilon_2_1E_1E, beam-leakage parameter, espilon_2, 143&times;143 EE;<br />
* bleak_epsilon_3_1E_1E, beam-leakage parameter, espilon_3, 143&times;143 EE;<br />
* bleak_epsilon_4_1E_1E, beam-leakage parameter, espilon_4, 143&times;143 EE;<br />
* bleak_epsilon_0_1E_2E, beam-leakage parameter, espilon_0, 143&times;217 EE;<br />
* bleak_epsilon_1_1E_2E, beam-leakage parameter, espilon_1, 143&times;217 EE;<br />
* bleak_epsilon_2_1E_2E, beam-leakage parameter, espilon_2, 143&times;217 EE;<br />
* bleak_epsilon_3_1E_2E, beam-leakage parameter, espilon_3, 143&times;217 EE;<br />
* bleak_epsilon_4_1E_2E, beam-leakage parameter, espilon_4, 143&times;217 EE;<br />
* bleak_epsilon_0_2E_2E, beam-leakage parameter, espilon_0, 217&times;217 EE;<br />
* bleak_epsilon_1_2E_2E, beam-leakage parameter, espilon_1, 217&times;217 EE;<br />
* bleak_epsilon_2_2E_2E, beam-leakage parameter, espilon_2, 217&times;217 EE;<br />
* bleak_epsilon_3_2E_2E, beam-leakage parameter, espilon_3, 217&times;217 EE;<br />
* bleak_epsilon_4_2E_2E, beam-leakage parameter, espilon_4, 217&times;217 EE;<br />
* calib_100T, the relative calibration between 100 and 143 TT spectra;<br />
* calib_217T, the relative calibration between 217 and 143 TT spectra;<br />
* calib_100P, the calibration of the 100 EE spectra, which should be set to 1;<br />
* calib_143P, the calibration of the 143 EE spectra, which should be set to 1;<br />
* calib_217P, the calibration of the 217 EE spectra, which should be set to 1;<br />
* A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;<br />
* A_planck, the Planck absolute calibration.<br />
<br />
We recommend using the following Gaussian priors:<br />
<br />
* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;<br />
* cib_index = -1.3;<br />
* gal545_A_100 = 7&plusmn;2;<br />
* gal545_A_143 = 9&plusmn;2;<br />
* gal545_A_143_217 = 21.0&plusmn;8.5;<br />
* gal545_A_217 = 80&plusmn;20;<br />
* galf_EE_A_100 = 0.060&plusmn;0.012;<br />
* galf_EE_A_100_143 = 0.050&plusmn;0.015;<br />
* galf_EE_A_100_217 = 0.110&plusmn;0.033;<br />
* galf_EE_A_143 = 0.10&plusmn;0.02;<br />
* galf_EE_A_143_217 = 0.240&plusmn;0.048;<br />
* galf_EE_A_217 = 0.72&plusmn;0.14;<br />
* galf_EE_index = -2.4;<br />
* galf_TE_A_100 = 0.140&plusmn;0.042;<br />
* galf_TE_A_100_143 = 0.120&plusmn;0.036;<br />
* galf_TE_A_100_217 = 0.30&plusmn;0.09;<br />
* galf_TE_A_143 = 0.240&plusmn;0.072;<br />
* galf_TE_A_143_217 = 0.60&plusmn;0.018;<br />
* galf_TE_A_217 = 1.80&plusmn;0.54;<br />
* galf_TE_index = -2.4;<br />
* bleak_epsilon_0_0T_0E = 0;<br />
* bleak_epsilon_1_0T_0E = 0;<br />
* bleak_epsilon_2_0T_0E = 0;<br />
* bleak_epsilon_3_0T_0E = 0;<br />
* bleak_epsilon_4_0T_0E = 0;<br />
* bleak_epsilon_0_0T_1E = 0;<br />
* bleak_epsilon_1_0T_1E = 0;<br />
* bleak_epsilon_2_0T_1E = 0;<br />
* bleak_epsilon_3_0T_1E = 0;<br />
* bleak_epsilon_4_0T_1E = 0;<br />
* bleak_epsilon_0_0T_2E = 0;<br />
* bleak_epsilon_1_0T_2E = 0;<br />
* bleak_epsilon_2_0T_2E = 0;<br />
* bleak_epsilon_3_0T_2E = 0;<br />
* bleak_epsilon_4_0T_2E = 0;<br />
* bleak_epsilon_0_1T_1E = 0;<br />
* bleak_epsilon_1_1T_1E = 0;<br />
* bleak_epsilon_2_1T_1E = 0;<br />
* bleak_epsilon_3_1T_1E = 0;<br />
* bleak_epsilon_4_1T_1E = 0;<br />
* bleak_epsilon_0_1T_2E = 0;<br />
* bleak_epsilon_1_1T_2E = 0;<br />
* bleak_epsilon_2_1T_2E = 0;<br />
* bleak_epsilon_3_1T_2E = 0;<br />
* bleak_epsilon_4_1T_2E = 0;<br />
* bleak_epsilon_0_2T_2E = 0;<br />
* bleak_epsilon_1_2T_2E = 0;<br />
* bleak_epsilon_2_2T_2E = 0;<br />
* bleak_epsilon_3_2T_2E = 0;<br />
* bleak_epsilon_4_2T_2E = 0;<br />
* bleak_epsilon_0_0E_0E = 0;<br />
* bleak_epsilon_1_0E_0E = 0;<br />
* bleak_epsilon_2_0E_0E = 0;<br />
* bleak_epsilon_3_0E_0E = 0;<br />
* bleak_epsilon_4_0E_0E = 0;<br />
* bleak_epsilon_0_0E_1E = 0;<br />
* bleak_epsilon_1_0E_1E = 0;<br />
* bleak_epsilon_2_0E_1E = 0;<br />
* bleak_epsilon_3_0E_1E = 0;<br />
* bleak_epsilon_4_0E_1E = 0;<br />
* bleak_epsilon_0_0E_2E = 0;<br />
* bleak_epsilon_1_0E_2E = 0;<br />
* bleak_epsilon_2_0E_2E = 0;<br />
* bleak_epsilon_3_0E_2E = 0;<br />
* bleak_epsilon_4_0E_2E = 0;<br />
* bleak_epsilon_0_1E_1E = 0;<br />
* bleak_epsilon_1_1E_1E = 0;<br />
* bleak_epsilon_2_1E_1E = 0;<br />
* bleak_epsilon_3_1E_1E = 0;<br />
* bleak_epsilon_4_1E_1E = 0;<br />
* bleak_epsilon_0_1E_2E = 0;<br />
* bleak_epsilon_1_1E_2E = 0;<br />
* bleak_epsilon_2_1E_2E = 0;<br />
* bleak_epsilon_3_1E_2E = 0;<br />
* bleak_epsilon_4_1E_2E = 0;<br />
* bleak_epsilon_0_2E_2E = 0;<br />
* bleak_epsilon_1_2E_2E = 0;<br />
* bleak_epsilon_2_2E_2E = 0;<br />
* bleak_epsilon_3_2E_2E = 0;<br />
* bleak_epsilon_4_2E_2E = 0;<br />
* calib_100T = 0.999&plusmn;0.001;<br />
* calib_217T = 0.995&plusmn;0.002;<br />
* calib_100P = 1;<br />
* calib_143P = 1; <br />
* calib_217P = 1; <br />
* A_pol = 1;<br />
* A_planck = 1.0000&plusmn;0.0025.<br />
<br />
'''TT only - Plik lite'''<br />
This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range &#8467;=30-2508. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT</i> spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-&#8467; likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TT likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TT, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.<br />
<br />
'''TT EE TE - Plik lite'''<br />
This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range &#8467;=30-2508 for temperature and &#8467;=30-1996 for TE and EE. It should not be used with the regular high-&#8467; TT or TTTEEE files.<br />
<br />
<br />
''' Production process'''<br />
The Plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT<i/>, <i>TE</i>, and <i>EE</i> spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the <br />
CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.<br />
<br />
<br />
''' Inputs: '''<br />
* Plik plik_dx11dr2_HM_v18_TTTEEE likelihood;<br />
* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.<br />
<br />
'''File name and usage'''<br />
The high-&#8467;, Plik TTTEEE, nuisance-marginalized likelihood is distributed in <br />
''plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the <i>EE</i>, and <i>TE</i> spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
''' Lensing likelihoods '''<br />
<br />
'''T only'''<br />
This file allows for the computation of the baseline lensing likelihood, using only the SMICA <i>T</i><br />
map-based lensing reconstruction. Only the lensing multipole range &#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of a model-dependent correction to the normalization and<br />
the "N1 bias." To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant "mean field" and "N0" contribution, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> CMB map;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i> spectrum is needed to compute the normalization and N1 corrections.<br />
<br />
'''T+P'''<br />
This file allows for the computation of the baseline lensing likelihood, using both the <br />
<i>T</i> and <i>P</i> SMICA map-based lensing reconstruction. Only the lensing multipole range&#8467;=40-400<br />
is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes <br />
the computation of model dependent correction to the normalization and<br />
the N1 bias. To speed up those computations, both are performed using a linear approximation.<br />
<br />
''' Production process'''<br />
The SMICA <i>T</i> and <i>P</i> maps are filtered and correlated to reconstruct an optimal <br />
lensing reconstruction map. Biases are corrected using Monte Carlo simulations<br />
for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured outside a large mask, and binned.<br />
The covariance matrix of this binned spectrum is evaluated using numerical simulations.<br />
The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.<br />
<br />
''' Inputs: '''<br />
* SMICA <i>T</i> and <i>E</i> CMB maps;<br />
* 60% Galactic mask;<br />
* best-fit Planck CMB model.<br />
<br />
'''File name and usage'''<br />
The T+P-only lensing likelihood is distributed in <br />
''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing''.<br />
<br />
When used with the library, this expects a vector of parameters consisting of the <br />
&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the <br />
<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive), the <i>EE</i> and <i>TE</i> power spectra (same range) and by the Planck absolute calibration nuisance parameter.<br />
<br />
The <i>TT</i>, <i>EE</i>, and <i>TE</i> spectra are needed to compute the normalization and N1 corrections.<br />
<br />
'''Data sets - Extended data'''<br />
<br />
Four other data files are available.<br />
Those extend the baseline delivery by adding:<br />
* TE, EE and other joint high-&#8467 Plik likelihoods, ''COM_Likelihood_Data-extra-plik-HM-ext_R2.00.tar.gz'';<br />
* TT and TTTEEE unbinned high-&#8467 Plik likelihood, ''COM_Likelihood_Data-extra-plik-unbinned_R2.00.tar.gz'';<br />
* TT, TE, EE, and TTTEEE Plik likelihood using the detset cross-spectra instead of the half-mission one, and including empirical correlated noise correction for the TT spectra, ''COM_Likelihood_Data-extra-plik-DS_R2.00.tar.gz'';<br />
* extended &#8467 range lensing likelihood, ''COM_Likelihood_Data-extra-lensing-ext_R2.00.tar.gz''.<br />
<br />
Note that although these products are discussed in the Planck papers, they are not used for the baseline results.<br />
<br />
Each file contains a '''readme.md''' description of the content and the use of the different likelihood files.<br />
<br />
<br />
<br />
<!-- <br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the {{PlanckPapers|planck2013-p08|1|Power spectrum & Likelihood Paper}} (for the CMB based likelihood) and in the {{PlanckPapers|planck2013-p12|1|Lensing Paper}} (for the lensing likelihood) .<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The Commander likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 &plusmn; 0.2 and a_gs = 0.4 &plusmn; 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first-order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first-order renormalization procedure. This means that the code will need both the TT and &phi;&phi; power spectrum up to &#8467; = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between &#8467; = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
</span><br />
<span style="color:red">OUTSTANDING: description of likelihood masks </span><br />
'''Production process'''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each data set comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<sup>-6</sup> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander''<nowiki>:</nowiki><br />
* all Planck channel maps;<br />
* compact source catalogues;<br />
* common masks;<br />
* beam transfer functions for all channels.<br />
<br />
; ''lowlike''<nowiki>:</nowiki><br />
* WMAP9 likelihood data;<br />
* Low-<math>\ell</math> Commander map.<br />
<br />
; ''CAMspec''<nowiki>:</nowiki><br />
* 100-, 143- and 217-GHz detector and detsets maps;<br />
* 857GHz channel map;<br />
* compact source catalogue;<br />
* common masks (0,1 and 3);<br />
* beam transfer function and error eigenmodes and covariance for 100-, 143- and 217-GHz detectors and detsets;<br />
* theoretical templates for the tSZ and kSZ contributions;<br />
* color corrections for the CIB emission for the 143- and 217-GHz detectors and detsets;<br />
* fiducial CMB model (bootstrapped from WMAP7 best-fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz.<br />
<br />
; ''lensing''<nowiki>:</nowiki><br />
* the lensing map;<br />
* beam error eigenmodes and covariance for the 143- and 217-GHz channel maps;<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt''<nowiki>:</nowiki><br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here];<br />
* the tSZ and kSZ template are changed to match those of CAMspec.<br />
<br />
''' File names and Meta-data '''<br />
<br />
'''Likelihood'''<br />
<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span><br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta-data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
--><br />
<br />
'''Likelihood Masks'''<br />
<br />
'''General description'''<br />
<br />
We provide the masks for Temperature and Polarisation used to exclude the regions of strongest foreground emission in the CMB maps when computing the empirical spectra that we use to form the high-&#8467 likelihood. The masks are provided for each frequency between 100 and 217 GHz, masking the appropriate part of the Galactic Plane and, for temperature only, the relevant population of point sources. Note that to compute the empirical power spectrum of the maps, one should also take into account missing pixels in a particular map. This is not included in the masks we distribute.<br />
<br />
'''Production Process'''<br />
Complete production process for those masks is described in {{PlanckPapers|planck2014-a13}}.<br />
<br />
The temperature masks are the combination of a Galactic mask, a point source mask and (for 100Ghz and 217GHz) a CO mask. Extended objects, planets, etc are included in the point source mask. <br />
The polarization masks are simply the Galactic masks.<br />
<br />
The Galactic masks are obtained by thresholding a CMB corrected and <math>10^o</math> smoothed 353GHz map. The threshold is tuned so as to retain a given fraction of the sky, between 50% and 80%. Each mask is apodized by a <math>4^o.71</math> FWHM gaussian window function using the distance map. Special care is taken to smooth this distance map, in order to avoid strong caustics. The apodization down-weights an effective 10% of the sky. Following {{PlanckPapers|planck2014-a13}}, the Galactic masks are named by the effective unmasked sky area G70, G60, G50 and G41.<br />
<br />
The point source masks are different for each frequency. They are based on the 2015 Planck catalog and cut out all the sources detected at S/N = 5 or higher in each channel. Each source is masked with a circular aperture of size 3xFWHM of that channel (i.e. 3x9.′66 at 100GHz, 3x7.′22 at 143GHz, and 3x4.′90 at 217GHz). Note that we include in the point source masks all sources above our threshold, including possible galactic ones. The mask is further apodized with a gaussian window function with FWHM=30'. <br />
<br />
The CO masks is used only at 100GHz and 217GHz, since there is no (strong) CO line in the 147 GHz channel. They are based on the Type 3 CO map from the Planck2013 delivery. The CO map is smoothed to 120' and a threshold is applied to mask all regions above <math>1 K_{RJ} km s^{−1}</math>. The mask is further apodized to 30'.<br />
<br />
Mask combinations are performed by multiplying a galactic, a point source, and possibly a CO mask together.<br />
<br />
The Temperature masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter T and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: T66 = G70+Point source mask 100Ghz+CO mask<br />
* 143Ghz: T57 = G60+Point source mask 143Ghz<br />
* 217Ghz: T47 = G50+Point source mask 217Ghz+CO mask<br />
<br />
The Polarization masks are named in {{PlanckPapers|planck2014-a13}} using the capital letter P and the effective sky fraction that is left unmasked. They are produced using the following <br />
* 100Ghz: P70 = G70<br />
* 143Ghz: P50 = G50<br />
* 217Ghz: P41 = G41<br />
<br />
'''Inputs'''<br />
* Galactic masks: The SMICA CMB temperature map, the 353GHz temperature map.<br />
* Point source masks: The Planck 2015 catalog, the FWHM of each of the frequencies.<br />
* CO mask: the Type 3 CO map from the Planck 2013 delivery.<br />
<br />
''' File names and meta-data '''<br />
The masks are distributed in a single tar file ''COM_Likelihood_Masks_R2.00.tar.gz''.<br />
The files extract to 6 files<br />
* temperature_100.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 100Ghz, i.e. T66<br />
* temperature_143.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 143Ghz, i.e. T57<br />
* temperature_217.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 217Ghz, i.e. T47<br />
* polarization_100.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 100Ghz, i.e. P70<br />
* polarization_143.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 143Ghz, i.e. P50<br />
* polarization_217.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 217Ghz, i.e. P41<br />
<br />
<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #EEE8AA;width:80%"><br />
'''2013 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''General description'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles <math> \ell </math> = 2-2479. Over the multipole range <math> \ell </math> = 2–49, the power spectrum is derived from a component-separation algorithm, ''Commander'', applied to maps in the frequency range 30–353 GHz over 91% of the sky {{PlanckPapers|planck2013-p06}}. The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction. For multipoles greater than <math>\ell=50</math>, instead, the spectrum is derived from the ''CAMspec'' likelihood {{PlanckPapers|planck2013-p08}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds. Associated 1-sigma errors include beam and foreground uncertainties. Both ''Commander'' and ''CAMspec'' are described in more details in the sections below.<br />
<br />
[[File: mission_spectrum.png|thumb|center|700px|'''CMB spectrum. Logarithmic x-scale up to <math>\ell=50</math>, linear at higher <math>\ell</math>; all points with error bars. The red line is the Planck best-fit primordial power spectrum (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}).''']]<br />
<br />
'''Likelihood'''<br />
<br />
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the Power spectrum & Likelihood Paper {{PlanckPapers|planck2013-p08}} (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) {{PlanckPapers|planck2013-p12}}.<br />
<br />
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute<br />
* one low-<math>\ell</math> temperature only likelihood (commander), <br />
* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and <br />
* one higl-<math>\ell</math> likelihood CAMspec. <br />
<br />
The ''Commander'' likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.<br />
<br />
The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.<br />
<br />
The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.<br />
<br />
The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 ± 0.2 and a_gs = 0.4 ± 0.2. Those priors are not included in the log likelihood computed by the code.<br />
<br />
The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. This means that the code will need both the TT and $\phi\phi$ power spectrum up to <math>\ell</math> = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between <math>\ell</math> = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.<br />
<br />
'''Production process'''<br />
<br />
'''CMB spectra'''<br />
<br />
The <math>\ell</math> < 50 part of the Planck power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters {{PlanckPapers|planck2013-p06}}. The power spectrum at any multipole <math>\ell</math> is given as the maximum probability point for the posterior <math>C_\ell</math> distribution, marginalized over the other multipoles, and the error bars are 68% confidence level {{PlanckPapers|planck2013-p08}}. <br />
<br />
The <math>\ell</math> > 50 part of the CMB temperature power spectrum has been derived by the CamSpec likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of {{PlanckPapers|planck2013-p08}}. Frequency spectra are computed as noise weighted averages of the cross-spectra between single detector and sets of detector maps. Mask and multipole range choices for each frequency spectrum are summarized in Table 4 of {{PlanckPapers|planck2013-p08}}. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of {{PlanckPapers|planck2013-p08}} and Sec. 4 of {{PlanckPapers|planck2013-p11}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with unresolved foreground and beam uncertainties. Both spectrum and associated covariance matrix are given as uniformly weighted band averages in 74 bins. <br />
<br />
'''Likelihood'''<br />
<br />
The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950 cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}} for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.<br />
<br />
Each dataset comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<math>^{-6}</math> or less are expected depending of the architecture.<br />
<br />
'''Inputs'''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
; Low-l spectrum (<math>\ell < 50</math>):<br />
* frequency maps from 30–353 GHz<br />
* common mask {{PlanckPapers|planck2013-p06}}<br />
* compact sources catalog<br />
<br />
; High-l spectrum (<math>50 < \ell < 2500</math>): <br />
<br />
* 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 2 in {{PlanckPapers|planck2013-p08}})<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of {{PlanckPapers|planck2013-p11}})<br />
* Beam transfer function uncertainties {{PlanckPapers|planck2013-p03c}}<br />
<br />
'''Likelihood'''<br />
<br />
; ''commander'' :<br />
* all Planck channels maps<br />
* compact source catalogs<br />
* common masks<br />
* beam transfer functions for all channels<br />
<br />
; ''lowlike'' :<br />
* WMAP9 likelihood data<br />
* Low-<math>\ell</math> Commander map<br />
<br />
; ''CAMspec'' :<br />
* 100, 143 and 217 GHz detector and detsets maps<br />
* 857GHz channel map<br />
* compact source catalog<br />
* common masks (0,1 & 3)<br />
* beam transfer function and error eigenmodes and covariance for 100, 143 and 217 GHz detectors & detsets<br />
* theoretical templates for the tSZ and kSZ contributions<br />
* color corrections for the CIB emission for the 143 and 217GHz detectors and detsets<br />
* fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz<br />
<br />
; ''lensing'' :<br />
* the lensing map<br />
* beam error eigenmodes and covariance for the 143 and 217GHz channel maps<br />
* fiducial CMB model (from Planck cosmological parameter best fit)<br />
<br />
; ''act/spt'' :<br />
* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]<br />
* the tSZ andkSZ template are changed to match those of CAMspec<br />
<br />
''' File names and Meta data '''<br />
<br />
<br />
'''CMB spectra'''<br />
<br />
The CMB spectrum and its covariance matrix are distributed in a single FITS file named <br />
* ''{{PLASingleFile | fileType=cosmo | name=COM_PowerSpect_CMB_R1.10.fits | link=COM_PowerSpect_CMB_R1.10.fits}}'' <br />
<br />
which contains 3 extensions<br />
<br />
; LOW-ELL (BINTABLE)<br />
: with the low ell part of the spectrum, not binned, and for l=2-49. The table columns are<br />
# ''ELL'' (integer): multipole number<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERRUP'' (float): the upward uncertainty<br />
# ''ERRDOWN'' (float): the downward uncertainty<br />
<br />
; HIGH-ELL (BINTABLE)<br />
: with the high-ell part of the spectrum, binned into 74 bins covering <math>\langle l \rangle = 47-2419\ </math> in bins of width <math>l=31</math> (with the exception of the last 4 bins that are wider). The table columns are as follows:<br />
# ''ELL'' (integer): mean multipole number of bin<br />
# ''L_MIN'' (integer): lowest multipole of bin<br />
# ''L_MAX'' (integer): highest multipole of bin<br />
# ''D_ELL'' (float): $D_l$ as described below<br />
# ''ERR'' (float): the uncertainty<br />
<br />
; COV-MAT (IMAGE)<br />
: with the covariance matrix of the high-ell part of the spectrum in a 74x74 pixel image, i.e., covering the same bins as the ''HIGH-ELL'' table.<br />
<br />
The spectra give $D_\ell = \ell(\ell+1)C_\ell / 2\pi$ in units of $\mu\, K^2$, and the covariance matrix is in units of $\mu\, K^4$. The spectra are shown in the figure below, in blue and red for the low- and high-<math>\ell</math> parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.<br />
<br />
[[File: CMBspect.jpg|thumb|center|700px|'''CMB spectrum. Linear x-scale; error bars only at high <math>\ell</math>.''']]<br />
<br />
'''Likelihood'''<br />
<br />
'''Likelihood source code'''<br />
<br />
The source code is in the file<br />
: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)<br />
<br />
'''Likelihood data packages'''<br />
<br />
The {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)<br />
: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)<br />
<br />
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to<br />
build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.<br />
<br />
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
'''Likelihood masks'''<br />
<br />
The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in<br />
{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}<br />
<br />
which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks: <br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Likelihodd masks file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|CL31 || Real*4 || none || mask<br />
|-<br />
|CL39 || Real*4 || none || mask<br />
|-<br />
|CL49 || Real*4 || none || mask<br />
|-<br />
|G22 || Real*4 || none || mask <br />
|-<br />
|G35 || Real*4 || none || mask<br />
|-<br />
|G45 || Real*4 || none || mask<br />
|-<br />
|G56 || Real*4 || none || mask<br />
|-<br />
|G65 || Real*4 || none || mask<br />
|-<br />
|PS96 || Real*4 || none || mask<br />
|-<br />
|PSA82 || Real*4 || none || mask<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COORDSYS || string || GALACTIC ||Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside <br />
|-<br />
|FIRSTPIX || Int*4 || 0 || First pixel number<br />
|-<br />
|LASTPIX || Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively<br />
<br />
|}<br />
<br />
</div><br />
</div><br />
<br />
<br />
== References ==<br />
<References /><br />
<br />
<br />
<br />
[[Category:Mission products|008]]</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=File:Screen_Shot_2018-07-16_at_05.52.24.png&diff=14375File:Screen Shot 2018-07-16 at 05.52.24.png2018-07-16T13:04:55Z<p>Jtauber: File uploaded with MsUpload</p>
<hr />
<div>File uploaded with MsUpload</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=File:Screen_Shot_2018-07-16_at_05.52.35.png&diff=14374File:Screen Shot 2018-07-16 at 05.52.35.png2018-07-16T13:02:27Z<p>Jtauber: File uploaded with MsUpload</p>
<hr />
<div>File uploaded with MsUpload</div>Jtauberhttps://wiki.cosmos.esa.int/planck-legacy-archive/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=14373CMB spectrum & Likelihood Code2018-07-16T12:54:59Z<p>Jtauber: </p>
<hr />
<div>{{DISPLAYTITLE:CMB spectra and likelihood code}}<br />
<br />
== 2018 CMB spectra==<br />
<br />
<br />
===General description===<br />
====TT====<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2016-l06}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood {{PlanckPapers|planck2016-l05}}, with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File:Screen Shot 2018-07-16 at 05.51.48.png|thumb|400px|center]]<br />
<br />
[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]<br />
<br />
====TE, EE, and TB, EB, BB ====<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
===Production process===<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
===Inputs===<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
=== File names and meta-data ===<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 10. TE high-&#8467;, unbinned (TEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole; <br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 11. EE high-&#8467;, binned (EEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 12. EE high-&#8467;, unbinned (EEHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.<br />
<br />
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.<br />
<br />
== 2018 Likelihood==<br />
<br />
The 2018 Likelihood code will be released at a later time.<br />
<br />
== Previous Releases: (2015) and (2013) CMB spectrum and Likelihood ==<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%"><br />
'''2015 CMB spectrum and Likelihood'''<br />
<div class="mw-collapsible-content"><br />
<br />
'''2015 CMB spectra'''<br />
<br />
'''General description'''<br />
<br />
'''TT'''<br />
The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2014-a12}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.<br />
<br />
For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP &Lambda;CDM run. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.<br />
<br />
[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]<br />
<br />
'''TE, EE, and TB, EB, BB '''<br />
<br />
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.<br />
Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run. <br />
<br />
{|style="margin: 0 auto;"<br />
|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}). Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]<br />
|}<br />
<br />
'''Production process'''<br />
The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors. <br />
<br />
The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.<br />
#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).<br />
#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.<br />
<br />
We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is<br />
<math>\\ C_{\ell_b}=\Sigma_{\ell \in b} w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math><br />
Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as<br />
<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math><br />
where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus<br />
<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\<br />
\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\<br />
\ell_b=B\, \ell .\\ </math><br />
Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as<br />
<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math><br />
<br />
'''Inputs'''<br />
<br />
; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki><br />
<br />
* Planck 30 and 44 GHz frequency maps;<br />
* Planck 70 to 857 GHz detector and detector-set maps;<br />
* 9-year WMAP temperature sky maps between 23 and 94 GHz;<br />
* 408-MHz survey of Haslam et al. (1982);<br />
* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).<br />
<br />
; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki><br />
<br />
* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});<br />
* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});<br />
* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).<br />
<br />
''' File names and meta-data '''<br />
<br />
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''. <br />
* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).<br />
* R2.01 corrects a small error in the <i>effective</i> &#8467; of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals. <br />
* R2.02 contains low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).<br />
<br />
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).<br />
<br />
; 1. TT low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 2. TE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 3. EE low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 4. TB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 5. EB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 6. BB low-&#8467;, unbinned (TTLOLUNB)<br />
: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29. The table columns are:<br />
# ''ELL'' (integer), multipole number;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERRUP'' (float), the upward uncertainty;<br />
# ''ERRDOWN'' (float), the downward uncertainty.<br />
<br />
; 7. TT high-&#8467;, binned (TTHILBIN)<br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:<br />
# ''ELL'' (float), mean multipole number of bin;<br />
# ''L_MIN'' (integer), lowest multipole of bin;<br />
# ''L_MAX'' (integer), highest multipole of bin;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 8. TT high-&#8467; unbinned (TTHILUNB) <br />
: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:<br />
# ''ELL'' (integer), multipole;<br />
# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;<br />
# ''ERR'' (float), the uncertainty.<br />
<br />
; 9. TE high-&#8467;, binned (TEHILBIN) <br />
: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins