https://wiki.cosmos.esa.int/planckpla2015/api.php?action=feedcontributions&user=Lvibert&feedformat=atomPlanck PLA 2015 Wiki - User contributions [en-gb]2022-11-30T03:43:26ZUser contributionsMediaWiki 1.31.6https://wiki.cosmos.esa.int/planckpla2015/index.php?title=ADC_correction&diff=11130ADC correction2015-02-04T10:31:29Z<p>Lvibert: </p>
<hr />
<div>The ADC non linearity correction is affecting the modulated signal of the bolometers before 40 of these fast samples are averaged and transmitted to the ground. The TOI data delivered in the HFI products are made of these average values. The raw signal of a bolometer for one modulation period is transmitted only at sparce intervals. This results in a complicated process to remove the systematic effects associated with ADC non linearity on the modulated signal taking into account the 40 Hz parasitics associated with the 4K cooler drive electronics.<br />
<br />
The principles of the correction are detailed in the "DPC paper 1". The correction cannot be done using only the TOI values but requires ancillary data from ground based tests and additional tests done during the LFI extension of the mission when the dilution cooler did not operate anymore.<br />
For this reason, there is no reason to detail more than what was described in the paper as the users cannot expect to improve this part of the processing.</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Effective_Beams&diff=7767Effective Beams2013-06-19T15:51:18Z<p>Lvibert: </p>
<hr />
<div><span style="color:red"></span><br />
<br />
==Product description==<br />
----------------------<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
Details of the beam processing are given in the respective pages for [[Beams|HFI]] and [[Beams_LFI|LFI]].<br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in [[http://arxiv.org/pdf/1005.1929| Mitra, Rocha, Gorski et al.]] <cite>#mitra2010</cite>, and a discussion of its application to Planck data is given in the appropriate LFI <cite>#planck2013-p02d</cite> and HFI <cite>#planck2013-p03c</cite> papers. Relevant details of the processing steps are given in the [[Beams|Effective Beams]] section of this document.<br />
<br />
<!-- Everything from here down to the "Production Process" section should eventually be moved to a new section the Joint Processing pages --><br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions, PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for all LFI and HFI frequency channels, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<center><br />
<br />
<gallery widths=400px heights=400px perrow=2 caption="Comparison images of compact sources and effective beams, PSFs"><br />
File:30.png| '''30GHz'''<br />
File:44.png| '''44GHz'''<br />
File:70.png| '''70GHz'''<br />
File:100.png| '''100GHz'''<br />
File:143.png| '''143GHz'''<br />
File:217.png| '''217GHz'''<br />
File:353.png| '''353GHz'''<br />
File:545.png| '''545GHz'''<br />
File:857.png| '''857GHz'''<br />
</gallery><br />
</center><br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 3072 directions which were chosen as HEALpix nside=16 pixel centers for HFI and at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''<math> 4 \pi \sum</math>(effbeam)/max(effbeam)'''<br />
i.e., <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 800px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
[[File:ist_BS_Mars12.png | 800px| thumb | center| '''Histograms for HFI effective beam parameters''' ]]<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky variation of effective beams ellipticity of the best-fit Gaussian"><br />
File:e_030_GB.png| '''ellipticity - 30GHz'''<br />
File:e_044_GB.png| '''ellipticity - 44GHz'''<br />
File:e_070_GB.png| '''ellipticity - 70GHz'''<br />
File:e_100_BS_Mars12.png| '''ellipticity - 100GHz'''<br />
File:e_143_BS_Mars12.png| '''ellipticity - 143GHz'''<br />
File:e_217_BS_Mars12.png| '''ellipticity - 217GHz'''<br />
File:e_353_BS_Mars12.png| '''ellipticity - 353GHz'''<br />
File:e_545_BS_Mars12.png| '''ellipticity - 545GHz'''<br />
File:e_857_BS_Mars12.png| '''ellipticity - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky (relative) variation of effective beams solid angle of the best-fit Gaussian"><br />
File:solidarc_030_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 30GHz'''<br />
File:solidarc_044_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 44GHz'''<br />
File:solidarc_070_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 70GHz'''<br />
File:solidarc_100_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 100GHz'''<br />
File:solidarc_143_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 143GHz'''<br />
File:solidarc_217_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 217GHz'''<br />
File:solidarc_353_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 353GHz'''<br />
File:solidarc_545_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 545GHz'''<br />
File:solidarc_857_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky (relative) variation of effective beams fwhm of the best-fit Gaussian"><br />
File:fwhm_030_GB.png| '''fwhm (relative) variations wrt scanning beam - 30GHz'''<br />
File:fwhm_044_GB.png| '''fwhm (relative) variations wrt scanning beam - 44GHz'''<br />
File:fwhm_070_GB.png| '''fwhm (relative) variations wrt scanning beam - 70GHz'''<br />
File:fwhm_100_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 100GHz'''<br />
File:fwhm_143_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 143GHz'''<br />
File:fwhm_217_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 217GHz'''<br />
File:fwhm_353_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 353GHz'''<br />
File:fwhm_545_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 545GHz'''<br />
File:fwhm_857_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky variation of effective beams $\psi$ angle of the best-fit Gaussian"><br />
File:psi_030_GB.png| '''$\psi$ - 30GHz'''<br />
File:psi_044_GB.png| '''$\psi$ - 44GHz'''<br />
File:psi_070_GB.png| '''$\psi$ - 70GHz'''<br />
File:psi_100_BS_Mars12.png| '''$\psi$ - 100GHz'''<br />
File:psi_143_BS_Mars12.png| '''$\psi$ - 143GHz'''<br />
File:psi_217_BS_Mars12.png| '''$\psi$ - 217GHz'''<br />
File:psi_353_BS_Mars12.png| '''$\psi$ - 353GHz'''<br />
File:psi_545_BS_Mars12.png| '''$\psi$ - 545GHz'''<br />
File:psi_857_BS_Mars12.png| '''$\psi$ - 857GHz'''<br />
</gallery><br />
<br />
<!--<br />
<gallery widths=500px heights=500px perrow=2 caption="Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian"><br />
File:e_030_GB.png| '''ellipticity - 30GHz'''<br />
File:solidarc_030_GB.png| '''beam solid angle (relative variations wrt scanning beam - 30GHz'''<br />
File:e_100_BS_Mars12.png| '''ellipticity - 100GHz'''<br />
File:solidarc_100_BS_Mars12.png| '''beam solid angle (relative variations wrt scanning beam - 100GHz'''<br />
</gallery><br />
--><br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 3072 and 768 directions on the sky for HFI and LFI data respectively. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 and 2048 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|-<br />
| 100 || 9.651 || 0.014 || 1.186 || 0.023 || -0.024 || 55.400 || 105.778 || 0.311 || 9.66 <br />
|-<br />
| 143 || 7.248 || 0.015 || 1.036 || 0.009 || 0.383 || 54.130 || 59.954 || 0.246 || 7.27 <br />
|-<br />
| 217 || 4.990 || 0.025 || 1.177 || 0.030 || 0.836 || 54.999 || 28.447 || 0.271 || 5.01<br />
|-<br />
| 353 || 4.818 || 0.024 || 1.147 || 0.028 || 0.655 || 54.745 || 26.714 || 0.250 || 4.86<br />
|- <br />
| 545 || 4.682 || 0.044 || 1.161 || 0.036 || 0.544 || 54.876 || 26.535 || 0.339 || 4.84 <br />
|-<br />
| 857 || 4.325 || 0.055 || 1.393 || 0.076 || 0.876 || 54.779 || 24.244 || 0.193 || 4.63 <br />
|}<br />
<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: '''<math>4 \pi \sum </math>(effbeam)/max(effbeam)''', i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|-<br />
| 100 || 105.778 || 0.311 || 100.830 || 0.410 || 105.777 || 0.311 <br />
|-<br />
| 143 || 59.954 || 0.246 || 56.811 || 0.419 || 59.952 || 0.246 <br />
|-<br />
| 217 || 28.447 || 0.271 || 26.442 || 0.537 || 28.426 || 0.271 <br />
|-<br />
| 353 || 26.714 || 0.250 || 24.827 || 0.435 || 26.653 || 0.250 <br />
|-<br />
| 545 || 26.535 || 0.339 || 24.287 || 0.455 || 26.302 || 0.337 <br />
|-<br />
| 857 || 24.244 || 0.193 || 22.646 || 0.263 || 23.985 || 0.191 <br />
|}<br />
<br />
==Production process==<br />
------------------------<br />
<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space [[http://arxiv.org/pdf/1005.1929| Mitra, Rocha, Gorski et al.]] <cite>#mitra2010</cite>, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
===Pixel Ordered Detector Angles (PODA)===<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels - the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
===effBeam===<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
===Computational Cost===<br />
<br />
The computation of the effective beams has been performed at the NERSC Supercomputing Center. The table below shows the computation cost for FEBeCoP processing of the nominal mission.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Computational cost for PODA, Effective Beam and single map convolution. Wall-clock time is given as a guide, as found on the NERSC supercomputers.'''<br />
|-<br />
|Channel ||030 || 044 || 070 || 100 || 143 || 217 || 353 || 545 || 857<br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 || 500 || 500 || 500 || 500 || 500 || 500 <br />
|-<br />
|PODA/Detector Computation time (wall clock hrs) || 7 || 10 || 20 || 20 || 20 || 20 || 20 || 20 || 20<br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 || 2800 || 3800 || 3200 || 3000 || 900 || 1100<br />
|-<br />
|Beam/Channel Computation time (wall clock hrs) || 0.5 || 0.8 || 1 || 1.5 || 2 || 1.2 || 1 || 0.5 || 0.5<br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 || 3.6 || 4.8 || 4.0 || 4.1 || 4.1 || 3.7 <br />
|-<br />
|Convolution Computation time (wall clock sec) || 1 || 1 || 1 || 4 || 4 || 4 || 4 || 4 || 4 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 || 187 || 182 || 146 || 132 || 139 || 124<br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
==Inputs==<br />
------------<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 500px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
===The Focal Plane DataBase (FPDB)===<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
*HFI - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
<br />
<!--<br />
*HFI - LFI_RIMO_DX9_PTCOR6 - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - HFI-RIMO-3_16_detilt_t2_ptcor6.fits - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
{{PLADoc|fileType=rimo|link=The Plank RIMOS}}<br />
--><br />
<br />
===The scanning strategy===<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
===The scanbeam===<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
* HFI: [[Beams#Scanning beams|B-Spline, BS]] based on 2 observations of Mars.<br />
<br />
(see the instrument [[The RIMO|RIMOs]]).<br />
<br />
<!--<br />
<br />
*HFI - LFI_RIMO_DX9_PTCOR6 - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - HFI-RIMO-3_16_detilt_t2_ptcor6.fits - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
[[Beams LFI#Effective beams|LFI effective beams]]<br />
--><br />
<br />
===Beam cutoff radii===<br />
<br />
N times geometric mean of FWHM of all detectors in a channel, where N<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' || '''fwhm of full beam extent''' <br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|-<br />
|100 || 2.25 || 23.703699<br />
|-<br />
|143 || 3 || 21.057402<br />
|-<br />
|217-353 || 4 || 18.782754<br />
|-<br />
|sub-mm || 4 || 18.327635(545GHz) ; 17.093706(857GHz) <br />
|}<br />
<br />
===Map resolution for the derived beam data object===<br />
<br />
* <math>N_{side} = 1024 </math> for LFI frequency channels<br />
* <math>N_{side} = 2048 </math> for HFI frequency channels<br />
<br />
==Related products==<br />
----------------------<br />
<br />
===Monte Carlo simulations===<br />
<br />
FEBeCoP software enables fast, full-sky convolutions of the sky signals with the Effective beams in pixel domain. Hence, a large number of Monte Carlo simulations of the sky signal maps map convolved with realistically rendered, spatially varying, asymmetric Planck beams can be easily generated. We performed the following steps:<br />
<br />
* generate the effective beams with FEBeCoP for all frequencies for dDX9 data and Nominal Mission<br />
* generate 100 realizations of maps from a fiducial CMB power spectrum<br />
* convolve each one of these maps with the effective beams using FEBeCoP<br />
* estimate the average of the Power Spectrum of each convolved realization, and 1 <math>\sigma</math> errors<br />
<br />
<br />
As FEBeCoP enables fast convolutions of the input signal sky with the effective beam, thousands of simulations are generated. These Monte Carlo simulations of the signal (might it be CMB or a foreground (e.g. dust)) sky along with LevelS+Madam noise simulations were used widely for the analysis of Planck data. A suite of simulations were rendered during the mission tagged as Full Focalplane simulations, FFP#.<br />
For example [[HL-sims#FFP6 data set|FFP6]] <br />
<br />
===Beam Window Functions===<br />
<br />
The '''Transfer Function''' or the '''Beam Window Function''' <math> W_l </math> relates the true angular power spectra <math>C_l </math> with the observed angular power spectra <math>\widetilde{C}_l </math>:<br />
<br />
<math><br />
W_l= \widetilde{C}_l / C_l <br />
\label{eqn:wl1}</math> <br />
<br />
Note that, the window function can contain a pixel window function (depending on the definition) and it is {\em not the angular power spectra of the scanbeams}, though, in principle, one may be able to connect them though fairly complicated algebra.<br />
<br />
The window functions are estimated by performing Monte-Carlo simulations. We generate several random realisations of the CMB sky starting from a given fiducial <math> C_l </math>, convolve the maps with the pre-computed effective beams, compute the convolved power spectra <math> C^\text{conv}_l </math>, divide by the power spectra of the unconvolved map <math>C^\text{in}_l </math> and average over their ratio. Thus, the estimated window function<br />
<br />
<math><br />
W^{est}_l = < C^{conv}_l / C^{in}_l ><br />
\label{eqn:wl2}</math> <br />
<br />
For subtle reasons, we perform a more rigorous estimation of the window function by comparing C^{conv}_l with convolved power spectra of the input maps convolved with a symmetric Gaussian beam of comparable (but need not be exact) size and then scaling the estimated window function accordingly.<br />
<br />
Beam window functions are provided in the [[The RIMO#Beam Window Functions|RIMO]]. <br />
<br />
<br />
====Beam Window functions, Wl, for Planck mission====<br />
<br />
<br />
<br />
[[File:plot_dx9_LFI_GB_pix.png | 600px | thumb | center |'''Beam Window functions, Wl, for LFI channels''']] <br />
[[File:plot_dx9_HFI_BS_M12_CMB.png | 600px | thumb | |center |'''Beam Window functions, Wl, for HFI channels''']]<br />
<br />
<br />
<br />
<br />
==File Names==<br />
-----------------<br />
<br />
The effective beams are stored as unformatted files in directories with the frequency channel's name, e.g., 100GHz, each subdirectory contains N unformatted files with names beams_###.unf, a beam_index.fits and a beams_run.log. For 100GHz and 143GHz: N=160, for 30, 44, 70 217 and 353GHz: N=128; for 545GHz: N=40; and 857GHz: N=32.<br />
<br />
* beam_index.fits<br />
* beams_run.log<br />
<br />
== Retrieval of effective beam information from the PLA interface ==<br />
<br />
In order to retrieve the effective beam information, the user should first launch the Java interface from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive| Planck Legacy Archive].<br />
<br />
One should click on "Sky maps" and then open the "Effective beams" area.<br />
There is the possibility to either retrieve one beam nearest to the input source (name or coordinates), or to retrieve a set of beams in a grid defined by the Nside and the size of the region around a source (name or coordinates).<br />
The resolution of this grid is defined by the Nside parameter.<br />
The size of the region is defined by the "Radius of ROI" parameter.<br />
<br />
Once the user proceeds with querying the beams, the PLA software retrieves the appropriate set of effective beams from the database and delivers it in a FITS file which can be directly downloaded.<br />
<br />
==Meta data==<br />
----------------<br />
<br />
The data format of the effective beams is unformatted.<br />
<br />
== References ==<br />
------------------<br />
<br />
<biblio force=false><br />
#[[References]]<br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|004]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Simulation_data&diff=7765Simulation data2013-06-19T15:44:59Z<p>Lvibert: </p>
<hr />
<div>== Introduction ==<br />
----<br />
The 2013 Planck data release is supported by a comprehensive set of simulated maps, including both a fiducial realization of the sky as seen by Planck and 1000-realization Monte Carlo (MC) sets of CMB and noise simulations, collectively known as FFP6.<br />
<br />
The simulation process consists of <br />
* modeling the sky using pre-Planck data and generating an input sky map for each sky component for each detector that incorporates our best estimate of that detector's band-pass<br />
* simulating each detector's observation of each input sky component, following the Planck scanning strategy and using our best estimates of the detector's beam and noise properties, and mapping the results.<br />
* generating Monte Carlo realizations of the CMB and noise maps, again following the Planck scanning strategy and using our best estimates of the detector beams and noise properties respectively.<br />
The first step is done by the ''Planck Sky Model'' (PSM), and the second and third by a suite of ''Planck Simulation Tools'' (PST). A brief description of these is given below.<br />
<br />
== The Planck Sky Model ==<br />
----<br />
=== Overall description ===<br />
<br />
The Planck Sky Model, a complete set data and code to simulate sky emission at millimeter-wave frequencies, is described in detail in the Planck pre-launch [http://adsabs.harvard.edu/abs/2012arXiv1207.3675D| PSM paper] <cite>Delabrouille2012</cite>.<br />
<br />
The main simulations used to test and validate the Planck data analysis pipelines (and, in particular, component separation) makes use of simulations generated with version 1.7.7 of the PSM software. Sky emission comprises the following components: CMB, thermal dust, spinning dust, synchrotron, CO lines, free-free, thermal Sunyaev-Zel'dovich (SZ) effect (with first order relativistic corrections), kinetic SZ effect, radio and infrared sources, Cosmic Infrared Background (CIB).<br />
<br />
The CMB is a based on adiabatic initial perturbations, with the following cosmological parameters:<br />
* T_CMB = 2.725<br />
* H = 0.684<br />
* OMEGA_M = 0.292<br />
* OMEGA_B = 0.04724<br />
* OMEGA_NU = 0<br />
* OMEGA_K = 0<br />
* SIGMA_8 = 0.789<br />
* N_S = 0.9732<br />
* N_S_RUNNING = 0<br />
* N_T = 0<br />
* R = 0.0844<br />
* TAU_REION = 0.085<br />
* HE_FRACTION = 0.245<br />
* N_MASSLESS_NU = 3.04<br />
* N_MASSIVE_NU = 0<br />
* W_DARK_ENERGY = -1<br />
* K_PIVOT = 0.002<br />
* SCALAR_AMPLITUDE = 2.441e-9<br />
<br />
All other parameters are set to the default standard of the Jan 2012 version of CAMB. In addition, this simulated CMB contains non-Gaussian corrections of the local type, with an f_NL parameter of 20.4075.<br />
<br />
The Galactic ISM emission comprises 5 major components: Thermal dust, spinning dust, synchrotron, CO lines, and free-free emission. We refer the reader to the PSM publication for details. For the simulations generated here, however, the thermal dust model has been modified in the following way: Instead of being based on the 100 micron map of Schlegel, Finkbeiner and Davis (2008) <cite>schlegel1998</cite>, the dust template uses an internal release of the 857 GHz Planck observed map itself, in which point sources have been subtracted, and which has been locally filtered to remove CIB fluctuations in the regions of lowest column density. A caveat is that while this reduces the level of CIB fluctuations in the dust map in some of the regions, in regions of moderate dust column density the CIB contamination is actually somewhat larger than in the SFD map (by reason of different emission laws for dust and CIB, and of the highr resolution of the Planck map).<br />
<br />
The other emissions of the galactic ISM are simulated using the prescription described in the PSM paper. <br />
Synchrotron, Free-free and spinning dust emission are based on WMAP observations, as analyzed by Miville-Deschenes et al. (2008) <cite>Miville2008</cite>. Small scale fluctuations have been added to increase the variance on small scales and compensate the lower resolution of WMAP as compared to Planck (in particular HFI channels). The main limitation of these maps is the presence at high galactic latitude of fluctuations that may be imputable to WMAP noise. The presence of noise and of added Gaussian fluctuations on small scales may result in a few occasional pixels being negative (e.g. in the spinning dust maps). Low frequency foreground maps are also contaminated by some residuals of bright radio sources that have not been properly subtracted from the templates of diffuse emission.<br />
<br />
The CO maps are simulated using the CO J=1-0 observations of Dame et al. (2001)<cite>dame2001</cite>. The main limitations are limited sky coverage, lower resolution than that of Planck high frequency channels, line ratios (J=2-1)/(J=1-0) and (J=3-2)/(J=2-1) constant over the sky. The CO in the simulation is limited to the three lowest 12CO lines.<br />
<br />
Galaxy clusters are generated on the basis of cluster number counts, following the Tinker et al. (2008) mass function, for the cosmological parameters listed above. Clusters are assumed perfectly spherical, isothermal, and are modeled using the universal pressure profile of Arnaud et al. (2010) <cite>arnaud2010</cite>. Relativistic corrections following Itoh et al. (1998) <cite>Nozawa1998</cite> are included to first order. The simulated kinetic SZ effect assumes no bulk flow, and a redshift-dependent average cluster velocity compatible with the linear growth of structures.<br />
<br />
Point sources comprise radio sources (based on extrapolations across frequencies of radio observations between 800 MHz and 5 GHz) and infrared sources (based on extrapolations in frequencies of IRAS sources). One small caveat that should be mentioned is that because of the unevenness of the radio source surveys, the equatorial southern part of the sky has less faint radio sources than the northern part. Although all the missing sources are well below the Planck detection level, this induces a small variation of the total emission background over the sky. Check the individual faint point source emission maps if this is a potential problem for your applications. See also the PSM publication for details about the PSM point source simulations.<br />
<br />
Finally, the far infrared background due to high redshift galaxies has been simulated using a procedure is based on the distribution of galaxies in shells of density contrast at various redshifts (Castex et al., PhD thesis; paper in preparation). This simulation has been modified by gradually substituting an uncorrelated extra term of CIB emission at low frequencies, artificially added in particular to decorrelate the CIB at frequencies below 217 GHz from the CIB above that frequency, to mimic the apparent decorrelation observed in the Planck Early Paper on CIB power spectrum. <br />
<br />
While the PSM simulations described here provide a reasonably representative multi-component model of sky emission, the users are warned that it has been put together mostly on the basis of data sets and knowledge pre-existing the Planck observations themselves. While it is sophisticated enough to include variations of emission laws of major components of ISM emission, different emission laws for most sources, and a reasonably coherent global picture, it is not (and is not supposed to be) identical to the real sky emission. The users are warned to use these simulations with caution.<br />
<br />
=== PSM Products ===<br />
<br />
The following products are available:<br />
<br />
* ''PR1_beta/HFI_SimMap_cmb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_co_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_firb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_strongps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_faintps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_freefree_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_synchrotron_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermaldust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_spindust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_kineticsz_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermalsz_2048_R1.10.fits''<br />
<br />
All files contains a single ''BINTABLE'' extension with either a single map (e.g., for the CMB) or one map for each HFI frequency (for all other components). In the latter case the columns are named ''F100'', ''F143'', … , ''F857''. Units are microK<sub>CMB</sub> for the CMB, and MJy/sr for the others. The structure is given below for multi-column files. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''FITS file structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'SIM-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|F100 || Real*4 || MJy/sr || 100GHz signal map<br />
|-<br />
|F143 || Real*4 || MJy/sr || 143GHz signal map<br />
|-<br />
|F217 || Real*4 || MJy/sr || 217GHz signal map<br />
|-<br />
|F353 || Real*4 || MJy/sr || 353GHz signal map<br />
|-<br />
|F545 || Real*4 || MJy/sr || 545GHz signal map<br />
|-<br />
|F857 || Real*4 || MJy/sr || 857GHz signal map<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COMP || string || component || Astrophysical omponent<br />
|-<br />
|COORDSYS || string || GALACTIC || Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside for LFI and HFI, respectively<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 />
|FREQ || string || GHz || The frequency channel <br />
|-<br />
|BAD_DATA || Real*4 || -1.63750E+30 || Healpix bad pixel value <br />
|-<br />
|BEAMTYPE || string || GAUSSIAN || Type of beam <br />
|-<br />
|BEAMSIZE || Real*4 || size || Beam size in arcmin<br />
|-<br />
|PSM-VERS || string || || PSM Versions used <br />
|}<br />
<br />
== The Planck Mission Simulations ==<br />
---------------------<br />
<br />
Since the full focal plane (FFP) simulations <br />
* involve both HFI and LFI data <br />
* include large, computationally challenging, MC realization sets<br />
they cannot be generated using either DPC's single-instrument cluster-based pipeline. Instead the PST consists of three distinct tool chains, each designed to run on the largest available supercomputers, that are used to generate the fiducial sky realization, the CMB MC, and the noise MC respectively. FFP6 was primarily generated on the Hopper and Edison systems at [http://www.nersc.gov NERSC], with some of the LFI noise MCs generated on the Louhi system at [http://www.csc.fi/english CSC].<br />
<br />
While FFP6 is guaranteed to be internally self-consistent there are a number of differences with the real data that should be borne in mind, although all tests performed to date indicate that these are statistically insignificant:<br />
* FFP6 includes our best measurements of the detector band-passes, main beams and noise power spectral densities - known issues include the absence of side-lobes and the use of a single, independent, noise spectrum per detector for the entire mission.<br />
* FFP6 excludes all pre-processing residuals, assuming perfect calibration, transfer function deconvolution and deglitching.<br />
* FFP6 uses the HFI pointing solution for the LFI frequencies, rather than the DPC's two focal plane model.<br />
* FFP6 uses a different map-maker to HFI, and as a consequence implements very slightly different data cuts - primarily at ring boundaries - resulting in marginally different hit-maps.<br />
<br />
=== Fiducial Sky ===<br />
<br />
For each detector, fiducial sky time-ordered data are generated separately for each of its 10 PSM component maps and its strong point source catalogue using the LevelS software <cite>#reinecke2006</cite> as follows:<br />
* The detector's beam and PSM map are converted to spherical harmonics using ''beam2alm'' and ''anafast'' respectively.<br />
* The beam-convolved map value is calculated over a 3-dimensional grid of sky locations and beam orientations using ''conviqt''.<br />
* The map-based time-ordered data are calculated sample-by-sample by interpolating over this grid using "multimod".<br />
* The catalogue-based time-ordered data are calculated sample-by-sample by beam-convolving any point source laying within a given angular distance of the pointing at each sample time using ''multimod''.<br />
<br />
For each frequency, fiducial sky maps are generated for <br />
* the total sky (including noise), <br />
* the foreground sky (excluding CMB but including noise), <br />
* the point source sky, and <br />
* the noise alone<br />
All maps are made using the ''MADAM'' destriping map-maker <cite>#[keihanen2010</cite> interfaced with the ''TOAST'' data abstraction layer . In order to construct the total time-ordered data required by each map, for each detector ''TOAST'' reads the various component time-streams separately and sums then, and, where necessary, simulates and adds a noise realization time-stream on the fly.<br />
<br />
HFI frequencies are mapped at ''HEALPix'' resolution nside=2048 using ring-length destriping baselines, while LFI frequencies are mapped at nside=1024 using 1s baselines.<br />
<br />
=== CMB Monte Carlo ===<br />
<br />
The CMB MC set is generated using ''FEBeCoP'' <cite>#mitra2010</cite>, which generates an effective beam for each pixel in a map at each frequency by accumulating the weights of all pixels within a fixed distance of that pixel, summed over all observations by all detectors at that frequency. It then applies this effective beam pixel-by-pixel to each of 1000 input CMB sky realizations.<br />
<br />
=== Noise Monte Carlo ===<br />
<br />
The noise MC set is generated just as the fiducial noise maps, using ''MADAM/TOAST''. In order to avoid spurious correlations within and between the 1000 realizations, each stationary interval for each detector for each realization is generated from a distinct sub-sequence of a single statistically robust, extremely long period, pseudo-random number sequence.<br />
<br />
== Products delivered ==<br />
<br />
A single simulation is delivered, which is divided into two types of products:<br />
; Six sky maps of the nominal mission at each HFI frequency: which is the basic simulation product. These files have the same structure as the equivalent ''SkyMap'' products described in the [[Frequency_Maps | Frequency Maps ]] chapter -- namely one ''BINTABLE'' extension with three columns containing 1) Signal, 2) hit-count, and 3) variance (TBC)<br />
; Three maps of the nominal mission containing 1) the sum of all astrophysical foregrounds, 2) the point sources alone, and 3) the noise alone: which are subproducts of the above, and are in the form of the PSM maps described in the previous section.<br />
<br />
Note that the cmb alone is not delivered as a separate product, but it can be recovered by simple subtraction of the component maps for the total signal map. It is envisaged that some number of separate noise realizations may be delivered in the future.<br />
<br />
<!-- [[CMB_and_astrophysical_component maps | CMB and astrophysical component maps]] chapter --><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
[[Category:Mission products|012]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Simulation_data&diff=7760Simulation data2013-06-19T15:35:52Z<p>Lvibert: </p>
<hr />
<div>== Introduction ==<br />
----<br />
The 2013 Planck data release is supported by a comprehensive set of simulated maps, including both a fiducial realization of the sky as seen by Planck and 1000-realization Monte Carlo (MC) sets of CMB and noise simulations, collectively known as FFP6.<br />
<br />
The simulation process consists of <br />
* modeling the sky using pre-Planck data and generating an input sky map for each sky component for each detector that incorporates our best estimate of that detector's band-pass<br />
* simulating each detector's observation of each input sky component, following the Planck scanning strategy and using our best estimates of the detector's beam and noise properties, and mapping the results.<br />
* generating Monte Carlo realizations of the CMB and noise maps, again following the Planck scanning strategy and using our best estimates of the detector beams and noise properties respectively.<br />
The first step is done by the ''Planck Sky Model'' (PSM), and the second and third by a suite of ''Planck Simulation Tools'' (PST). A brief description of these is given below.<br />
<br />
== The Planck Sky Model ==<br />
----<br />
=== Overall description ===<br />
<br />
The Planck Sky Model, a complete set data and code to simulate sky emission at millimeter-wave frequencies, is described in detail in the Planck pre-launch [http://adsabs.harvard.edu/abs/2012arXiv1207.3675D| PSM paper] <cite>Delabrouille2012</cite>.<br />
<br />
The main simulations used to test and validate the Planck data analysis pipelines (and, in particular, component separation) makes use of simulations generated with version 1.7.7 of the PSM software. Sky emission comprises the following components: CMB, thermal dust, spinning dust, synchrotron, CO lines, free-free, thermal Sunyaev-Zel'dovich (SZ) effect (with first order relativistic corrections), kinetic SZ effect, radio and infrared sources, Cosmic Infrared Background (CIB).<br />
<br />
The CMB is a based on adiabatic initial perturbations, with the following cosmological parameters:<br />
* T_CMB = 2.725<br />
* H = 0.684<br />
* OMEGA_M = 0.292<br />
* OMEGA_B = 0.04724<br />
* OMEGA_NU = 0<br />
* OMEGA_K = 0<br />
* SIGMA_8 = 0.789<br />
* N_S = 0.9732<br />
* N_S_RUNNING = 0<br />
* N_T = 0<br />
* R = 0.0844<br />
* TAU_REION = 0.085<br />
* HE_FRACTION = 0.245<br />
* N_MASSLESS_NU = 3.04<br />
* N_MASSIVE_NU = 0<br />
* W_DARK_ENERGY = -1<br />
* K_PIVOT = 0.002<br />
* SCALAR_AMPLITUDE = 2.441e-9<br />
<br />
All other parameters are set to the default standard of the Jan 2012 version of CAMB. In addition, this simulated CMB contains non-Gaussian corrections of the local type, with an f_NL parameter of 20.4075.<br />
<br />
The Galactic ISM emission comprises 5 major components: Thermal dust, spinning dust, synchrotron, CO lines, and free-free emission. We refer the reader to the PSM publication for details. For the simulations generated here, however, the thermal dust model has been modified in the following way: Instead of being based on the 100 micron map of Schlegel, Finkbeiner and Davis (2008) <cite>schlegel1998</cite>, the dust template uses an internal release of the 857 GHz Planck observed map itself, in which point sources have been subtracted, and which has been locally filtered to remove CIB fluctuations in the regions of lowest column density. A caveat is that while this reduces the level of CIB fluctuations in the dust map in some of the regions, in regions of moderate dust column density the CIB contamination is actually somewhat larger than in the SFD map (by reason of different emission laws for dust and CIB, and of the highr resolution of the Planck map).<br />
<br />
The other emissions of the galactic ISM are simulated using the prescription described in the PSM paper. <br />
Synchrotron, Free-free and spinning dust emission are based on WMAP observations, as analyzed by Miville-Deschenes et al. (2008) <cite>Miville2008</cite>. Small scale fluctuations have been added to increase the variance on small scales and compensate the lower resolution of WMAP as compared to Planck (in particular HFI channels). The main limitation of these maps is the presence at high galactic latitude of fluctuations that may be imputable to WMAP noise. The presence of noise and of added Gaussian fluctuations on small scales may result in a few occasional pixels being negative (e.g. in the spinning dust maps). Low frequency foreground maps are also contaminated by some residuals of bright radio sources that have not been properly subtracted from the templates of diffuse emission.<br />
<br />
The CO maps are simulated using the CO J=1-0 observations of Dame et al. (2001)<cite>dame2001</cite>. The main limitations are limited sky coverage, lower resolution than that of Planck high frequency channels, line ratios (J=2-1)/(J=1-0) and (J=3-2)/(J=2-1) constant over the sky. The CO in the simulation is limited to the three lowest 12CO lines.<br />
<br />
Galaxy clusters are generated on the basis of cluster number counts, following the Tinker et al. (2008) mass function, for the cosmological parameters listed above. Clusters are assumed perfectly spherical, isothermal, and are modeled using the universal pressure profile of Arnaud et al. (2010) <cite>arnaud2010</cite>. Relativistic corrections following Itoh et al. (1998) are included to first order. The simulated kinetic SZ effect assumes no bulk flow, and a redshift-dependent average cluster velocity compatible with the linear growth of structures.<br />
<br />
Point sources comprise radio sources (based on extrapolations across frequencies of radio observations between 800 MHz and 5 GHz) and infrared sources (based on extrapolations in frequencies of IRAS sources). One small caveat that should be mentioned is that because of the unevenness of the radio source surveys, the equatorial southern part of the sky has less faint radio sources than the northern part. Although all the missing sources are well below the Planck detection level, this induces a small variation of the total emission background over the sky. Check the individual faint point source emission maps if this is a potential problem for your applications. See also the PSM publication for details about the PSM point source simulations.<br />
<br />
Finally, the far infrared background due to high redshift galaxies has been simulated using a procedure is based on the distribution of galaxies in shells of density contrast at various redshifts (Castex et al., PhD thesis; paper in preparation). This simulation has been modified by gradually substituting an uncorrelated extra term of CIB emission at low frequencies, artificially added in particular to decorrelate the CIB at frequencies below 217 GHz from the CIB above that frequency, to mimic the apparent decorrelation observed in the Planck Early Paper on CIB power spectrum. <br />
<br />
While the PSM simulations described here provide a reasonably representative multi-component model of sky emission, the users are warned that it has been put together mostly on the basis of data sets and knowledge pre-existing the Planck observations themselves. While it is sophisticated enough to include variations of emission laws of major components of ISM emission, different emission laws for most sources, and a reasonably coherent global picture, it is not (and is not supposed to be) identical to the real sky emission. The users are warned to use these simulations with caution.<br />
<br />
=== PSM Products ===<br />
<br />
The following products are available:<br />
<br />
* ''PR1_beta/HFI_SimMap_cmb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_co_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_firb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_strongps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_faintps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_freefree_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_synchrotron_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermaldust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_spindust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_kineticsz_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermalsz_2048_R1.10.fits''<br />
<br />
All files contains a single ''BINTABLE'' extension with either a single map (e.g., for the CMB) or one map for each HFI frequency (for all other components). In the latter case the columns are named ''F100'', ''F143'', … , ''F857''. Units are microK<sub>CMB</sub> for the CMB, and MJy/sr for the others. The structure is given below for multi-column files. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''FITS file structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'SIM-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|F100 || Real*4 || MJy/sr || 100GHz signal map<br />
|-<br />
|F143 || Real*4 || MJy/sr || 143GHz signal map<br />
|-<br />
|F217 || Real*4 || MJy/sr || 217GHz signal map<br />
|-<br />
|F353 || Real*4 || MJy/sr || 353GHz signal map<br />
|-<br />
|F545 || Real*4 || MJy/sr || 545GHz signal map<br />
|-<br />
|F857 || Real*4 || MJy/sr || 857GHz signal map<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COMP || string || component || Astrophysical omponent<br />
|-<br />
|COORDSYS || string || GALACTIC || Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside for LFI and HFI, respectively<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 />
|FREQ || string || GHz || The frequency channel <br />
|-<br />
|BAD_DATA || Real*4 || -1.63750E+30 || Healpix bad pixel value <br />
|-<br />
|BEAMTYPE || string || GAUSSIAN || Type of beam <br />
|-<br />
|BEAMSIZE || Real*4 || size || Beam size in arcmin<br />
|-<br />
|PSM-VERS || string || || PSM Versions used <br />
|}<br />
<br />
== The Planck Mission Simulations ==<br />
---------------------<br />
<br />
Since the full focal plane (FFP) simulations <br />
* involve both HFI and LFI data <br />
* include large, computationally challenging, MC realization sets<br />
they cannot be generated using either DPC's single-instrument cluster-based pipeline. Instead the PST consists of three distinct tool chains, each designed to run on the largest available supercomputers, that are used to generate the fiducial sky realization, the CMB MC, and the noise MC respectively. FFP6 was primarily generated on the Hopper and Edison systems at [http://www.nersc.gov NERSC], with some of the LFI noise MCs generated on the Louhi system at [http://www.csc.fi/english CSC].<br />
<br />
While FFP6 is guaranteed to be internally self-consistent there are a number of differences with the real data that should be borne in mind, although all tests performed to date indicate that these are statistically insignificant:<br />
* FFP6 includes our best measurements of the detector band-passes, main beams and noise power spectral densities - known issues include the absence of side-lobes and the use of a single, independent, noise spectrum per detector for the entire mission.<br />
* FFP6 excludes all pre-processing residuals, assuming perfect calibration, transfer function deconvolution and deglitching.<br />
* FFP6 uses the HFI pointing solution for the LFI frequencies, rather than the DPC's two focal plane model.<br />
* FFP6 uses a different map-maker to HFI, and as a consequence implements very slightly different data cuts - primarily at ring boundaries - resulting in marginally different hit-maps.<br />
<br />
=== Fiducial Sky ===<br />
<br />
For each detector, fiducial sky time-ordered data are generated separately for each of its 10 PSM component maps and its strong point source catalogue using the LevelS software <cite>#reinecke2006</cite> as follows:<br />
* The detector's beam and PSM map are converted to spherical harmonics using ''beam2alm'' and ''anafast'' respectively.<br />
* The beam-convolved map value is calculated over a 3-dimensional grid of sky locations and beam orientations using ''conviqt''.<br />
* The map-based time-ordered data are calculated sample-by-sample by interpolating over this grid using "multimod".<br />
* The catalogue-based time-ordered data are calculated sample-by-sample by beam-convolving any point source laying within a given angular distance of the pointing at each sample time using ''multimod''.<br />
<br />
For each frequency, fiducial sky maps are generated for <br />
* the total sky (including noise), <br />
* the foreground sky (excluding CMB but including noise), <br />
* the point source sky, and <br />
* the noise alone<br />
All maps are made using the ''MADAM'' destriping map-maker <cite>#[keihanen2010</cite> interfaced with the ''TOAST'' data abstraction layer . In order to construct the total time-ordered data required by each map, for each detector ''TOAST'' reads the various component time-streams separately and sums then, and, where necessary, simulates and adds a noise realization time-stream on the fly.<br />
<br />
HFI frequencies are mapped at ''HEALPix'' resolution nside=2048 using ring-length destriping baselines, while LFI frequencies are mapped at nside=1024 using 1s baselines.<br />
<br />
=== CMB Monte Carlo ===<br />
<br />
The CMB MC set is generated using ''FEBeCoP'' <cite>#mitra2010</cite>, which generates an effective beam for each pixel in a map at each frequency by accumulating the weights of all pixels within a fixed distance of that pixel, summed over all observations by all detectors at that frequency. It then applies this effective beam pixel-by-pixel to each of 1000 input CMB sky realizations.<br />
<br />
=== Noise Monte Carlo ===<br />
<br />
The noise MC set is generated just as the fiducial noise maps, using ''MADAM/TOAST''. In order to avoid spurious correlations within and between the 1000 realizations, each stationary interval for each detector for each realization is generated from a distinct sub-sequence of a single statistically robust, extremely long period, pseudo-random number sequence.<br />
<br />
== Products delivered ==<br />
<br />
A single simulation is delivered, which is divided into two types of products:<br />
; Six sky maps of the nominal mission at each HFI frequency: which is the basic simulation product. These files have the same structure as the equivalent ''SkyMap'' products described in the [[Frequency_Maps | Frequency Maps ]] chapter -- namely one ''BINTABLE'' extension with three columns containing 1) Signal, 2) hit-count, and 3) variance (TBC)<br />
; Three maps of the nominal mission containing 1) the sum of all astrophysical foregrounds, 2) the point sources alone, and 3) the noise alone: which are subproducts of the above, and are in the form of the PSM maps described in the previous section.<br />
<br />
Note that the cmb alone is not delivered as a separate product, but it can be recovered by simple subtraction of the component maps for the total signal map. It is envisaged that some number of separate noise realizations may be delivered in the future.<br />
<br />
<!-- [[CMB_and_astrophysical_component maps | CMB and astrophysical component maps]] chapter --><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
[[Category:Mission products|012]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Simulation_data&diff=7758Simulation data2013-06-19T15:19:48Z<p>Lvibert: /* Overall description */</p>
<hr />
<div>== Introduction ==<br />
----<br />
The 2013 Planck data release is supported by a comprehensive set of simulated maps, including both a fiducial realization of the sky as seen by Planck and 1000-realization Monte Carlo (MC) sets of CMB and noise simulations, collectively known as FFP6.<br />
<br />
The simulation process consists of <br />
* modeling the sky using pre-Planck data and generating an input sky map for each sky component for each detector that incorporates our best estimate of that detector's band-pass<br />
* simulating each detector's observation of each input sky component, following the Planck scanning strategy and using our best estimates of the detector's beam and noise properties, and mapping the results.<br />
* generating Monte Carlo realizations of the CMB and noise maps, again following the Planck scanning strategy and using our best estimates of the detector beams and noise properties respectively.<br />
The first step is done by the ''Planck Sky Model'' (PSM), and the second and third by a suite of ''Planck Simulation Tools'' (PST). A brief description of these is given below.<br />
<br />
== The Planck Sky Model ==<br />
----<br />
=== Overall description ===<br />
<br />
The Planck Sky Model, a complete set data and code to simulate sky emission at millimeter-wave frequencies, is described in detail in the Planck pre-launch [http://adsabs.harvard.edu/abs/2012arXiv1207.3675D| PSM paper] <cite>Delabrouille2012</cite>.<br />
<br />
The main simulations used to test and validate the Planck data analysis pipelines (and, in particular, component separation) makes use of simulations generated with version 1.7.7 of the PSM software. Sky emission comprises the following components: CMB, thermal dust, spinning dust, synchrotron, CO lines, free-free, thermal Sunyaev-Zel'dovich (SZ) effect (with first order relativistic corrections), kinetic SZ effect, radio and infrared sources, Cosmic Infrared Background (CIB).<br />
<br />
The CMB is a based on adiabatic initial perturbations, with the following cosmological parameters:<br />
* T_CMB = 2.725<br />
* H = 0.684<br />
* OMEGA_M = 0.292<br />
* OMEGA_B = 0.04724<br />
* OMEGA_NU = 0<br />
* OMEGA_K = 0<br />
* SIGMA_8 = 0.789<br />
* N_S = 0.9732<br />
* N_S_RUNNING = 0<br />
* N_T = 0<br />
* R = 0.0844<br />
* TAU_REION = 0.085<br />
* HE_FRACTION = 0.245<br />
* N_MASSLESS_NU = 3.04<br />
* N_MASSIVE_NU = 0<br />
* W_DARK_ENERGY = -1<br />
* K_PIVOT = 0.002<br />
* SCALAR_AMPLITUDE = 2.441e-9<br />
<br />
All other parameters are set to the default standard of the Jan 2012 version of CAMB. In addition, this simulated CMB contains non-Gaussian corrections of the local type, with an f_NL parameter of 20.4075.<br />
<br />
The Galactic ISM emission comprises 5 major components: Thermal dust, spinning dust, synchrotron, CO lines, and free-free emission. We refer the reader to the PSM publication for details. For the simulations generated here, however, the thermal dust model has been modified in the following way: Instead of being based on the 100 micron map of Schlegel, Finkbeiner and Davis (2008) <cite>schlegel1998</cite>, the dust template uses an internal release of the 857 GHz Planck observed map itself, in which point sources have been subtracted, and which has been locally filtered to remove CIB fluctuations in the regions of lowest column density. A caveat is that while this reduces the level of CIB fluctuations in the dust map in some of the regions, in regions of moderate dust column density the CIB contamination is actually somewhat larger than in the SFD map (by reason of different emission laws for dust and CIB, and of the highr resolution of the Planck map).<br />
<br />
The other emissions of the galactic ISM are simulated using the prescription described in the PSM paper. <br />
Synchrotron, Free-free and spinning dust emission are based on WMAP observations, as analyzed by Miville-Deschenes et al., 2008. Small scale fluctuations have been added to increase the variance on small scales and compensate the lower resolution of WMAP as compared to Planck (in particular HFI channels). The main limitation of these maps is the presence at high galactic latitude of fluctuations that may be imputable to WMAP noise. The presence of noise and of added Gaussian fluctuations on small scales may result in a few occasional pixels being negative (e.g. in the spinning dust maps). Low frequency foreground maps are also contaminated by some residuals of bright radio sources that have not been properly subtracted from the templates of diffuse emission.<br />
<br />
The CO maps are simulated using the CO J=1-0 observations of Dame et al. (2001)<cite>dame2001</cite>. The main limitations are limited sky coverage, lower resolution than that of Planck high frequency channels, line ratios (J=2-1)/(J=1-0) and (J=3-2)/(J=2-1) constant over the sky. The CO in the simulation is limited to the three lowest 12CO lines.<br />
<br />
Galaxy clusters are generated on the basis of cluster number counts, following the Tinker et al. (2008) mass function, for the cosmological parameters listed above. Clusters are assumed perfectly spherical, isothermal, and are modeled using the universal pressure profile of Arnaud et al. (2010) <cite>arnaud2010</cite>. Relativistic corrections following Itoh et al. (1998) are included to first order. The simulated kinetic SZ effect assumes no bulk flow, and a redshift-dependent average cluster velocity compatible with the linear growth of structures.<br />
<br />
Point sources comprise radio sources (based on extrapolations across frequencies of radio observations between 800 MHz and 5 GHz) and infrared sources (based on extrapolations in frequencies of IRAS sources). One small caveat that should be mentioned is that because of the unevenness of the radio source surveys, the equatorial southern part of the sky has less faint radio sources than the northern part. Although all the missing sources are well below the Planck detection level, this induces a small variation of the total emission background over the sky. Check the individual faint point source emission maps if this is a potential problem for your applications. See also the PSM publication for details about the PSM point source simulations.<br />
<br />
Finally, the far infrared background due to high redshift galaxies has been simulated using a procedure is based on the distribution of galaxies in shells of density contrast at various redshifts (Castex et al., PhD thesis; paper in preparation). This simulation has been modified by gradually substituting an uncorrelated extra term of CIB emission at low frequencies, artificially added in particular to decorrelate the CIB at frequencies below 217 GHz from the CIB above that frequency, to mimic the apparent decorrelation observed in the Planck Early Paper on CIB power spectrum. <br />
<br />
While the PSM simulations described here provide a reasonably representative multi-component model of sky emission, the users are warned that it has been put together mostly on the basis of data sets and knowledge pre-existing the Planck observations themselves. While it is sophisticated enough to include variations of emission laws of major components of ISM emission, different emission laws for most sources, and a reasonably coherent global picture, it is not (and is not supposed to be) identical to the real sky emission. The users are warned to use these simulations with caution.<br />
<br />
=== PSM Products ===<br />
<br />
The following products are available:<br />
<br />
* ''PR1_beta/HFI_SimMap_cmb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_co_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_firb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_strongps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_faintps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_freefree_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_synchrotron_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermaldust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_spindust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_kineticsz_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermalsz_2048_R1.10.fits''<br />
<br />
All files contains a single ''BINTABLE'' extension with either a single map (e.g., for the CMB) or one map for each HFI frequency (for all other components). In the latter case the columns are named ''F100'', ''F143'', … , ''F857''. Units are microK<sub>CMB</sub> for the CMB, and MJy/sr for the others. The structure is given below for multi-column files. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''FITS file structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'SIM-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|F100 || Real*4 || MJy/sr || 100GHz signal map<br />
|-<br />
|F143 || Real*4 || MJy/sr || 143GHz signal map<br />
|-<br />
|F217 || Real*4 || MJy/sr || 217GHz signal map<br />
|-<br />
|F353 || Real*4 || MJy/sr || 353GHz signal map<br />
|-<br />
|F545 || Real*4 || MJy/sr || 545GHz signal map<br />
|-<br />
|F857 || Real*4 || MJy/sr || 857GHz signal map<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COMP || string || component || Astrophysical omponent<br />
|-<br />
|COORDSYS || string || GALACTIC || Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside for LFI and HFI, respectively<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 />
|FREQ || string || GHz || The frequency channel <br />
|-<br />
|BAD_DATA || Real*4 || -1.63750E+30 || Healpix bad pixel value <br />
|-<br />
|BEAMTYPE || string || GAUSSIAN || Type of beam <br />
|-<br />
|BEAMSIZE || Real*4 || size || Beam size in arcmin<br />
|-<br />
|PSM-VERS || string || || PSM Versions used <br />
|}<br />
<br />
== The Planck Mission Simulations ==<br />
---------------------<br />
<br />
Since the full focal plane (FFP) simulations <br />
* involve both HFI and LFI data <br />
* include large, computationally challenging, MC realization sets<br />
they cannot be generated using either DPC's single-instrument cluster-based pipeline. Instead the PST consists of three distinct tool chains, each designed to run on the largest available supercomputers, that are used to generate the fiducial sky realization, the CMB MC, and the noise MC respectively. FFP6 was primarily generated on the Hopper and Edison systems at [http://www.nersc.gov NERSC], with some of the LFI noise MCs generated on the Louhi system at [http://www.csc.fi/english CSC].<br />
<br />
While FFP6 is guaranteed to be internally self-consistent there are a number of differences with the real data that should be borne in mind, although all tests performed to date indicate that these are statistically insignificant:<br />
* FFP6 includes our best measurements of the detector band-passes, main beams and noise power spectral densities - known issues include the absence of side-lobes and the use of a single, independent, noise spectrum per detector for the entire mission.<br />
* FFP6 excludes all pre-processing residuals, assuming perfect calibration, transfer function deconvolution and deglitching.<br />
* FFP6 uses the HFI pointing solution for the LFI frequencies, rather than the DPC's two focal plane model.<br />
* FFP6 uses a different map-maker to HFI, and as a consequence implements very slightly different data cuts - primarily at ring boundaries - resulting in marginally different hit-maps.<br />
<br />
=== Fiducial Sky ===<br />
<br />
For each detector, fiducial sky time-ordered data are generated separately for each of its 10 PSM component maps and its strong point source catalogue using the LevelS software <cite>#reinecke2006</cite> as follows:<br />
* The detector's beam and PSM map are converted to spherical harmonics using ''beam2alm'' and ''anafast'' respectively.<br />
* The beam-convolved map value is calculated over a 3-dimensional grid of sky locations and beam orientations using ''conviqt''.<br />
* The map-based time-ordered data are calculated sample-by-sample by interpolating over this grid using "multimod".<br />
* The catalogue-based time-ordered data are calculated sample-by-sample by beam-convolving any point source laying within a given angular distance of the pointing at each sample time using ''multimod''.<br />
<br />
For each frequency, fiducial sky maps are generated for <br />
* the total sky (including noise), <br />
* the foreground sky (excluding CMB but including noise), <br />
* the point source sky, and <br />
* the noise alone<br />
All maps are made using the ''MADAM'' destriping map-maker <cite>#[keihanen2010</cite> interfaced with the ''TOAST'' data abstraction layer . In order to construct the total time-ordered data required by each map, for each detector ''TOAST'' reads the various component time-streams separately and sums then, and, where necessary, simulates and adds a noise realization time-stream on the fly.<br />
<br />
HFI frequencies are mapped at ''HEALPix'' resolution nside=2048 using ring-length destriping baselines, while LFI frequencies are mapped at nside=1024 using 1s baselines.<br />
<br />
=== CMB Monte Carlo ===<br />
<br />
The CMB MC set is generated using ''FEBeCoP'' <cite>#mitra2010</cite>, which generates an effective beam for each pixel in a map at each frequency by accumulating the weights of all pixels within a fixed distance of that pixel, summed over all observations by all detectors at that frequency. It then applies this effective beam pixel-by-pixel to each of 1000 input CMB sky realizations.<br />
<br />
=== Noise Monte Carlo ===<br />
<br />
The noise MC set is generated just as the fiducial noise maps, using ''MADAM/TOAST''. In order to avoid spurious correlations within and between the 1000 realizations, each stationary interval for each detector for each realization is generated from a distinct sub-sequence of a single statistically robust, extremely long period, pseudo-random number sequence.<br />
<br />
== Products delivered ==<br />
<br />
A single simulation is delivered, which is divided into two types of products:<br />
; Six sky maps of the nominal mission at each HFI frequency: which is the basic simulation product. These files have the same structure as the equivalent ''SkyMap'' products described in the [[Frequency_Maps | Frequency Maps ]] chapter -- namely one ''BINTABLE'' extension with three columns containing 1) Signal, 2) hit-count, and 3) variance (TBC)<br />
; Three maps of the nominal mission containing 1) the sum of all astrophysical foregrounds, 2) the point sources alone, and 3) the noise alone: which are subproducts of the above, and are in the form of the PSM maps described in the previous section.<br />
<br />
Note that the cmb alone is not delivered as a separate product, but it can be recovered by simple subtraction of the component maps for the total signal map. It is envisaged that some number of separate noise realizations may be delivered in the future.<br />
<br />
<!-- [[CMB_and_astrophysical_component maps | CMB and astrophysical component maps]] chapter --><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
[[Category:Mission products|012]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Simulation_data&diff=7757Simulation data2013-06-19T15:13:31Z<p>Lvibert: /* Overall description */</p>
<hr />
<div>== Introduction ==<br />
----<br />
The 2013 Planck data release is supported by a comprehensive set of simulated maps, including both a fiducial realization of the sky as seen by Planck and 1000-realization Monte Carlo (MC) sets of CMB and noise simulations, collectively known as FFP6.<br />
<br />
The simulation process consists of <br />
* modeling the sky using pre-Planck data and generating an input sky map for each sky component for each detector that incorporates our best estimate of that detector's band-pass<br />
* simulating each detector's observation of each input sky component, following the Planck scanning strategy and using our best estimates of the detector's beam and noise properties, and mapping the results.<br />
* generating Monte Carlo realizations of the CMB and noise maps, again following the Planck scanning strategy and using our best estimates of the detector beams and noise properties respectively.<br />
The first step is done by the ''Planck Sky Model'' (PSM), and the second and third by a suite of ''Planck Simulation Tools'' (PST). A brief description of these is given below.<br />
<br />
== The Planck Sky Model ==<br />
----<br />
=== Overall description ===<br />
<br />
The Planck Sky Model, a complete set data and code to simulate sky emission at millimeter-wave frequencies, is described in detail in the Planck pre-launch [http://adsabs.harvard.edu/abs/2012arXiv1207.3675D| PSM paper] <cite>Delabrouille2012</cite>.<br />
<br />
The main simulations used to test and validate the Planck data analysis pipelines (and, in particular, component separation) makes use of simulations generated with version 1.7.7 of the PSM software. Sky emission comprises the following components: CMB, thermal dust, spinning dust, synchrotron, CO lines, free-free, thermal Sunyaev-Zel'dovich (SZ) effect (with first order relativistic corrections), kinetic SZ effect, radio and infrared sources, Cosmic Infrared Background (CIB).<br />
<br />
The CMB is a based on adiabatic initial perturbations, with the following cosmological parameters:<br />
* T_CMB = 2.725<br />
* H = 0.684<br />
* OMEGA_M = 0.292<br />
* OMEGA_B = 0.04724<br />
* OMEGA_NU = 0<br />
* OMEGA_K = 0<br />
* SIGMA_8 = 0.789<br />
* N_S = 0.9732<br />
* N_S_RUNNING = 0<br />
* N_T = 0<br />
* R = 0.0844<br />
* TAU_REION = 0.085<br />
* HE_FRACTION = 0.245<br />
* N_MASSLESS_NU = 3.04<br />
* N_MASSIVE_NU = 0<br />
* W_DARK_ENERGY = -1<br />
* K_PIVOT = 0.002<br />
* SCALAR_AMPLITUDE = 2.441e-9<br />
<br />
All other parameters are set to the default standard of the Jan 2012 version of CAMB. In addition, this simulated CMB contains non-Gaussian corrections of the local type, with an f_NL parameter of 20.4075.<br />
<br />
The Galactic ISM emission comprises 5 major components: Thermal dust, spinning dust, synchrotron, CO lines, and free-free emission. We refer the reader to the PSM publication for details. For the simulations generated here, however, the thermal dust model has been modified in the following way: Instead of being based on the 100 micron map of Schlegel, Finkbeiner and Davis <cite>schlegel1998</cite>, the dust template uses an internal release of the 857 GHz Planck observed map itself, in which point sources have been subtracted, and which has been locally filtered to remove CIB fluctuations in the regions of lowest column density. A caveat is that while this reduces the level of CIB fluctuations in the dust map in some of the regions, in regions of moderate dust column density the CIB contamination is actually somewhat larger than in the SFD map (by reason of different emission laws for dust and CIB, and of the highr resolution of the Planck map).<br />
<br />
The other emissions of the galactic ISM are simulated using the prescription described in the PSM paper. <br />
Synchrotron, Free-free and spinning dust emission are based on WMAP observations, as analyzed by Miville-Deschenes et al., 2008. Small scale fluctuations have been added to increase the variance on small scales and compensate the lower resolution of WMAP as compared to Planck (in particular HFI channels). The main limitation of these maps is the presence at high galactic latitude of fluctuations that may be imputable to WMAP noise. The presence of noise and of added Gaussian fluctuations on small scales may result in a few occasional pixels being negative (e.g. in the spinning dust maps). Low frequency foreground maps are also contaminated by some residuals of bright radio sources that have not been properly subtracted from the templates of diffuse emission.<br />
<br />
The CO maps are simulated using the CO J=1-0 observations of Dame et al. (2001)<cite>dame2001</cite>. The main limitations are limited sky coverage, lower resolution than that of Planck high frequency channels, line ratios (J=2-1)/(J=1-0) and (J=3-2)/(J=2-1) constant over the sky. The CO in the simulation is limited to the three lowest 12CO lines.<br />
<br />
Galaxy clusters are generated on the basis of cluster number counts, following the Tinker et al. (2008) mass function, for the cosmological parameters listed above. Clusters are assumed perfectly spherical, isothermal, and are modeled using the universal pressure profile of Arnaud et al. (2010) <cite>arnaud2010</cite>. Relativistic corrections following Itoh et al. (1998) are included to first order. The simulated kinetic SZ effect assumes no bulk flow, and a redshift-dependent average cluster velocity compatible with the linear growth of structures.<br />
<br />
Point sources comprise radio sources (based on extrapolations across frequencies of radio observations between 800 MHz and 5 GHz) and infrared sources (based on extrapolations in frequencies of IRAS sources). One small caveat that should be mentioned is that because of the unevenness of the radio source surveys, the equatorial southern part of the sky has less faint radio sources than the northern part. Although all the missing sources are well below the Planck detection level, this induces a small variation of the total emission background over the sky. Check the individual faint point source emission maps if this is a potential problem for your applications. See also the PSM publication for details about the PSM point source simulations.<br />
<br />
Finally, the far infrared background due to high redshift galaxies has been simulated using a procedure is based on the distribution of galaxies in shells of density contrast at various redshifts (Castex et al., PhD thesis; paper in preparation). This simulation has been modified by gradually substituting an uncorrelated extra term of CIB emission at low frequencies, artificially added in particular to decorrelate the CIB at frequencies below 217 GHz from the CIB above that frequency, to mimic the apparent decorrelation observed in the Planck Early Paper on CIB power spectrum. <br />
<br />
While the PSM simulations described here provide a reasonably representative multi-component model of sky emission, the users are warned that it has been put together mostly on the basis of data sets and knowledge pre-existing the Planck observations themselves. While it is sophisticated enough to include variations of emission laws of major components of ISM emission, different emission laws for most sources, and a reasonably coherent global picture, it is not (and is not supposed to be) identical to the real sky emission. The users are warned to use these simulations with caution.<br />
<br />
=== PSM Products ===<br />
<br />
The following products are available:<br />
<br />
* ''PR1_beta/HFI_SimMap_cmb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_co_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_firb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_strongps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_faintps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_freefree_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_synchrotron_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermaldust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_spindust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_kineticsz_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermalsz_2048_R1.10.fits''<br />
<br />
All files contains a single ''BINTABLE'' extension with either a single map (e.g., for the CMB) or one map for each HFI frequency (for all other components). In the latter case the columns are named ''F100'', ''F143'', … , ''F857''. Units are microK<sub>CMB</sub> for the CMB, and MJy/sr for the others. The structure is given below for multi-column files. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''FITS file structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'SIM-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|F100 || Real*4 || MJy/sr || 100GHz signal map<br />
|-<br />
|F143 || Real*4 || MJy/sr || 143GHz signal map<br />
|-<br />
|F217 || Real*4 || MJy/sr || 217GHz signal map<br />
|-<br />
|F353 || Real*4 || MJy/sr || 353GHz signal map<br />
|-<br />
|F545 || Real*4 || MJy/sr || 545GHz signal map<br />
|-<br />
|F857 || Real*4 || MJy/sr || 857GHz signal map<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COMP || string || component || Astrophysical omponent<br />
|-<br />
|COORDSYS || string || GALACTIC || Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside for LFI and HFI, respectively<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 />
|FREQ || string || GHz || The frequency channel <br />
|-<br />
|BAD_DATA || Real*4 || -1.63750E+30 || Healpix bad pixel value <br />
|-<br />
|BEAMTYPE || string || GAUSSIAN || Type of beam <br />
|-<br />
|BEAMSIZE || Real*4 || size || Beam size in arcmin<br />
|-<br />
|PSM-VERS || string || || PSM Versions used <br />
|}<br />
<br />
== The Planck Mission Simulations ==<br />
---------------------<br />
<br />
Since the full focal plane (FFP) simulations <br />
* involve both HFI and LFI data <br />
* include large, computationally challenging, MC realization sets<br />
they cannot be generated using either DPC's single-instrument cluster-based pipeline. Instead the PST consists of three distinct tool chains, each designed to run on the largest available supercomputers, that are used to generate the fiducial sky realization, the CMB MC, and the noise MC respectively. FFP6 was primarily generated on the Hopper and Edison systems at [http://www.nersc.gov NERSC], with some of the LFI noise MCs generated on the Louhi system at [http://www.csc.fi/english CSC].<br />
<br />
While FFP6 is guaranteed to be internally self-consistent there are a number of differences with the real data that should be borne in mind, although all tests performed to date indicate that these are statistically insignificant:<br />
* FFP6 includes our best measurements of the detector band-passes, main beams and noise power spectral densities - known issues include the absence of side-lobes and the use of a single, independent, noise spectrum per detector for the entire mission.<br />
* FFP6 excludes all pre-processing residuals, assuming perfect calibration, transfer function deconvolution and deglitching.<br />
* FFP6 uses the HFI pointing solution for the LFI frequencies, rather than the DPC's two focal plane model.<br />
* FFP6 uses a different map-maker to HFI, and as a consequence implements very slightly different data cuts - primarily at ring boundaries - resulting in marginally different hit-maps.<br />
<br />
=== Fiducial Sky ===<br />
<br />
For each detector, fiducial sky time-ordered data are generated separately for each of its 10 PSM component maps and its strong point source catalogue using the LevelS software <cite>#reinecke2006</cite> as follows:<br />
* The detector's beam and PSM map are converted to spherical harmonics using ''beam2alm'' and ''anafast'' respectively.<br />
* The beam-convolved map value is calculated over a 3-dimensional grid of sky locations and beam orientations using ''conviqt''.<br />
* The map-based time-ordered data are calculated sample-by-sample by interpolating over this grid using "multimod".<br />
* The catalogue-based time-ordered data are calculated sample-by-sample by beam-convolving any point source laying within a given angular distance of the pointing at each sample time using ''multimod''.<br />
<br />
For each frequency, fiducial sky maps are generated for <br />
* the total sky (including noise), <br />
* the foreground sky (excluding CMB but including noise), <br />
* the point source sky, and <br />
* the noise alone<br />
All maps are made using the ''MADAM'' destriping map-maker <cite>#[keihanen2010</cite> interfaced with the ''TOAST'' data abstraction layer . In order to construct the total time-ordered data required by each map, for each detector ''TOAST'' reads the various component time-streams separately and sums then, and, where necessary, simulates and adds a noise realization time-stream on the fly.<br />
<br />
HFI frequencies are mapped at ''HEALPix'' resolution nside=2048 using ring-length destriping baselines, while LFI frequencies are mapped at nside=1024 using 1s baselines.<br />
<br />
=== CMB Monte Carlo ===<br />
<br />
The CMB MC set is generated using ''FEBeCoP'' <cite>#mitra2010</cite>, which generates an effective beam for each pixel in a map at each frequency by accumulating the weights of all pixels within a fixed distance of that pixel, summed over all observations by all detectors at that frequency. It then applies this effective beam pixel-by-pixel to each of 1000 input CMB sky realizations.<br />
<br />
=== Noise Monte Carlo ===<br />
<br />
The noise MC set is generated just as the fiducial noise maps, using ''MADAM/TOAST''. In order to avoid spurious correlations within and between the 1000 realizations, each stationary interval for each detector for each realization is generated from a distinct sub-sequence of a single statistically robust, extremely long period, pseudo-random number sequence.<br />
<br />
== Products delivered ==<br />
<br />
A single simulation is delivered, which is divided into two types of products:<br />
; Six sky maps of the nominal mission at each HFI frequency: which is the basic simulation product. These files have the same structure as the equivalent ''SkyMap'' products described in the [[Frequency_Maps | Frequency Maps ]] chapter -- namely one ''BINTABLE'' extension with three columns containing 1) Signal, 2) hit-count, and 3) variance (TBC)<br />
; Three maps of the nominal mission containing 1) the sum of all astrophysical foregrounds, 2) the point sources alone, and 3) the noise alone: which are subproducts of the above, and are in the form of the PSM maps described in the previous section.<br />
<br />
Note that the cmb alone is not delivered as a separate product, but it can be recovered by simple subtraction of the component maps for the total signal map. It is envisaged that some number of separate noise realizations may be delivered in the future.<br />
<br />
<!-- [[CMB_and_astrophysical_component maps | CMB and astrophysical component maps]] chapter --><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
[[Category:Mission products|012]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Simulation_data&diff=7753Simulation data2013-06-19T15:07:32Z<p>Lvibert: </p>
<hr />
<div>== Introduction ==<br />
----<br />
The 2013 Planck data release is supported by a comprehensive set of simulated maps, including both a fiducial realization of the sky as seen by Planck and 1000-realization Monte Carlo (MC) sets of CMB and noise simulations, collectively known as FFP6.<br />
<br />
The simulation process consists of <br />
* modeling the sky using pre-Planck data and generating an input sky map for each sky component for each detector that incorporates our best estimate of that detector's band-pass<br />
* simulating each detector's observation of each input sky component, following the Planck scanning strategy and using our best estimates of the detector's beam and noise properties, and mapping the results.<br />
* generating Monte Carlo realizations of the CMB and noise maps, again following the Planck scanning strategy and using our best estimates of the detector beams and noise properties respectively.<br />
The first step is done by the ''Planck Sky Model'' (PSM), and the second and third by a suite of ''Planck Simulation Tools'' (PST). A brief description of these is given below.<br />
<br />
== The Planck Sky Model ==<br />
----<br />
=== Overall description ===<br />
<br />
The Planck Sky Model, a complete set data and code to simulate sky emission at millimeter-wave frequencies, is described in detail in the Planck pre-launch [http://adsabs.harvard.edu/abs/2012arXiv1207.3675D| PSM paper] <cite>Delabrouille2012</cite>.<br />
<br />
The main simulations used to test and validate the Planck data analysis pipelines (and, in particular, component separation) makes use of simulations generated with version 1.7.7 of the PSM software. Sky emission comprises the following components: CMB, thermal dust, spinning dust, synchrotron, CO lines, free-free, thermal Sunyaev-Zel'dovich (SZ) effect (with first order relativistic corrections), kinetic SZ effect, radio and infrared sources, Cosmic Infrared Background (CIB).<br />
<br />
The CMB is a based on adiabatic initial perturbations, with the following cosmological parameters:<br />
* T_CMB = 2.725<br />
* H = 0.684<br />
* OMEGA_M = 0.292<br />
* OMEGA_B = 0.04724<br />
* OMEGA_NU = 0<br />
* OMEGA_K = 0<br />
* SIGMA_8 = 0.789<br />
* N_S = 0.9732<br />
* N_S_RUNNING = 0<br />
* N_T = 0<br />
* R = 0.0844<br />
* TAU_REION = 0.085<br />
* HE_FRACTION = 0.245<br />
* N_MASSLESS_NU = 3.04<br />
* N_MASSIVE_NU = 0<br />
* W_DARK_ENERGY = -1<br />
* K_PIVOT = 0.002<br />
* SCALAR_AMPLITUDE = 2.441e-9<br />
<br />
All other parameters are set to the default standard of the Jan 2012 version of CAMB. In addition, this simulated CMB contains non-Gaussian corrections of the local type, with an f_NL parameter of 20.4075.<br />
<br />
The Galactic ISM emission comprises 5 major components: Thermal dust, spinning dust, synchrotron, CO lines, and free-free emission. We refer the reader to the PSM publication for details. For the simulations generated here, however, the thermal dust model has been modified in the following way: Instead of being based on the 100 micron map of Schlegel, Finkbeiner and Davis (SFD; 1998), the dust template uses an internal release of the 857 GHz Planck observed map itself, in which point sources have been subtracted, and which has been locally filtered to remove CIB fluctuations in the regions of lowest column density. A caveat is that while this reduces the level of CIB fluctuations in the dust map in some of the regions, in regions of moderate dust column density the CIB contamination is actually somewhat larger than in the SFD map (by reason of different emission laws for dust and CIB, and of the highr resolution of the Planck map).<br />
<br />
The other emissions of the galactic ISM are simulated using the prescription described in the PSM paper. <br />
Synchrotron, Free-free and spinning dust emission are based on WMAP observations, as analyzed by Miville-Deschenes et al., 2008. Small scale fluctuations have been added to increase the variance on small scales and compensate the lower resolution of WMAP as compared to Planck (in particular HFI channels). The main limitation of these maps is the presence at high galactic latitude of fluctuations that may be imputable to WMAP noise. The presence of noise and of added Gaussian fluctuations on small scales may result in a few occasional pixels being negative (e.g. in the spinning dust maps). Low frequency foreground maps are also contaminated by some residuals of bright radio sources that have not been properly subtracted from the templates of diffuse emission.<br />
<br />
The CO maps are simulated using the CO J=1-0 observations of Dame et al. (2001). The main limitations are limited sky coverage, lower resolution than that of Planck high frequency channels, line ratios (J=2-1)/(J=1-0) and (J=3-2)/(J=2-1) constant over the sky. The CO in the simulation is limited to the three lowest 12CO lines.<br />
<br />
Galaxy clusters are generated on the basis of cluster number counts, following the Tinker et al. (2008) mass function, for the cosmological parameters listed above. Clusters are assumed perfectly spherical, isothermal, and are modeled using the universal pressure profile of Arnaud et al. (2010). Relativistic corrections following Itoh et al. (1998) are included to first order. The simulated kinetic SZ effect assumes no bulk flow, and a redshift-dependent average cluster velocity compatible with the linear growth of structures.<br />
<br />
Point sources comprise radio sources (based on extrapolations across frequencies of radio observations between 800 MHz and 5 GHz) and infrared sources (based on extrapolations in frequencies of IRAS sources). One small caveat that should be mentioned is that because of the unevenness of the radio source surveys, the equatorial southern part of the sky has less faint radio sources than the northern part. Although all the missing sources are well below the Planck detection level, this induces a small variation of the total emission background over the sky. Check the individual faint point source emission maps if this is a potential problem for your applications. See also the PSM publication for details about the PSM point source simulations.<br />
<br />
Finally, the far infrared background due to high redshift galaxies has been simulated using a procedure is based on the distribution of galaxies in shells of density contrast at various redshifts (Castex et al., PhD thesis; paper in preparation). This simulation has been modified by gradually substituting an uncorrelated extra term of CIB emission at low frequencies, artificially added in particular to decorrelate the CIB at frequencies below 217 GHz from the CIB above that frequency, to mimic the apparent decorrelation observed in the Planck Early Paper on CIB power spectrum. <br />
<br />
While the PSM simulations described here provide a reasonably representative multi-component model of sky emission, the users are warned that it has been put together mostly on the basis of data sets and knowledge pre-existing the Planck observations themselves. While it is sophisticated enough to include variations of emission laws of major components of ISM emission, different emission laws for most sources, and a reasonably coherent global picture, it is not (and is not supposed to be) identical to the real sky emission. The users are warned to use these simulations with caution.<br />
<br />
=== PSM Products ===<br />
<br />
The following products are available:<br />
<br />
* ''PR1_beta/HFI_SimMap_cmb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_co_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_firb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_strongps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_faintps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_freefree_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_synchrotron_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermaldust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_spindust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_kineticsz_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermalsz_2048_R1.10.fits''<br />
<br />
All files contains a single ''BINTABLE'' extension with either a single map (e.g., for the CMB) or one map for each HFI frequency (for all other components). In the latter case the columns are named ''F100'', ''F143'', … , ''F857''. Units are microK<sub>CMB</sub> for the CMB, and MJy/sr for the others. The structure is given below for multi-column files. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''FITS file structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'SIM-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|F100 || Real*4 || MJy/sr || 100GHz signal map<br />
|-<br />
|F143 || Real*4 || MJy/sr || 143GHz signal map<br />
|-<br />
|F217 || Real*4 || MJy/sr || 217GHz signal map<br />
|-<br />
|F353 || Real*4 || MJy/sr || 353GHz signal map<br />
|-<br />
|F545 || Real*4 || MJy/sr || 545GHz signal map<br />
|-<br />
|F857 || Real*4 || MJy/sr || 857GHz signal map<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COMP || string || component || Astrophysical omponent<br />
|-<br />
|COORDSYS || string || GALACTIC || Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside for LFI and HFI, respectively<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 />
|FREQ || string || GHz || The frequency channel <br />
|-<br />
|BAD_DATA || Real*4 || -1.63750E+30 || Healpix bad pixel value <br />
|-<br />
|BEAMTYPE || string || GAUSSIAN || Type of beam <br />
|-<br />
|BEAMSIZE || Real*4 || size || Beam size in arcmin<br />
|-<br />
|PSM-VERS || string || || PSM Versions used <br />
|}<br />
<br />
== The Planck Mission Simulations ==<br />
---------------------<br />
<br />
Since the full focal plane (FFP) simulations <br />
* involve both HFI and LFI data <br />
* include large, computationally challenging, MC realization sets<br />
they cannot be generated using either DPC's single-instrument cluster-based pipeline. Instead the PST consists of three distinct tool chains, each designed to run on the largest available supercomputers, that are used to generate the fiducial sky realization, the CMB MC, and the noise MC respectively. FFP6 was primarily generated on the Hopper and Edison systems at [http://www.nersc.gov NERSC], with some of the LFI noise MCs generated on the Louhi system at [http://www.csc.fi/english CSC].<br />
<br />
While FFP6 is guaranteed to be internally self-consistent there are a number of differences with the real data that should be borne in mind, although all tests performed to date indicate that these are statistically insignificant:<br />
* FFP6 includes our best measurements of the detector band-passes, main beams and noise power spectral densities - known issues include the absence of side-lobes and the use of a single, independent, noise spectrum per detector for the entire mission.<br />
* FFP6 excludes all pre-processing residuals, assuming perfect calibration, transfer function deconvolution and deglitching.<br />
* FFP6 uses the HFI pointing solution for the LFI frequencies, rather than the DPC's two focal plane model.<br />
* FFP6 uses a different map-maker to HFI, and as a consequence implements very slightly different data cuts - primarily at ring boundaries - resulting in marginally different hit-maps.<br />
<br />
=== Fiducial Sky ===<br />
<br />
For each detector, fiducial sky time-ordered data are generated separately for each of its 10 PSM component maps and its strong point source catalogue using the LevelS software <cite>#reinecke2006</cite> as follows:<br />
* The detector's beam and PSM map are converted to spherical harmonics using ''beam2alm'' and ''anafast'' respectively.<br />
* The beam-convolved map value is calculated over a 3-dimensional grid of sky locations and beam orientations using ''conviqt''.<br />
* The map-based time-ordered data are calculated sample-by-sample by interpolating over this grid using "multimod".<br />
* The catalogue-based time-ordered data are calculated sample-by-sample by beam-convolving any point source laying within a given angular distance of the pointing at each sample time using ''multimod''.<br />
<br />
For each frequency, fiducial sky maps are generated for <br />
* the total sky (including noise), <br />
* the foreground sky (excluding CMB but including noise), <br />
* the point source sky, and <br />
* the noise alone<br />
All maps are made using the ''MADAM'' destriping map-maker <cite>#[keihanen2010</cite> interfaced with the ''TOAST'' data abstraction layer . In order to construct the total time-ordered data required by each map, for each detector ''TOAST'' reads the various component time-streams separately and sums then, and, where necessary, simulates and adds a noise realization time-stream on the fly.<br />
<br />
HFI frequencies are mapped at ''HEALPix'' resolution nside=2048 using ring-length destriping baselines, while LFI frequencies are mapped at nside=1024 using 1s baselines.<br />
<br />
=== CMB Monte Carlo ===<br />
<br />
The CMB MC set is generated using ''FEBeCoP'' <cite>#mitra2010</cite>, which generates an effective beam for each pixel in a map at each frequency by accumulating the weights of all pixels within a fixed distance of that pixel, summed over all observations by all detectors at that frequency. It then applies this effective beam pixel-by-pixel to each of 1000 input CMB sky realizations.<br />
<br />
=== Noise Monte Carlo ===<br />
<br />
The noise MC set is generated just as the fiducial noise maps, using ''MADAM/TOAST''. In order to avoid spurious correlations within and between the 1000 realizations, each stationary interval for each detector for each realization is generated from a distinct sub-sequence of a single statistically robust, extremely long period, pseudo-random number sequence.<br />
<br />
== Products delivered ==<br />
<br />
A single simulation is delivered, which is divided into two types of products:<br />
; Six sky maps of the nominal mission at each HFI frequency: which is the basic simulation product. These files have the same structure as the equivalent ''SkyMap'' products described in the [[Frequency_Maps | Frequency Maps ]] chapter -- namely one ''BINTABLE'' extension with three columns containing 1) Signal, 2) hit-count, and 3) variance (TBC)<br />
; Three maps of the nominal mission containing 1) the sum of all astrophysical foregrounds, 2) the point sources alone, and 3) the noise alone: which are subproducts of the above, and are in the form of the PSM maps described in the previous section.<br />
<br />
Note that the cmb alone is not delivered as a separate product, but it can be recovered by simple subtraction of the component maps for the total signal map. It is envisaged that some number of separate noise realizations may be delivered in the future.<br />
<br />
<!-- [[CMB_and_astrophysical_component maps | CMB and astrophysical component maps]] chapter --><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
[[Category:Mission products|012]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Simulation_data&diff=7751Simulation data2013-06-19T15:06:00Z<p>Lvibert: /* Overall description */</p>
<hr />
<div>== Introduction ==<br />
----<br />
The 2013 Planck data release is supported by a comprehensive set of simulated maps, including both a fiducial realization of the sky as seen by Planck and 1000-realization Monte Carlo (MC) sets of CMB and noise simulations, collectively known as FFP6.<br />
<br />
The simulation process consists of <br />
* modeling the sky using pre-Planck data and generating an input sky map for each sky component for each detector that incorporates our best estimate of that detector's band-pass<br />
* simulating each detector's observation of each input sky component, following the Planck scanning strategy and using our best estimates of the detector's beam and noise properties, and mapping the results.<br />
* generating Monte Carlo realizations of the CMB and noise maps, again following the Planck scanning strategy and using our best estimates of the detector beams and noise properties respectively.<br />
The first step is done by the ''Planck Sky Model'' (PSM), and the second and third by a suite of ''Planck Simulation Tools'' (PST). A brief description of these is given below.<br />
<br />
== The Planck Sky Model ==<br />
---<br />
=== Overall description ===<br />
<br />
The Planck Sky Model, a complete set data and code to simulate sky emission at millimeter-wave frequencies, is described in detail in the Planck pre-launch [http://adsabs.harvard.edu/abs/2012arXiv1207.3675D| PSM paper] <cite>Delabrouille2012</cite>.<br />
<br />
The main simulations used to test and validate the Planck data analysis pipelines (and, in particular, component separation) makes use of simulations generated with version 1.7.7 of the PSM software. Sky emission comprises the following components: CMB, thermal dust, spinning dust, synchrotron, CO lines, free-free, thermal Sunyaev-Zel'dovich (SZ) effect (with first order relativistic corrections), kinetic SZ effect, radio and infrared sources, Cosmic Infrared Background (CIB).<br />
<br />
The CMB is a based on adiabatic initial perturbations, with the following cosmological parameters:<br />
* T_CMB = 2.725<br />
* H = 0.684<br />
* OMEGA_M = 0.292<br />
* OMEGA_B = 0.04724<br />
* OMEGA_NU = 0<br />
* OMEGA_K = 0<br />
* SIGMA_8 = 0.789<br />
* N_S = 0.9732<br />
* N_S_RUNNING = 0<br />
* N_T = 0<br />
* R = 0.0844<br />
* TAU_REION = 0.085<br />
* HE_FRACTION = 0.245<br />
* N_MASSLESS_NU = 3.04<br />
* N_MASSIVE_NU = 0<br />
* W_DARK_ENERGY = -1<br />
* K_PIVOT = 0.002<br />
* SCALAR_AMPLITUDE = 2.441e-9<br />
<br />
All other parameters are set to the default standard of the Jan 2012 version of CAMB. In addition, this simulated CMB contains non-Gaussian corrections of the local type, with an f_NL parameter of 20.4075.<br />
<br />
The Galactic ISM emission comprises 5 major components: Thermal dust, spinning dust, synchrotron, CO lines, and free-free emission. We refer the reader to the PSM publication for details. For the simulations generated here, however, the thermal dust model has been modified in the following way: Instead of being based on the 100 micron map of Schlegel, Finkbeiner and Davis (SFD; 1998), the dust template uses an internal release of the 857 GHz Planck observed map itself, in which point sources have been subtracted, and which has been locally filtered to remove CIB fluctuations in the regions of lowest column density. A caveat is that while this reduces the level of CIB fluctuations in the dust map in some of the regions, in regions of moderate dust column density the CIB contamination is actually somewhat larger than in the SFD map (by reason of different emission laws for dust and CIB, and of the highr resolution of the Planck map).<br />
<br />
The other emissions of the galactic ISM are simulated using the prescription described in the PSM paper. <br />
Synchrotron, Free-free and spinning dust emission are based on WMAP observations, as analyzed by Miville-Deschenes et al., 2008. Small scale fluctuations have been added to increase the variance on small scales and compensate the lower resolution of WMAP as compared to Planck (in particular HFI channels). The main limitation of these maps is the presence at high galactic latitude of fluctuations that may be imputable to WMAP noise. The presence of noise and of added Gaussian fluctuations on small scales may result in a few occasional pixels being negative (e.g. in the spinning dust maps). Low frequency foreground maps are also contaminated by some residuals of bright radio sources that have not been properly subtracted from the templates of diffuse emission.<br />
<br />
The CO maps are simulated using the CO J=1-0 observations of Dame et al. (2001). The main limitations are limited sky coverage, lower resolution than that of Planck high frequency channels, line ratios (J=2-1)/(J=1-0) and (J=3-2)/(J=2-1) constant over the sky. The CO in the simulation is limited to the three lowest 12CO lines.<br />
<br />
Galaxy clusters are generated on the basis of cluster number counts, following the Tinker et al. (2008) mass function, for the cosmological parameters listed above. Clusters are assumed perfectly spherical, isothermal, and are modeled using the universal pressure profile of Arnaud et al. (2010). Relativistic corrections following Itoh et al. (1998) are included to first order. The simulated kinetic SZ effect assumes no bulk flow, and a redshift-dependent average cluster velocity compatible with the linear growth of structures.<br />
<br />
Point sources comprise radio sources (based on extrapolations across frequencies of radio observations between 800 MHz and 5 GHz) and infrared sources (based on extrapolations in frequencies of IRAS sources). One small caveat that should be mentioned is that because of the unevenness of the radio source surveys, the equatorial southern part of the sky has less faint radio sources than the northern part. Although all the missing sources are well below the Planck detection level, this induces a small variation of the total emission background over the sky. Check the individual faint point source emission maps if this is a potential problem for your applications. See also the PSM publication for details about the PSM point source simulations.<br />
<br />
Finally, the far infrared background due to high redshift galaxies has been simulated using a procedure is based on the distribution of galaxies in shells of density contrast at various redshifts (Castex et al., PhD thesis; paper in preparation). This simulation has been modified by gradually substituting an uncorrelated extra term of CIB emission at low frequencies, artificially added in particular to decorrelate the CIB at frequencies below 217 GHz from the CIB above that frequency, to mimic the apparent decorrelation observed in the Planck Early Paper on CIB power spectrum. <br />
<br />
While the PSM simulations described here provide a reasonably representative multi-component model of sky emission, the users are warned that it has been put together mostly on the basis of data sets and knowledge pre-existing the Planck observations themselves. While it is sophisticated enough to include variations of emission laws of major components of ISM emission, different emission laws for most sources, and a reasonably coherent global picture, it is not (and is not supposed to be) identical to the real sky emission. The users are warned to use these simulations with caution.<br />
<br />
=== PSM Products ===<br />
<br />
The following products are available:<br />
<br />
* ''PR1_beta/HFI_SimMap_cmb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_co_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_firb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_strongps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_faintps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_freefree_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_synchrotron_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermaldust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_spindust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_kineticsz_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermalsz_2048_R1.10.fits''<br />
<br />
All files contains a single ''BINTABLE'' extension with either a single map (e.g., for the CMB) or one map for each HFI frequency (for all other components). In the latter case the columns are named ''F100'', ''F143'', … , ''F857''. Units are microK<sub>CMB</sub> for the CMB, and MJy/sr for the others. The structure is given below for multi-column files. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''FITS file structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'SIM-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|F100 || Real*4 || MJy/sr || 100GHz signal map<br />
|-<br />
|F143 || Real*4 || MJy/sr || 143GHz signal map<br />
|-<br />
|F217 || Real*4 || MJy/sr || 217GHz signal map<br />
|-<br />
|F353 || Real*4 || MJy/sr || 353GHz signal map<br />
|-<br />
|F545 || Real*4 || MJy/sr || 545GHz signal map<br />
|-<br />
|F857 || Real*4 || MJy/sr || 857GHz signal map<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COMP || string || component || Astrophysical omponent<br />
|-<br />
|COORDSYS || string || GALACTIC || Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside for LFI and HFI, respectively<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 />
|FREQ || string || GHz || The frequency channel <br />
|-<br />
|BAD_DATA || Real*4 || -1.63750E+30 || Healpix bad pixel value <br />
|-<br />
|BEAMTYPE || string || GAUSSIAN || Type of beam <br />
|-<br />
|BEAMSIZE || Real*4 || size || Beam size in arcmin<br />
|-<br />
|PSM-VERS || string || || PSM Versions used <br />
|}<br />
<br />
== The Planck Mission Simulations ==<br />
---------------------<br />
<br />
Since the full focal plane (FFP) simulations <br />
* involve both HFI and LFI data <br />
* include large, computationally challenging, MC realization sets<br />
they cannot be generated using either DPC's single-instrument cluster-based pipeline. Instead the PST consists of three distinct tool chains, each designed to run on the largest available supercomputers, that are used to generate the fiducial sky realization, the CMB MC, and the noise MC respectively. FFP6 was primarily generated on the Hopper and Edison systems at [http://www.nersc.gov NERSC], with some of the LFI noise MCs generated on the Louhi system at [http://www.csc.fi/english CSC].<br />
<br />
While FFP6 is guaranteed to be internally self-consistent there are a number of differences with the real data that should be borne in mind, although all tests performed to date indicate that these are statistically insignificant:<br />
* FFP6 includes our best measurements of the detector band-passes, main beams and noise power spectral densities - known issues include the absence of side-lobes and the use of a single, independent, noise spectrum per detector for the entire mission.<br />
* FFP6 excludes all pre-processing residuals, assuming perfect calibration, transfer function deconvolution and deglitching.<br />
* FFP6 uses the HFI pointing solution for the LFI frequencies, rather than the DPC's two focal plane model.<br />
* FFP6 uses a different map-maker to HFI, and as a consequence implements very slightly different data cuts - primarily at ring boundaries - resulting in marginally different hit-maps.<br />
<br />
=== Fiducial Sky ===<br />
<br />
For each detector, fiducial sky time-ordered data are generated separately for each of its 10 PSM component maps and its strong point source catalogue using the LevelS software <cite>#reinecke2006</cite> as follows:<br />
* The detector's beam and PSM map are converted to spherical harmonics using ''beam2alm'' and ''anafast'' respectively.<br />
* The beam-convolved map value is calculated over a 3-dimensional grid of sky locations and beam orientations using ''conviqt''.<br />
* The map-based time-ordered data are calculated sample-by-sample by interpolating over this grid using "multimod".<br />
* The catalogue-based time-ordered data are calculated sample-by-sample by beam-convolving any point source laying within a given angular distance of the pointing at each sample time using ''multimod''.<br />
<br />
For each frequency, fiducial sky maps are generated for <br />
* the total sky (including noise), <br />
* the foreground sky (excluding CMB but including noise), <br />
* the point source sky, and <br />
* the noise alone<br />
All maps are made using the ''MADAM'' destriping map-maker <cite>#[keihanen2010</cite> interfaced with the ''TOAST'' data abstraction layer . In order to construct the total time-ordered data required by each map, for each detector ''TOAST'' reads the various component time-streams separately and sums then, and, where necessary, simulates and adds a noise realization time-stream on the fly.<br />
<br />
HFI frequencies are mapped at ''HEALPix'' resolution nside=2048 using ring-length destriping baselines, while LFI frequencies are mapped at nside=1024 using 1s baselines.<br />
<br />
=== CMB Monte Carlo ===<br />
<br />
The CMB MC set is generated using ''FEBeCoP'' <cite>#mitra2010</cite>, which generates an effective beam for each pixel in a map at each frequency by accumulating the weights of all pixels within a fixed distance of that pixel, summed over all observations by all detectors at that frequency. It then applies this effective beam pixel-by-pixel to each of 1000 input CMB sky realizations.<br />
<br />
=== Noise Monte Carlo ===<br />
<br />
The noise MC set is generated just as the fiducial noise maps, using ''MADAM/TOAST''. In order to avoid spurious correlations within and between the 1000 realizations, each stationary interval for each detector for each realization is generated from a distinct sub-sequence of a single statistically robust, extremely long period, pseudo-random number sequence.<br />
<br />
== Products delivered ==<br />
<br />
A single simulation is delivered, which is divided into two types of products:<br />
; Six sky maps of the nominal mission at each HFI frequency: which is the basic simulation product. These files have the same structure as the equivalent ''SkyMap'' products described in the [[Frequency_Maps | Frequency Maps ]] chapter -- namely one ''BINTABLE'' extension with three columns containing 1) Signal, 2) hit-count, and 3) variance (TBC)<br />
; Three maps of the nominal mission containing 1) the sum of all astrophysical foregrounds, 2) the point sources alone, and 3) the noise alone: which are subproducts of the above, and are in the form of the PSM maps described in the previous section.<br />
<br />
Note that the cmb alone is not delivered as a separate product, but it can be recovered by simple subtraction of the component maps for the total signal map. It is envisaged that some number of separate noise realizations may be delivered in the future.<br />
<br />
<!-- [[CMB_and_astrophysical_component maps | CMB and astrophysical component maps]] chapter --><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
[[Category:Mission products|012]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Simulation_data&diff=7748Simulation data2013-06-19T15:04:28Z<p>Lvibert: /* Overall description */</p>
<hr />
<div>== Introduction ==<br />
----<br />
The 2013 Planck data release is supported by a comprehensive set of simulated maps, including both a fiducial realization of the sky as seen by Planck and 1000-realization Monte Carlo (MC) sets of CMB and noise simulations, collectively known as FFP6.<br />
<br />
The simulation process consists of <br />
* modeling the sky using pre-Planck data and generating an input sky map for each sky component for each detector that incorporates our best estimate of that detector's band-pass<br />
* simulating each detector's observation of each input sky component, following the Planck scanning strategy and using our best estimates of the detector's beam and noise properties, and mapping the results.<br />
* generating Monte Carlo realizations of the CMB and noise maps, again following the Planck scanning strategy and using our best estimates of the detector beams and noise properties respectively.<br />
The first step is done by the ''Planck Sky Model'' (PSM), and the second and third by a suite of ''Planck Simulation Tools'' (PST). A brief description of these is given below.<br />
<br />
== The Planck Sky Model ==<br />
---<br />
=== Overall description ===<br />
<br />
The Planck Sky Model, a complete set data and code to simulate sky emission at millimeter-wave frequencies, is described in detail in the [http://adsabs.harvard.edu/abs/2012arXiv1207.3675D | Planck pre-launch PSM paper] <cite>Delabrouille2012</cite>.<br />
<br />
The main simulations used to test and validate the Planck data analysis pipelines (and, in particular, component separation) makes use of simulations generated with version 1.7.7 of the PSM software. Sky emission comprises the following components: CMB, thermal dust, spinning dust, synchrotron, CO lines, free-free, thermal Sunyaev-Zel'dovich (SZ) effect (with first order relativistic corrections), kinetic SZ effect, radio and infrared sources, Cosmic Infrared Background (CIB).<br />
<br />
The CMB is a based on adiabatic initial perturbations, with the following cosmological parameters:<br />
* T_CMB = 2.725<br />
* H = 0.684<br />
* OMEGA_M = 0.292<br />
* OMEGA_B = 0.04724<br />
* OMEGA_NU = 0<br />
* OMEGA_K = 0<br />
* SIGMA_8 = 0.789<br />
* N_S = 0.9732<br />
* N_S_RUNNING = 0<br />
* N_T = 0<br />
* R = 0.0844<br />
* TAU_REION = 0.085<br />
* HE_FRACTION = 0.245<br />
* N_MASSLESS_NU = 3.04<br />
* N_MASSIVE_NU = 0<br />
* W_DARK_ENERGY = -1<br />
* K_PIVOT = 0.002<br />
* SCALAR_AMPLITUDE = 2.441e-9<br />
<br />
All other parameters are set to the default standard of the Jan 2012 version of CAMB. In addition, this simulated CMB contains non-Gaussian corrections of the local type, with an f_NL parameter of 20.4075.<br />
<br />
The Galactic ISM emission comprises 5 major components: Thermal dust, spinning dust, synchrotron, CO lines, and free-free emission. We refer the reader to the PSM publication for details. For the simulations generated here, however, the thermal dust model has been modified in the following way: Instead of being based on the 100 micron map of Schlegel, Finkbeiner and Davis (SFD; 1998), the dust template uses an internal release of the 857 GHz Planck observed map itself, in which point sources have been subtracted, and which has been locally filtered to remove CIB fluctuations in the regions of lowest column density. A caveat is that while this reduces the level of CIB fluctuations in the dust map in some of the regions, in regions of moderate dust column density the CIB contamination is actually somewhat larger than in the SFD map (by reason of different emission laws for dust and CIB, and of the highr resolution of the Planck map).<br />
<br />
The other emissions of the galactic ISM are simulated using the prescription described in the PSM paper. <br />
Synchrotron, Free-free and spinning dust emission are based on WMAP observations, as analyzed by Miville-Deschenes et al., 2008. Small scale fluctuations have been added to increase the variance on small scales and compensate the lower resolution of WMAP as compared to Planck (in particular HFI channels). The main limitation of these maps is the presence at high galactic latitude of fluctuations that may be imputable to WMAP noise. The presence of noise and of added Gaussian fluctuations on small scales may result in a few occasional pixels being negative (e.g. in the spinning dust maps). Low frequency foreground maps are also contaminated by some residuals of bright radio sources that have not been properly subtracted from the templates of diffuse emission.<br />
<br />
The CO maps are simulated using the CO J=1-0 observations of Dame et al. (2001). The main limitations are limited sky coverage, lower resolution than that of Planck high frequency channels, line ratios (J=2-1)/(J=1-0) and (J=3-2)/(J=2-1) constant over the sky. The CO in the simulation is limited to the three lowest 12CO lines.<br />
<br />
Galaxy clusters are generated on the basis of cluster number counts, following the Tinker et al. (2008) mass function, for the cosmological parameters listed above. Clusters are assumed perfectly spherical, isothermal, and are modeled using the universal pressure profile of Arnaud et al. (2010). Relativistic corrections following Itoh et al. (1998) are included to first order. The simulated kinetic SZ effect assumes no bulk flow, and a redshift-dependent average cluster velocity compatible with the linear growth of structures.<br />
<br />
Point sources comprise radio sources (based on extrapolations across frequencies of radio observations between 800 MHz and 5 GHz) and infrared sources (based on extrapolations in frequencies of IRAS sources). One small caveat that should be mentioned is that because of the unevenness of the radio source surveys, the equatorial southern part of the sky has less faint radio sources than the northern part. Although all the missing sources are well below the Planck detection level, this induces a small variation of the total emission background over the sky. Check the individual faint point source emission maps if this is a potential problem for your applications. See also the PSM publication for details about the PSM point source simulations.<br />
<br />
Finally, the far infrared background due to high redshift galaxies has been simulated using a procedure is based on the distribution of galaxies in shells of density contrast at various redshifts (Castex et al., PhD thesis; paper in preparation). This simulation has been modified by gradually substituting an uncorrelated extra term of CIB emission at low frequencies, artificially added in particular to decorrelate the CIB at frequencies below 217 GHz from the CIB above that frequency, to mimic the apparent decorrelation observed in the Planck Early Paper on CIB power spectrum. <br />
<br />
While the PSM simulations described here provide a reasonably representative multi-component model of sky emission, the users are warned that it has been put together mostly on the basis of data sets and knowledge pre-existing the Planck observations themselves. While it is sophisticated enough to include variations of emission laws of major components of ISM emission, different emission laws for most sources, and a reasonably coherent global picture, it is not (and is not supposed to be) identical to the real sky emission. The users are warned to use these simulations with caution.<br />
<br />
=== PSM Products ===<br />
<br />
The following products are available:<br />
<br />
* ''PR1_beta/HFI_SimMap_cmb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_co_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_firb_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_strongps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_faintps_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_freefree_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_synchrotron_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermaldust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_spindust_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_kineticsz_2048_R1.10.fits''<br />
* ''PR1_beta/HFI_SimMap_thermalsz_2048_R1.10.fits''<br />
<br />
All files contains a single ''BINTABLE'' extension with either a single map (e.g., for the CMB) or one map for each HFI frequency (for all other components). In the latter case the columns are named ''F100'', ''F143'', … , ''F857''. Units are microK<sub>CMB</sub> for the CMB, and MJy/sr for the others. The structure is given below for multi-column files. <br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''FITS file structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'SIM-MAP' : Data columns<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|F100 || Real*4 || MJy/sr || 100GHz signal map<br />
|-<br />
|F143 || Real*4 || MJy/sr || 143GHz signal map<br />
|-<br />
|F217 || Real*4 || MJy/sr || 217GHz signal map<br />
|-<br />
|F353 || Real*4 || MJy/sr || 353GHz signal map<br />
|-<br />
|F545 || Real*4 || MJy/sr || 545GHz signal map<br />
|-<br />
|F857 || Real*4 || MJy/sr || 857GHz signal map<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX ||<br />
|-<br />
|COMP || string || component || Astrophysical omponent<br />
|-<br />
|COORDSYS || string || GALACTIC || Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int || 2048 || Healpix Nside for LFI and HFI, respectively<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 />
|FREQ || string || GHz || The frequency channel <br />
|-<br />
|BAD_DATA || Real*4 || -1.63750E+30 || Healpix bad pixel value <br />
|-<br />
|BEAMTYPE || string || GAUSSIAN || Type of beam <br />
|-<br />
|BEAMSIZE || Real*4 || size || Beam size in arcmin<br />
|-<br />
|PSM-VERS || string || || PSM Versions used <br />
|}<br />
<br />
== The Planck Mission Simulations ==<br />
---------------------<br />
<br />
Since the full focal plane (FFP) simulations <br />
* involve both HFI and LFI data <br />
* include large, computationally challenging, MC realization sets<br />
they cannot be generated using either DPC's single-instrument cluster-based pipeline. Instead the PST consists of three distinct tool chains, each designed to run on the largest available supercomputers, that are used to generate the fiducial sky realization, the CMB MC, and the noise MC respectively. FFP6 was primarily generated on the Hopper and Edison systems at [http://www.nersc.gov NERSC], with some of the LFI noise MCs generated on the Louhi system at [http://www.csc.fi/english CSC].<br />
<br />
While FFP6 is guaranteed to be internally self-consistent there are a number of differences with the real data that should be borne in mind, although all tests performed to date indicate that these are statistically insignificant:<br />
* FFP6 includes our best measurements of the detector band-passes, main beams and noise power spectral densities - known issues include the absence of side-lobes and the use of a single, independent, noise spectrum per detector for the entire mission.<br />
* FFP6 excludes all pre-processing residuals, assuming perfect calibration, transfer function deconvolution and deglitching.<br />
* FFP6 uses the HFI pointing solution for the LFI frequencies, rather than the DPC's two focal plane model.<br />
* FFP6 uses a different map-maker to HFI, and as a consequence implements very slightly different data cuts - primarily at ring boundaries - resulting in marginally different hit-maps.<br />
<br />
=== Fiducial Sky ===<br />
<br />
For each detector, fiducial sky time-ordered data are generated separately for each of its 10 PSM component maps and its strong point source catalogue using the LevelS software <cite>#reinecke2006</cite> as follows:<br />
* The detector's beam and PSM map are converted to spherical harmonics using ''beam2alm'' and ''anafast'' respectively.<br />
* The beam-convolved map value is calculated over a 3-dimensional grid of sky locations and beam orientations using ''conviqt''.<br />
* The map-based time-ordered data are calculated sample-by-sample by interpolating over this grid using "multimod".<br />
* The catalogue-based time-ordered data are calculated sample-by-sample by beam-convolving any point source laying within a given angular distance of the pointing at each sample time using ''multimod''.<br />
<br />
For each frequency, fiducial sky maps are generated for <br />
* the total sky (including noise), <br />
* the foreground sky (excluding CMB but including noise), <br />
* the point source sky, and <br />
* the noise alone<br />
All maps are made using the ''MADAM'' destriping map-maker <cite>#[keihanen2010</cite> interfaced with the ''TOAST'' data abstraction layer . In order to construct the total time-ordered data required by each map, for each detector ''TOAST'' reads the various component time-streams separately and sums then, and, where necessary, simulates and adds a noise realization time-stream on the fly.<br />
<br />
HFI frequencies are mapped at ''HEALPix'' resolution nside=2048 using ring-length destriping baselines, while LFI frequencies are mapped at nside=1024 using 1s baselines.<br />
<br />
=== CMB Monte Carlo ===<br />
<br />
The CMB MC set is generated using ''FEBeCoP'' <cite>#mitra2010</cite>, which generates an effective beam for each pixel in a map at each frequency by accumulating the weights of all pixels within a fixed distance of that pixel, summed over all observations by all detectors at that frequency. It then applies this effective beam pixel-by-pixel to each of 1000 input CMB sky realizations.<br />
<br />
=== Noise Monte Carlo ===<br />
<br />
The noise MC set is generated just as the fiducial noise maps, using ''MADAM/TOAST''. In order to avoid spurious correlations within and between the 1000 realizations, each stationary interval for each detector for each realization is generated from a distinct sub-sequence of a single statistically robust, extremely long period, pseudo-random number sequence.<br />
<br />
== Products delivered ==<br />
<br />
A single simulation is delivered, which is divided into two types of products:<br />
; Six sky maps of the nominal mission at each HFI frequency: which is the basic simulation product. These files have the same structure as the equivalent ''SkyMap'' products described in the [[Frequency_Maps | Frequency Maps ]] chapter -- namely one ''BINTABLE'' extension with three columns containing 1) Signal, 2) hit-count, and 3) variance (TBC)<br />
; Three maps of the nominal mission containing 1) the sum of all astrophysical foregrounds, 2) the point sources alone, and 3) the noise alone: which are subproducts of the above, and are in the form of the PSM maps described in the previous section.<br />
<br />
Note that the cmb alone is not delivered as a separate product, but it can be recovered by simple subtraction of the component maps for the total signal map. It is envisaged that some number of separate noise realizations may be delivered in the future.<br />
<br />
<!-- [[CMB_and_astrophysical_component maps | CMB and astrophysical component maps]] chapter --><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
[[Category:Mission products|012]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=7733CMB spectrum & Likelihood Code2013-06-19T13:50:09Z<p>Lvibert: /* Inputs */</p>
<hr />
<div>{{DISPLAYTITLE:CMB spectrum and likelihood code}}<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 =2-2479</math>. Over the multipole range <math> \ell =2–49</math>, 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 <cite>#planck2013-p06</cite>. 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 <cite>#planck2013-p08</cite> 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. <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 <cite>#planck2013-p11</cite>).''']]<br />
<br />
===Likelihood===<br />
<br />
The likelihood code and data allow to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum and foreground and some instrumental parameters. The data file are built from the Planck mission results, as well as the some ancillary data from the wmap9 data release. The data file are in a specific internal format and can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code allows to read the data files, and provided model power spectra and nuisance parameters to compute the log likelihood of the model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes six data files: five for the CMB likelihoods and one for the lensing likelihood.<br />
All of the likelihood delivered are described full in the Power spectrum & Likelihood Paper <cite>#planck2013-p08</cite> (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) <cite>#planck2013-p12</cite>.<br />
<br />
The CMB full likelihood has been cut in 3 different part to allow using selectively different range of multipoles. It also reflects the fact that the mathematical approximation used for those different part are very different, as well as the underlying data. In details, we are distributing one low-<math>\ell</math> Temperature only likelihood (commander), one low-<math>\ell</math> Temperature and Polarisation likelihood (lowlike) and one higl-<math>\ell</math> likelihood CAMspec.<br />
<br />
The commander likelihood is covering 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 do the likelihood computation in the code. See <cite>#planck2013-p08</cite> section 8.1 for more details.<br />
<br />
The lowlike likelihood is covering the multipole 2 to 32 for Temperature and Polarization data. Planck is not releasing any polarisation data in this release. We are using here the WMAP9 polarization map which are included in the data package. A temperature map is needed to perform the computation nevertheless, and we are using 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 is essentially providing 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 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 <cite>#planck2013-p08</cite> section 8.3 for more details. Note that the version of the WMAP code we are currently using (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrix, 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 is covering the multipoles 50 to 2500 for Temperature. 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 217Ghz channels. Doing so it must model the foreground in each of those frequency using a 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. Detailled description of the different nuisance parameter names and meaning is given below. Priors are included in the likelihood on the cib spectral index, relative calibration factors and beam error eigenmodes. See <cite>#planck2013-p08</cite> section 2.1 for more details.<br />
<br />
The actspt likelihood covers the multipole 1500 to 10000 for Temperature. It is described in <cite>#dun2013,#Keis2011,#Reic2012</cite><!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012]-->. It uses the code and data that can be retrieved [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in <cite>#dun2013</cite>, 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 is covering the multipoles 40 to 400. It uses 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 one 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 <cite>#planck2013-p12</cite> section 6.1 for more details.<br />
<br />
==Production process==<br />
----------------------<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 <cite>#planck2013-p06</cite>. 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% CL <cite>#planck2013-p08</cite>. <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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p11</cite>). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of <cite>#planck2013-p08</cite> and Sec. 4 of <cite>#planck2013-p11</cite>. 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 upon some basic routine 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 <cite>#dun2013,#Keis2011,#Reic2012</cite> <!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012] --> for the actspt 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 <cite>#planck2013-p08</cite> (section 2 and 8) and in the lensing paper <cite>#planck2013-p12</cite> (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 <cite>#planck2013-p06</cite><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 <cite>#planck2013-p08</cite>)<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of <cite>#planck2013-p11</cite>)<br />
* Beam transfer function uncertainties <cite>#planck2013-p03c</cite><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-ell commander map<br />
<br />
;CAMspec :<br />
* 100,143 and 217GHz 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 217Ghz detectors & detsets<br />
* theoretical templates for the tSZ and kSZ contributions<br />
* color corrections for the CIB emission for the 143GHz 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 217GHz<br />
<br />
;lensing :<br />
* the lensing map<br />
* beam error eigenmodes and covariance for the 143GHz and 217GHz chanel 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 and KSZ 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 is distributed in a single FITS file named ''COM_PowerSpect_CMB_R1.10.fits'' 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 $\langle l \rangle = 47-2419$ in bins of width $l=31$ (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 {{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 />
: ''COM_Data_Likelihood-commander_R1.10.tar.gz'' (low-ell TT likelihood)<br />
: ''COM_Data_Likelihood-lowlike_R1.10.tar.gz'' (low-ell TE,EE,BB likelihood)<br />
: ''COM_Data_Likelihood-CAMspec_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''COM_Data_Likelihood-actspt_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''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 of the package comes with a README file describing the full package. 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 modelling granted 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 into 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.<br />
<br />
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 <cite>#planck2013-p08</cite> are found in<br />
: ''COM_Mask_Likelihood_2048_R1.10.fits''<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 />
=== Retrieval from the Planck Legacy Archive ===<br />
<br />
The CMB spectra and likelihood files can be retrieved from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive| Planck Legacy Archive]. One should select "Cosmology products" and look at the "CMB angular power spectra" and "Likelihood" sections.<br />
The files can be downloaded directly or through the "Shopping Basket".<br />
<br />
== References ==<br />
<br />
<biblio force=false><br />
#[[References]]<br />
#[[References2]]<br />
</biblio><br />
[[Category:Mission products|008]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=7732CMB spectrum & Likelihood Code2013-06-19T13:40:30Z<p>Lvibert: /* Likelihood */</p>
<hr />
<div>{{DISPLAYTITLE:CMB spectrum and likelihood code}}<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 =2-2479</math>. Over the multipole range <math> \ell =2–49</math>, 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 <cite>#planck2013-p06</cite>. 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 <cite>#planck2013-p08</cite> 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. <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 <cite>#planck2013-p11</cite>).''']]<br />
<br />
===Likelihood===<br />
<br />
The likelihood code and data allow to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum and foreground and some instrumental parameters. The data file are built from the Planck mission results, as well as the some ancillary data from the wmap9 data release. The data file are in a specific internal format and can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code allows to read the data files, and provided model power spectra and nuisance parameters to compute the log likelihood of the model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes six data files: five for the CMB likelihoods and one for the lensing likelihood.<br />
All of the likelihood delivered are described full in the Power spectrum & Likelihood Paper <cite>#planck2013-p08</cite> (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) <cite>#planck2013-p12</cite>.<br />
<br />
The CMB full likelihood has been cut in 3 different part to allow using selectively different range of multipoles. It also reflects the fact that the mathematical approximation used for those different part are very different, as well as the underlying data. In details, we are distributing one low-<math>\ell</math> Temperature only likelihood (commander), one low-<math>\ell</math> Temperature and Polarisation likelihood (lowlike) and one higl-<math>\ell</math> likelihood CAMspec.<br />
<br />
The commander likelihood is covering 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 do the likelihood computation in the code. See <cite>#planck2013-p08</cite> section 8.1 for more details.<br />
<br />
The lowlike likelihood is covering the multipole 2 to 32 for Temperature and Polarization data. Planck is not releasing any polarisation data in this release. We are using here the WMAP9 polarization map which are included in the data package. A temperature map is needed to perform the computation nevertheless, and we are using 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 is essentially providing 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 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 <cite>#planck2013-p08</cite> section 8.3 for more details. Note that the version of the WMAP code we are currently using (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrix, 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 is covering the multipoles 50 to 2500 for Temperature. 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 217Ghz channels. Doing so it must model the foreground in each of those frequency using a 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. Detailled description of the different nuisance parameter names and meaning is given below. Priors are included in the likelihood on the cib spectral index, relative calibration factors and beam error eigenmodes. See <cite>#planck2013-p08</cite> section 2.1 for more details.<br />
<br />
The actspt likelihood covers the multipole 1500 to 10000 for Temperature. It is described in <cite>#dun2013,#Keis2011,#Reic2012</cite><!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012]-->. It uses the code and data that can be retrieved [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in <cite>#dun2013</cite>, 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 is covering the multipoles 40 to 400. It uses 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 one 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 <cite>#planck2013-p12</cite> section 6.1 for more details.<br />
<br />
==Production process==<br />
----------------------<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 <cite>#planck2013-p06</cite>. 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% CL <cite>#planck2013-p08</cite>. <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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p11</cite>). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of <cite>#planck2013-p08</cite> and Sec. 4 of <cite>#planck2013-p11</cite>. 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 upon some basic routine 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 <cite>#dun2013,#Keis2011,#Reic2012</cite> <!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012] --> for the actspt 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 <cite>#planck2013-p08</cite> (section 2 and 8) and in the lensing paper <cite>#planck2013-p12</cite> (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 />
<br />
* frequency maps from 30–353 GHz;<br />
* common mask <cite>#planck2013-p06</cite>;<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 <cite>#planck2013-p08</cite>);<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of <cite>#planck2013-p11</cite>);<br />
* Beam transfer function uncertainties <cite>#planck2013-p03c</cite>;<br />
<br />
===Likelihood===<br />
<br />
;commander : All Planck channels maps, compact source catalogs, common masks, beam transfer functions for all channels.<br />
<br />
;lowlike : WMAP9 likelihood data. Low-ell commander map.<br />
<br />
;CAMspec : 100,143 & 217GHz detector and detests maps. 857GHz chanel Map. compact source catalog. Common masks (0,1 & 3). beam transfer function and error eigenmodes and covariance for 100,143 and 217Ghz detectors & detsets. Theoretical templates for the tSZ and kSZ contributions. Color corrections for the CIB emission for the 143GHz and 217GHz detectors & detsets. Fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 & 217GHz. <br />
<br />
;lensing : the lensing map, beam error eigenmodes and covariance for the 143GHz and 217GHz chanel maps. Fiducial CMB model (from Planck cosmological parameter best fit).<br />
<br />
;act/spt : The data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]. The TSZ and KSZ 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 is distributed in a single FITS file named ''COM_PowerSpect_CMB_R1.10.fits'' 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 $\langle l \rangle = 47-2419$ in bins of width $l=31$ (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 {{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 />
: ''COM_Data_Likelihood-commander_R1.10.tar.gz'' (low-ell TT likelihood)<br />
: ''COM_Data_Likelihood-lowlike_R1.10.tar.gz'' (low-ell TE,EE,BB likelihood)<br />
: ''COM_Data_Likelihood-CAMspec_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''COM_Data_Likelihood-actspt_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''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 of the package comes with a README file describing the full package. 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 modelling granted 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 into 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.<br />
<br />
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 <cite>#planck2013-p08</cite> are found in<br />
: ''COM_Mask_Likelihood_2048_R1.10.fits''<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 />
=== Retrieval from the Planck Legacy Archive ===<br />
<br />
The CMB spectra and likelihood files can be retrieved from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive| Planck Legacy Archive]. One should select "Cosmology products" and look at the "CMB angular power spectra" and "Likelihood" sections.<br />
The files can be downloaded directly or through the "Shopping Basket".<br />
<br />
== References ==<br />
<br />
<biblio force=false><br />
#[[References]]<br />
#[[References2]]<br />
</biblio><br />
[[Category:Mission products|008]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Frequency_maps_angular_power_spectra&diff=7709Frequency maps angular power spectra2013-06-19T10:16:52Z<p>Lvibert: </p>
<hr />
<div>{{DISPLAYTITLE:Sky temperature power spectra}}<br />
<span style="color:Red"><br />
<br />
== HFI maps power spectra ==<br />
-----------------------------<br />
<br />
Angular power spectra of cut sky CMB dominated maps are provided to allow independent cosmological analysis at high <math>\ell</math>.<br />
<br />
===Product description===<br />
<br />
The auto and cross-spectra of the 13 [[Frequency Maps#Types of maps | detector set ]] (detset) maps at 100, 143 and 217 GHz, all analyzed on the same 42.8% of the sky, are provided.<br />
The mask used is apodized to reduce the power leakage from large scale to small scale (see input section). Except for the removal of the most contaminated pixels through masking, no attempt at astrophysical components separation has been performed. <br />
<br />
For each pair of detectors <math>X</math> and <math>Y</math>, are provided,<br />
* the unbinned ''estimated'' power spectrum <math>\hat{C}^{XY}_\ell</math> for all <math>\ell</math> from 0 to 3508 (see [[#all_dscl|Figure 1]] below), as well as<br />
* the unbinned symmetric covariance matrix<br />
\begin{align}<br />
\hat{M}^{XY}_{\ell \ell'} \equiv \langle\Delta \hat{C}^{XY}_\ell\Delta \hat{C}^{XY}_{\ell'}\rangle<br />
\label{eq:covmatCl}<br />
\end{align}<br />
for all <math>\ell</math> on the same range. At the price of some extra hypotheses, that information can be used to build the likelihood of a given theoretical power spectrum <math>C_{\ell}</math> given the data, and therefore determine the best cosmological models fitting the data. Several examples of such high-<math>\ell</math> likelihoods are described, discussed and compared in <cite>#planck2013-p08</cite> {{p2013|8}}.<br />
<br />
$<br />
\newcommand{\bfE}{\boldsymbol{\mathrm{E}}}<br />
\newcommand{\bfM}{\boldsymbol{\mathrm{M}}}<br />
\newcommand{\bfx}{\boldsymbol{\mathrm{x}}}<br />
\newcommand{\lmax}{\ell_{\mathrm{max}}}<br />
$<br />
Note that <math>\hat{\bfM}</math> only describes the statistical covariance of the power spectrum<br />
induced by the signal and noise of the input map on the cut sky begin analyzed. <br />
Most sources of systematic effects (such as uncertainty on the beam modeling) as well as post-processing steps (such as foreground subtraction) will increase the covariance. In the particular case of the uncertainty on the beam window functions <math>B(l)</math>,<br />
the [[The RIMO|RIMO]] provides for each pair <math>XY</math> a set of eigen-vectors <math>E_{p}^{XY}(\ell)</math> of the relative error on <math>B^{XY}_{\ell}</math> (see "HFI time response and beams paper"<cite>planck2013-p03c</cite> {{P2013|7}}), defined for <math>p</math> in <math>[1,5]</math> and <math>\ell</math> in <math>[0, \lmax]</math> (with <math>\lmax</math> being 2500, 3000 or 4000 when the lowest of the nominal frequencies of the detectors <math>X</math> and <math>Y</math> is respectively 100, 143 or 217GHz). The extra contribution to the covariance of <math>C^{XY}_\ell</math> is then <br />
\begin{align}<br />
\hat{M}^{XY, \mathrm{beam}}_{\ell_1 \ell_2} = 4 \hat{C}^{XY}_{\ell_1} \hat{C}^{XY}_{\ell_2} \sum_{p=1}^{5} E^{XY}_p(\ell_1) E^{XY}_p(\ell_2).<br />
\label{eq:covmatBeam}<br />
\end{align}<br />
<br />
<!-- =================================================== --><br />
<div id="all_dscl"><br />
[[File:all_dscl.png | 500px | center | thumb | '''Figure 1:''' The 91 auto- (dotted lines) and cross- (solid lines) angular power spectra <math>\hat{C}_\ell</math>, shown here after a binning of <math>\Delta \ell = 31</math>, grouped by frequencies. For instance the top left panel, tagged ''100x100 (3)'', contains the three spectra 100-ds1x100-ds2, 100-ds1x100-ds1 and 100-ds1x100-ds2. The auto spectra are contaminated at high <math>\ell</math> by the instrumental noise, and all of them may be affected by foreground contamination. The grey circles show the best Planck CMB high-<math>\ell</math> power spectrum described in the [[CMB spectrum & Likelihood Code | CMB spectrum & Likelihood Code section]] ]]<br />
</div><br />
<!-- =================================================== --><br />
<br />
<br />
====Auto and Cross Power Spectra====<br />
<br />
The spectra computed up to <math>l=3508</math> using [http://prof.planck.fr/article141.html PolSpice] (<cite>Szapudi2001</cite>, <cite>Chon2004</cite>) <br />
are corrected from the effect of the cut sky, and from the nominal beam window function and average pixel function. The different steps of the calculation are<br />
* computation of the Spherical Harmonics coefficients of the masked input maps <math>\Delta T^X(p)</math> and of the input mask <math>w(p)</math>,<br />
\begin{align}<br />
\tilde{a}^X_{\ell m} = \sum_p \Omega_p\, \Delta T^X(p)\, w(p)\, Y^*_{\ell m}(p), \label{eq:almdef}<br />
\end{align}<br />
\begin{align}<br />
\tilde{w}^{(n)}_{\ell m} = \sum_p \Omega_p\ w^n(p)\, Y^*_{\ell m}(p); \label{eq:wlmdef}<br />
\end{align}<br />
where the sum is done over all sky pixels <math>p</math>, <math>\Omega_p</math> is the pixel area, and <math>n</math> is either 1 or 2;<br />
* the sky (cross or auto) pseudo-power spectrum and mask power spectrum are computed from the <math>\tilde{a}_{\ell m}</math> and <math>\tilde{w}_{\ell m}</math>,<br />
\begin{align}<br />
\tilde{C}^{XY}_\ell = \sum_{\ell m} \tilde{a}^X_{ m} \tilde{a}^{Y^*}_{\ell m} / (2 \ell + 1), \label{eq:alm2cl}<br />
\end{align}<br />
\begin{align}<br />
\tilde{W}^{(n)}_\ell = \sum_{\ell m} \tilde{w}^{(n)}_{ m} {\tilde{w}^{(n)}}^*_{\ell m} / (2 \ell + 1); \label{eq:wlm2wl}<br />
\end{align}<br />
* the sky and mask angular correlation function are computed from the respective power spectra,<br />
\begin{align}<br />
\tilde{\xi}(\theta) = \sum_\ell \frac{2\ell+1}{4\pi} \tilde{C}_{\ell} P_\ell(\theta),\label{eq:cl2xi}<br />
\end{align}<br />
\begin{align}<br />
\tilde{\xi}_W(\theta) = \sum_\ell \frac{2\ell+1}{4\pi} \tilde{W}^{(1)}_{\ell} P_\ell(\theta),<br />
\end{align}<br />
where <math>P_\ell</math> is the Legendre Polynomial of order <math>\ell</math>;<br />
* the ratio of the sky angular correlation by the mask correlation provides the cut sky corrected angular correlation,<br />
\begin{align}<br />
\xi(\theta) = \tilde{\xi}(\theta) / \tilde{\xi}_W(\theta); \label{eq:xi_deconv}<br />
\end{align}<br />
* the sky angular correlation function which is then turned into a angular power spectrum,<br />
\begin{align}<br />
{C'}_\ell = 2\pi \sum_i w_i \xi(\theta_i) P_\ell(\theta_i), \label{eq:xi2cl}<br />
\end{align}<br />
where <math>w_i</math> are the weights of the Gauss-Legendre quadrature, for <math>\theta</math> in <math>[0, \pi]</math>;<br />
* the resulting power spectrum is corrected from the nominal beam window function <math>B_\ell</math> and average pixel window function <math>w_{\mathrm{pix}}(\ell)</math>, to provide the final Spice estimator <math>\hat{C}_\ell</math>,<br />
\begin{align}<br />
\hat{C}_\ell = {C'}_\ell / \left( B^2_\ell w^2_{\mathrm{pix}}(\ell) \right). \label{eq:clfinal}<br />
\end{align}<br />
<br />
====Covariance Matrices====<br />
The covariance matrix for the pair <math>XY</math> is computed by PolSpice<br />
using the formalism described in <cite>Efstathiou2004</cite><!--[http://adsabs.harvard.edu/abs/2004MNRAS.349..603E Efstathiou (2004)]-->, also sketched in the appendix<br />
of "CMB power spectra and likelihood paper"<cite>planck2013-p08</cite>, assuming the instrumental noise to be white and uniform.<br />
<br />
$<br />
\newcommand{\hC}{\hat C}<br />
$<br />
One note that a good approximation of the covariance matrix <math>\tilde{M}</math> of the pseudo <math>\tilde{C}_{\ell}</math> is related to the underlying ''estimated'' auto- and cross-spectra <math>\hC_{\ell}</math> through<br />
\begin{align}<br />
\tilde{M}_{\ell_1\ell_2} \equiv \langle\Delta \tilde{C}^{XY}_{\ell_1}\Delta \tilde{C}^{XY}_{\ell_2}\rangle = <br />
\left( \left(\hC^{XX}_{\ell_1} \hC^{YY}_{\ell_1} \hC^{XX}_{\ell_2} \hC^{YY}_{\ell_2}\right)^{1/2}<br />
+ \hC^{XY}_{\ell_1} \hC^{XY}_{\ell_2} \right) <br />
\sum_{\ell_3} \frac{2\ell_3+1}{4\pi} \tilde{W}^{(2)}_{\ell_3} \left( <br />
\begin{array}{ccc}<br />
\! \ell_1\! & \ell_2\! & \ell_3\! \\<br />
\! 0 \! & 0 \! & 0 \!<br />
\end{array}<br />
\right)^2,<br />
\label{eq:covpseudo}<br />
\end{align}<br />
where <math>\tilde{W}^{(2)}_{\ell}</math> is the power spectrum of the square of the pixel mask (Eqs. \ref{eq:wlmdef} and \ref{eq:wlm2wl} for <math>n=2</math>). The covariance matrix <math>\hat{M}</math><br />
of the Spice estimator is then computed by applying Eqs. \ref{eq:cl2xi}, \ref{eq:xi_deconv}, \ref{eq:xi2cl} and \ref{eq:clfinal} on each row and column of <math>\tilde{M}</math>.<br />
<br />
<br />
<!-- The products described here, spectra <math>{\hat C}_{\ell}</math> and covariances <math>{\hat M}_{\ell \ell'}</math> can be used to <br />
estimate the high-<math>\ell</math> likelihood of a given theoretical model given the data available. --><br />
<br />
===Inputs===<br />
<br />
; Maps<br />
: The input maps are the 13 HFI detset (see [[Frequency_Maps#Types_of_maps | ''Type of maps'']] section for details) maps available at 100, 143 and 217 GHz. These are the same as the ones used for high-ell part of the [[CMB spectrum & Likelihood Code | likelihood code]], but that code applies different masks for each cross-spectra in order to minimize further the foreground contamination.<br />
; Sky mask<br />
: All maps were analyzed on the 42.8% of the sky defined by the apodized mask ''HFI_PowerSpect_Mask_2048_R1.10.fits'', which masks out Galactic Plane and point sources (see <cite>planck2013-p08</cite>), and which is shown in [[#mask_Cl|Figure 2]] below<br />
<br />
<div id="mask_Cl"><br />
[[File:mask_Cl.png | 500px | center | thumb | '''Figure 2:''' Apodized pixel mask used for HFI power spectrum estimation ]]<br />
</div><br />
<br />
; Beam Window Function<br />
: The beam window functions <math>B(l)</math>, and their uncertainties, are the ones used in the high-ell likelihood analysis, described in section 6.1 "Error Eigenmodes" of <cite>planck2013-p08</cite> and provided in the HFI [[The RIMO|RIMO]].<br />
<br />
===Related products===<br />
<br />
None<br />
<br />
===FITS file structure===<br />
<br />
Power spectra are provided for the auto and cross products built from the 13 detsets available at 100, 143 and 217 GHz, namely: <br />
* 100-ds1, 100-ds2,<br />
* 143-ds1, 143-ds2, 143-5, 143-6, 143-7, <br />
* 217-ds1, 217-ds2, 217-1, 217-2, 217-3, 217-4<br />
which makes 13*(13+1)/2 = 91 spectra. Filenames for the auto spectra are ''HFI_PowerSPect_{detset}_Relnum.fits'' and ''HFI_PowerSPect_{detset1}x{detset2}_Relnum.fits'' for the auto- and cross-spectra, respectively. The list of the 91 files is given below. Each files contains 2 BINTABLE extensions:<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Power spectrum file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'POW-SPEC' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|TEMP_CL || Real*4 || <math>\mu</math>K<sub>cmb</sub><sup>2</sup>|| the power spectrum<br />
|-<br />
|TEMP_CL_ERR || Real*4 || <math>\mu</math>K<sub>cmb</sub><sup>2</sup> || estimate of the uncertainty in the power spectrum<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Integer || 0 || First monopole<br />
|-<br />
|LMAX || Integer || value || Last monopole<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 2. EXTNAME = 'PSCOVMAT' (IMAGE)<br />
|-<br />
|COVMAT || Real*4 || <math>\mu</math>K<sub>cmb</sub><sup>4</sup> || the covariance matrix<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|NAXIS1 || Integer || dim1 || matrix first dimension<br />
|-<br />
|NAXIS2 || Integer || dim2 || matrix second dimension<br />
|}<br />
<br />
where LMAX is the same for both vectors, and dim1 = dim2 = LMAX+1 by construction.<br />
<br />
<br />
===List of filenames===<br />
<br />
{| align="center" style="text-align:left" border="1" cellpadding="2" cellspacing="0" width=400px<br />
|+ '''FITS filenames''' <br />
|- bgcolor="ffdead" <br />
! Auto power spectra<br />
|-<br />
| HFI_PowerSpect_100-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-ds2_R1.10.fits <br />
|- bgcolor="ffdead" <br />
! Cross power spectra<br />
|-<br />
| HFI_PowerSpect_100-ds1x100-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-4x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-4x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-ds1x217-ds2_R1.10.fits <br />
|- bgcolor="ffdead" <br />
! Sky mask<br />
|-<br />
| {{PLASingleFile|fileType=map|name=HFI_PowerSpect_Mask_2048_R1.10.fits|link=HFI_PowerSpect_Mask_2048_R1.10.fits}}<br />
|}<br />
<br />
The full list of HFI power spectra with links to the files in the PLA can be found {{PLASpec|inst=HFI|link=here}}.<br />
<br />
== LFI maps power spectra ==<br />
---------------------------------<br />
<br />
===Product description===<br />
The angular power spectrum provides information about the distribution of power on the sky map at the various angular scales. It is especially important for CMB, because it is characterized by a number of features, most notably the acoustic peaks, that encode the dependence from cosmological parameters. Therefore, angular power spectra are the basic inputs for the [[CMB spectrum & Likelihood Code | Planck Likelihood Code]], and for estimation of cosmological parameters in general.<br />
<br />
For this release we have computed only temperature power spectra. Polarization is not included.<br />
<br />
Please note that these spectra come from frequency maps. No component separation has been applied, and we have only masked Galactic Plane and detected point sources. Units are <math> \rm{ \mu K^2_{CMB}} </math>.<br />
<br />
===Production process===<br />
Spectra are computed using cROMAster, a implementation of the pseudo-Cl method described in <cite>#master</cite>. In addition to the original approach, our implementation allows for estimation of cross-power spectra from two or more maps (see <cite>#polenta_CrossSpectra</cite> for details). The software package uses [http://healpix.sourceforge.net/ HEALPix] modules for spherical harmonic transform and Cl calculation. The schematic of the estimation process is as follows:<br />
<br />
* computing the a_lm coefficients from the input temperature map after masking Galactic Plane and point sources.<br />
* computing the pseudo power spectrum from the alms.<br />
* estimating the bias due to the noise power spectrum of the map from noise-only Monte Carlo simulations based on detector noise properties<br />
* correcting for the effect of the adopted mask by computing the mode-mode coupling kernel corresponding to that mask<br />
* deconvolving the effect due to the finite angular resolution of the telescope by using the beam window function<br />
* deconvolving the effect due to the finite size of the pixel in the map by using a pixel window function<br />
* binning the power spectrum from individual multipoles into bandpowers<br />
* estimating error bars on bandpowers from signal plus noise Monte Carlo simulations, where signal simulations include only CMB anisotropies.<br />
<br />
===Inputs===<br />
<br />
The inputs are the following:<br />
<br />
* [[Frequency Maps| LFI Frequency Maps]]<br />
* Point source and galactic plane masks (the name being specified in the comment keyword in the header, see Note in ''Meta Data'' section below): <br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"! Mask Name || <br />
|-<br />
!colspan="4" | Point source masks<br />
|-<br />
|{{PLASingleFile|fileType=map|name=LFI_MASK_030-ps_2048_R1.00.fits|link=LFI_MASK_030-ps_2048_R1.00.fits}}<br />
|-<br />
|{{PLASingleFile|fileType=map|name=LFI_MASK_044-ps_2048_R1.00.fits|link=LFI_MASK_044-ps_2048_R1.00.fits}}<br />
|-<br />
|{{PLASingleFile|fileType=map|name=LFI_MASK_070-ps_2048_R1.00.fits|link=LFI_MASK_070-ps_2048_R1.00.fits}}<br />
|-<br />
!colspan="4" | Galactic plane masks<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_MASK_gal-06_2048_R1.00.fits|link=COM_MASK_gal-06_2048_R1.00.fits}}<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_MASK_gal-07_2048_R1.00.fits|link=COM_MASK_gal-07_2048_R1.00.fits}}<br />
|}<br />
* [[The RIMO#Beam_Window_Functions| Beam window functions]]<br />
* Monte Carlo simulations<br />
* binning scheme [[Media:Power_spectra_CTP_bin_tt.pdf]].<br />
<br />
===File Names===<br />
<br />
: {{PLASingleFile|fileType=cosmo|name=LFI_PowerSpect_030_R1.10.fits|link=LFI_PowerSpect_030_R1.10.fits}}<br />
: {{PLASingleFile|fileType=cosmo|name=LFI_PowerSpect_044_R1.10.fits|link=LFI_PowerSpect_044_R1.10.fits}}<br />
: {{PLASingleFile|fileType=cosmo|name=LFI_PowerSpect_070_R1.10.fits|link=LFI_PowerSpect_070_R1.10.fits}}<br />
<br />
===Meta Data ===<br />
<br />
The angular power spectra source list in each frequency is structured as a FITS binary table. <br />
The Fits extension is composed by the columns described below:<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|L || Integer*4 || || ell parameter<br />
|-<br />
|TEMP_CL || Real*8 || uK<math>_{CMB}^2</math> || <math>C_l</math> (temperature) <br />
|-<br />
|TEMP_CL_ERR || Real*8 || uK<math>_{CMB}^2</math> || <math>C_l</math> error<br />
|-<br />
|}<br />
<br />
<br />
'''Note.-''' in the comment keyword in the header, the galactic and point source maps used to generate the angular spectra are specified (LFI_MASK_030-ps_2048_R1.00.fits and COM_MASK_gal-06_2048_R1.00.fits in the example below). Note also that, due to an oversight, the mask description related to COM_MASK_gal-xxx is wrong and should refer to the galactic mask. <br />
<br />
Below an example of the header. <br />
<br />
<pre><br />
XTENSION= 'BINTABLE' /Written by IDL: Sat Feb 16 00:44:22 2013<br />
BITPIX = 8 /<br />
NAXIS = 2 /Binary table<br />
NAXIS1 = 20 /Number of bytes per row<br />
NAXIS2 = 130 /Number of rows<br />
PCOUNT = 0 /Random parameter count<br />
GCOUNT = 1 /Group count<br />
TFIELDS = 3 /Number of columns<br />
TFORM1 = '1J ' /Integer*4 (long integer)<br />
TTYPE1 = 'L ' /<br />
TFORM2 = '1D ' /Real*8 (double precision)<br />
TTYPE2 = 'TEMP_CL ' /<br />
TFORM3 = '1D ' /Real*8 (double precision)<br />
TTYPE3 = 'TEMP_CL_ERR' /<br />
EXTNAME = 'POW-SPEC' / Extension name<br />
EXTVER = 1 /Extension version<br />
DATE = '2013-02-15' /Creation date<br />
TUNIT2 = 'uK_CMB^2' /<br />
TUNIT3 = 'uK_CMB^2' /<br />
FILENAME= 'LFI_PowerSpect_030_R1.00.fits' /<br />
PROCVER = 'Dx9_delta' /<br />
COMMENT ---------------------------------------------<br />
COMMENT Original Inputs<br />
COMMENT ---------------------------------------------<br />
COMMENT TT_30GHz_maskCS0.60_PS30GHzdet_febecopWls<br />
COMMENT Used Point source Mask LFI_MASK_030-ps_2048_R1.00.fits<br />
COMMENT Used Point source Mask COM_MASK_gal-06_2048_R1.00.fits<br />
COMMENT Used FebeCoP 30 GHz wls<br />
END<br />
</pre><br />
<br />
Below an example of the header of two masks used as input: COM_MASK_gal-06_2048_R1.00.fits and LFI_MASK_030-ps_2048_R1.00.fits:<br />
<pre><br />
XTENSION= 'BINTABLE' / binary table extension<br />
BITPIX = 8 / 8-bit bytes<br />
NAXIS = 2 / 2-dimensional binary table<br />
NAXIS1 = 4 / width of table in bytes<br />
NAXIS2 = 50331648 / number of rows in table<br />
PCOUNT = 0 / size of special data area<br />
GCOUNT = 1 / one data group (required keyword)<br />
TFIELDS = 1 / number of fields in each row<br />
TTYPE1 = 'Mask ' / label for field 1<br />
TFORM1 = 'E ' / data format of field: 4-byte REAL<br />
TUNIT1 = 'none ' / physical unit of field<br />
EXTNAME = '06-GalMask'<br />
DATE = '2013-02-16T11:07:42' / file creation date (YYYY-MM-DDThh:mm:ss UT)<br />
CHECKSUM= 'NaGVNZGUNaGUNYGU' / HDU checksum updated 2013-02-16T11:07:43<br />
DATASUM = '2540860986' / data unit checksum updated 2013-02-16T11:07:43<br />
COMMENT<br />
COMMENT *** Planck params ***<br />
COMMENT<br />
PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation<br />
ORDERING= 'NESTED ' / Pixel ordering scheme, either RING or NESTED<br />
NSIDE = 2048 / Resolution parameter for HEALPIX<br />
FIRSTPIX= 0 / First pixel # (0 based)<br />
LASTPIX = 50331647 / Last pixel # (0 based)<br />
INDXSCHM= 'IMPLICIT' / Indexing: IMPLICIT or EXPLICIT<br />
OBJECT = 'FULLSKY ' / Sky coverage, either FULLSKY or PARTIAL<br />
BAD_DATA= -1.6375E+30<br />
COORDSYS= 'GALACTIC'<br />
FILENAME= 'COM_MASK_gal-06_2048_R1.00.fits'<br />
COMMENT ---------------------------------------------------------------------<br />
COMMENT Combined galactic mask 0.6 sky fraction<br />
COMMENT Objects used:<br />
COMMENT /sci_planck/lfi_dpc_test/ashdown/repository/masks/component_separation/d<br />
COMMENT x9/combined_mask_0.60_sky_fraction.fits<br />
COMMENT ---------------------------------------------------------------------<br />
END<br />
</pre><br />
<br />
<pre><br />
XTENSION= 'BINTABLE' / binary table extension<br />
BITPIX = 8 / 8-bit bytes<br />
NAXIS = 2 / 2-dimensional binary table<br />
NAXIS1 = 4 / width of table in bytes<br />
NAXIS2 = 50331648 / number of rows in table<br />
PCOUNT = 0 / size of special data area<br />
GCOUNT = 1 / one data group (required keyword)<br />
TFIELDS = 1 / number of fields in each row<br />
TTYPE1 = 'Mask ' / label for field 1<br />
TFORM1 = 'E ' / data format of field: 4-byte REAL<br />
TUNIT1 = 'none ' / physical unit of field<br />
EXTNAME = '030-PSMask'<br />
DATE = '2013-02-16T11:03:20' / file creation date (YYYY-MM-DDThh:mm:ss UT)<br />
CHECKSUM= 'fR7ThO7RfO7RfO7R' / HDU checksum updated 2013-02-16T11:03:21<br />
DATASUM = '3828742620' / data unit checksum updated 2013-02-16T11:03:21<br />
COMMENT<br />
COMMENT *** Planck params ***<br />
COMMENT<br />
PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation<br />
ORDERING= 'NESTED ' / Pixel ordering scheme, either RING or NESTED<br />
NSIDE = 2048 / Resolution parameter for HEALPIX<br />
FIRSTPIX= 0 / First pixel # (0 based)<br />
LASTPIX = 50331647 / Last pixel # (0 based)<br />
INDXSCHM= 'IMPLICIT' / Indexing: IMPLICIT or EXPLICIT<br />
OBJECT = 'FULLSKY ' / Sky coverage, either FULLSKY or PARTIAL<br />
BAD_DATA= -1.6375E+30<br />
COORDSYS= 'GALACTIC'<br />
FILENAME= 'LFI_MASK_030-ps_2048_R1.00.fits'<br />
COMMENT ---------------------------------------------------------------------<br />
COMMENT The radius of the holes is 3 times the sigma of the beam at the correspo<br />
COMMENT nding frequency and sigma is FWHM/(2*sqrt(2ln2))<br />
COMMENT FWHM at 30GHz used = 33.158 arcmin<br />
COMMENT Objects used:<br />
COMMENT /planck/sci_ops1/LFI_MAPs/DX9_Delta/MASKs/mask_ps_30GHz_beam33amin_nside<br />
COMMENT 2048.00_DX9_nonblind_holesize3.fits<br />
COMMENT ---------------------------------------------------------------------<br />
END<br />
</pre><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
[[Category:Mission products|006]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Frequency_maps_angular_power_spectra&diff=7708Frequency maps angular power spectra2013-06-19T10:07:02Z<p>Lvibert: </p>
<hr />
<div>{{DISPLAYTITLE:Sky temperature power spectra}}<br />
<span style="color:Red"><br />
<br />
== HFI maps power spectra ==<br />
-----------------------------<br />
<br />
Angular power spectra of cut sky CMB dominated maps are provided to allow independent cosmological analysis at high <math>\ell</math>.<br />
<br />
===Product description===<br />
<br />
The auto and cross-spectra of the 13 [[Frequency Maps#Types of maps | detector set ]] (detset) maps at 100, 143 and 217 GHz, all analyzed on the same 42.8% of the sky, are provided.<br />
The mask used is apodized to reduce the power leakage from large scale to small scale (see input section). Except for the removal of the most contaminated pixels through masking, no attempt at astrophysical components separation has been performed. <br />
<br />
For each pair of detectors <math>X</math> and <math>Y</math>, are provided,<br />
* the unbinned ''estimated'' power spectrum <math>\hat{C}^{XY}_\ell</math> for all <math>\ell</math> from 0 to 3508 (see [[#all_dscl|Figure 1]] below), as well as<br />
* the unbinned symmetric covariance matrix<br />
\begin{align}<br />
\hat{M}^{XY}_{\ell \ell'} \equiv \langle\Delta \hat{C}^{XY}_\ell\Delta \hat{C}^{XY}_{\ell'}\rangle<br />
\label{eq:covmatCl}<br />
\end{align}<br />
for all <math>\ell</math> on the same range. At the price of some extra hypotheses, that information can be used to build the likelihood of a given theoretical power spectrum <math>C_{\ell}</math> given the data, and therefore determine the best cosmological models fitting the data. Several examples of such high-<math>\ell</math> likelihoods are described, discussed and compared in <cite>#planck2013-p08</cite> {{p2013|8}}.<br />
<br />
$<br />
\newcommand{\bfE}{\boldsymbol{\mathrm{E}}}<br />
\newcommand{\bfM}{\boldsymbol{\mathrm{M}}}<br />
\newcommand{\bfx}{\boldsymbol{\mathrm{x}}}<br />
\newcommand{\lmax}{\ell_{\mathrm{max}}}<br />
$<br />
Note that <math>\hat{\bfM}</math> only describes the statistical covariance of the power spectrum<br />
induced by the signal and noise of the input map on the cut sky begin analyzed. <br />
Most sources of systematic effects (such as uncertainty on the beam modeling) as well as post-processing steps (such as foreground subtraction) will increase the covariance. In the particular case of the uncertainty on the beam window functions <math>B(l)</math>,<br />
the [[The RIMO|RIMO]] provides for each pair <math>XY</math> a set of eigen-vectors <math>E_{p}^{XY}(\ell)</math> of the relative error on <math>B^{XY}_{\ell}</math> (see "HFI time response and beams paper"<cite>planck2013-p03c</cite> {{P2013|7}}), defined for <math>p</math> in <math>[1,5]</math> and <math>\ell</math> in <math>[0, \lmax]</math> (with <math>\lmax</math> being 2500, 3000 or 4000 when the lowest of the nominal frequencies of the detectors <math>X</math> and <math>Y</math> is respectively 100, 143 or 217GHz). The extra contribution to the covariance of <math>C^{XY}_\ell</math> is then <br />
\begin{align}<br />
\hat{M}^{XY, \mathrm{beam}}_{\ell_1 \ell_2} = 4 \hat{C}^{XY}_{\ell_1} \hat{C}^{XY}_{\ell_2} \sum_{p=1}^{5} E^{XY}_p(\ell_1) E^{XY}_p(\ell_2).<br />
\label{eq:covmatBeam}<br />
\end{align}<br />
<br />
<!-- =================================================== --><br />
<div id="all_dscl"><br />
[[File:all_dscl.png | 500px | center | thumb | '''Figure 1:''' The 91 auto- (dotted lines) and cross- (solid lines) angular power spectra <math>\hat{C}_\ell</math>, shown here after a binning of <math>\Delta \ell = 31</math>, grouped by frequencies. For instance the top left panel, tagged ''100x100 (3)'', contains the three spectra 100-ds1x100-ds2, 100-ds1x100-ds1 and 100-ds1x100-ds2. The auto spectra are contaminated at high <math>\ell</math> by the instrumental noise, and all of them may be affected by foreground contamination. The grey circles show the best Planck CMB high-<math>\ell</math> power spectrum described in the [[CMB spectrum & Likelihood Code | CMB spectrum & Likelihood Code section]] ]]<br />
</div><br />
<!-- =================================================== --><br />
<br />
<br />
====Auto and Cross Power Spectra====<br />
<br />
The spectra computed up to <math>l=3508</math> using [http://prof.planck.fr/article141.html PolSpice] (<cite>Szapudi2001</cite>, <cite>Chon2004</cite>) <br />
are corrected from the effect of the cut sky, and from the nominal beam window function and average pixel function. The different steps of the calculation are<br />
* computation of the Spherical Harmonics coefficients of the masked input maps <math>\Delta T^X(p)</math> and of the input mask <math>w(p)</math>,<br />
\begin{align}<br />
\tilde{a}^X_{\ell m} = \sum_p \Omega_p\, \Delta T^X(p)\, w(p)\, Y^*_{\ell m}(p), \label{eq:almdef}<br />
\end{align}<br />
\begin{align}<br />
\tilde{w}^{(n)}_{\ell m} = \sum_p \Omega_p\ w^n(p)\, Y^*_{\ell m}(p); \label{eq:wlmdef}<br />
\end{align}<br />
where the sum is done over all sky pixels <math>p</math>, <math>\Omega_p</math> is the pixel area, and <math>n</math> is either 1 or 2;<br />
* the sky (cross or auto) pseudo-power spectrum and mask power spectrum are computed from the <math>\tilde{a}_{\ell m}</math> and <math>\tilde{w}_{\ell m}</math>,<br />
\begin{align}<br />
\tilde{C}^{XY}_\ell = \sum_{\ell m} \tilde{a}^X_{ m} \tilde{a}^{Y^*}_{\ell m} / (2 \ell + 1), \label{eq:alm2cl}<br />
\end{align}<br />
\begin{align}<br />
\tilde{W}^{(n)}_\ell = \sum_{\ell m} \tilde{w}^{(n)}_{ m} {\tilde{w}^{(n)}}^*_{\ell m} / (2 \ell + 1); \label{eq:wlm2wl}<br />
\end{align}<br />
* the sky and mask angular correlation function are computed from the respective power spectra,<br />
\begin{align}<br />
\tilde{\xi}(\theta) = \sum_\ell \frac{2\ell+1}{4\pi} \tilde{C}_{\ell} P_\ell(\theta),\label{eq:cl2xi}<br />
\end{align}<br />
\begin{align}<br />
\tilde{\xi}_W(\theta) = \sum_\ell \frac{2\ell+1}{4\pi} \tilde{W}^{(1)}_{\ell} P_\ell(\theta),<br />
\end{align}<br />
where <math>P_\ell</math> is the Legendre Polynomial of order <math>\ell</math>;<br />
* the ratio of the sky angular correlation by the mask correlation provides the cut sky corrected angular correlation,<br />
\begin{align}<br />
\xi(\theta) = \tilde{\xi}(\theta) / \tilde{\xi}_W(\theta); \label{eq:xi_deconv}<br />
\end{align}<br />
* the sky angular correlation function which is then turned into a angular power spectrum,<br />
\begin{align}<br />
{C'}_\ell = 2\pi \sum_i w_i \xi(\theta_i) P_\ell(\theta_i), \label{eq:xi2cl}<br />
\end{align}<br />
where <math>w_i</math> are the weights of the Gauss-Legendre quadrature, for <math>\theta</math> in <math>[0, \pi]</math>;<br />
* the resulting power spectrum is corrected from the nominal beam window function <math>B_\ell</math> and average pixel window function <math>w_{\mathrm{pix}}(\ell)</math>, to provide the final Spice estimator <math>\hat{C}_\ell</math>,<br />
\begin{align}<br />
\hat{C}_\ell = {C'}_\ell / \left( B^2_\ell w^2_{\mathrm{pix}}(\ell) \right). \label{eq:clfinal}<br />
\end{align}<br />
<br />
====Covariance Matrices====<br />
The covariance matrix for the pair <math>XY</math> is computed by PolSpice<br />
using the formalism described in <cite>Efstathiou2004</cite><!--[http://adsabs.harvard.edu/abs/2004MNRAS.349..603E Efstathiou (2004)]-->, also sketched in the appendix<br />
of "CMB power spectra and likelihood paper"<cite>planck2013-p08</cite>, assuming the instrumental noise to be white and uniform.<br />
<br />
$<br />
\newcommand{\hC}{\hat C}<br />
$<br />
One note that a good approximation of the covariance matrix <math>\tilde{M}</math> of the pseudo <math>\tilde{C}_{\ell}</math> is related to the underlying ''estimated'' auto- and cross-spectra <math>\hC_{\ell}</math> through<br />
\begin{align}<br />
\tilde{M}_{\ell_1\ell_2} \equiv \langle\Delta \tilde{C}^{XY}_{\ell_1}\Delta \tilde{C}^{XY}_{\ell_2}\rangle = <br />
\left( \left(\hC^{XX}_{\ell_1} \hC^{YY}_{\ell_1} \hC^{XX}_{\ell_2} \hC^{YY}_{\ell_2}\right)^{1/2}<br />
+ \hC^{XY}_{\ell_1} \hC^{XY}_{\ell_2} \right) <br />
\sum_{\ell_3} \frac{2\ell_3+1}{4\pi} \tilde{W}^{(2)}_{\ell_3} \left( <br />
\begin{array}{ccc}<br />
\! \ell_1\! & \ell_2\! & \ell_3\! \\<br />
\! 0 \! & 0 \! & 0 \!<br />
\end{array}<br />
\right)^2,<br />
\label{eq:covpseudo}<br />
\end{align}<br />
where <math>\tilde{W}^{(2)}_{\ell}</math> is the power spectrum of the square of the pixel mask (Eqs. \ref{eq:wlmdef} and \ref{eq:wlm2wl} for <math>n=2</math>). The covariance matrix <math>\hat{M}</math><br />
of the Spice estimator is then computed by applying Eqs. \ref{eq:cl2xi}, \ref{eq:xi_deconv}, \ref{eq:xi2cl} and \ref{eq:clfinal} on each row and column of <math>\tilde{M}</math>.<br />
<br />
<br />
<!-- The products described here, spectra ${\hat C}_{\ell}$ and covariances ${\hat M}_{\ell \ell'}$ can be used to <br />
estimate the high-$\ell$ likelihood of a given theoretical model given the data available. --><br />
<br />
===Inputs===<br />
<br />
; Maps<br />
: The input maps are the 13 HFI detset (see [[Frequency_Maps#Types_of_maps | ''Type of maps'']] section for details) maps available at 100, 143 and 217 GHz. These are the same as the ones used for high-ell part of the [[CMB spectrum & Likelihood Code | likelihood code]], but that code applies different masks for each cross-spectra in order to minimize further the foreground contamination.<br />
; Sky mask<br />
: All maps were analyzed on the 42.8% of the sky defined by the apodized mask ''HFI_PowerSpect_Mask_2048_R1.10.fits'', which masks out Galactic Plane and point sources (see <cite>planck2013-p08</cite>), and which is shown in [[#mask_Cl|Figure 2]] below<br />
<br />
<div id="mask_Cl"><br />
[[File:mask_Cl.png | 500px | center | thumb | '''Figure 2:''' Apodized pixel mask used for HFI power spectrum estimation ]]<br />
</div><br />
<br />
; Beam Window Function<br />
: The beam window functions $B(l)$, and their uncertainties, are the ones used in the high-ell likelihood analysis, described in section 6.1 "Error Eigenmodes" of <cite>planck2013-p08</cite> and provided in the HFI [[The RIMO|RIMO]].<br />
<br />
===Related products===<br />
<br />
None<br />
<br />
===FITS file structure===<br />
<br />
Power spectra are provided for the auto and cross products built from the 13 detsets available at 100, 143 and 217 GHz, namely: <br />
* 100-ds1, 100-ds2,<br />
* 143-ds1, 143-ds2, 143-5, 143-6, 143-7, <br />
* 217-ds1, 217-ds2, 217-1, 217-2, 217-3, 217-4<br />
which makes 13*(13+1)/2 = 91 spectra. Filenames for the auto spectra are ''HFI_PowerSPect_{detset}_Relnum.fits'' and ''HFI_PowerSPect_{detset1}x{detset2}_Relnum.fits'' for the auto- and cross-spectra, respectively. The list of the 91 files is given below. Each files contains 2 BINTABLE extensions:<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Power spectrum file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'POW-SPEC' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|TEMP_CL || Real*4 || $\mu$K<sub>cmb</sub><sup>2</sup> || the power spectrum<br />
|-<br />
|TEMP_CL_ERR || Real*4 || $\mu$K<sub>cmb</sub><sup>2</sup> || estimate of the uncertainty in the power spectrum<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Integer || 0 || First monopole<br />
|-<br />
|LMAX || Integer || value || Last monopole<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 2. EXTNAME = 'PSCOVMAT' (IMAGE)<br />
|-<br />
|COVMAT || Real*4 || $\mu$K<sub>cmb</sub><sup>4</sup> || the covariance matrix<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|NAXIS1 || Integer || dim1 || matrix first dimension<br />
|-<br />
|NAXIS2 || Integer || dim2 || matrix second dimension<br />
|}<br />
<br />
where LMAX is the same for both vectors, and dim1 = dim2 = LMAX+1 by construction.<br />
<br />
<br />
===List of filenames===<br />
<br />
{| align="center" style="text-align:left" border="1" cellpadding="2" cellspacing="0" width=400px<br />
|+ '''FITS filenames''' <br />
|- bgcolor="ffdead" <br />
! Auto power spectra<br />
|-<br />
| HFI_PowerSpect_100-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-ds2_R1.10.fits <br />
|- bgcolor="ffdead" <br />
! Cross power spectra<br />
|-<br />
| HFI_PowerSpect_100-ds1x100-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-4x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-4x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-ds1x217-ds2_R1.10.fits <br />
|- bgcolor="ffdead" <br />
! Sky mask<br />
|-<br />
| {{PLASingleFile|fileType=map|name=HFI_PowerSpect_Mask_2048_R1.10.fits|link=HFI_PowerSpect_Mask_2048_R1.10.fits}}<br />
|}<br />
<br />
The full list of HFI power spectra with links to the files in the PLA can be found {{PLASpec|inst=HFI|link=here}}.<br />
<br />
== LFI maps power spectra ==<br />
---------------------------------<br />
<br />
===Product description===<br />
The angular power spectrum provides information about the distribution of power on the sky map at the various angular scales. It is especially important for CMB, because it is characterized by a number of features, most notably the acoustic peaks, that encode the dependence from cosmological parameters. Therefore, angular power spectra are the basic inputs for the [[CMB spectrum & Likelihood Code | Planck Likelihood Code]], and for estimation of cosmological parameters in general.<br />
<br />
For this release we have computed only temperature power spectra. Polarization is not included.<br />
<br />
Please note that these spectra come from frequency maps. No component separation has been applied, and we have only masked Galactic Plane and detected point sources. Units are <math> \rm{ \mu K^2_{CMB}} </math>.<br />
<br />
===Production process===<br />
Spectra are computed using cROMAster, a implementation of the pseudo-Cl method described in <cite>#master</cite>. In addition to the original approach, our implementation allows for estimation of cross-power spectra from two or more maps (see <cite>#polenta_CrossSpectra</cite> for details). The software package uses [http://healpix.sourceforge.net/ HEALPix] modules for spherical harmonic transform and Cl calculation. The schematic of the estimation process is as follows:<br />
<br />
* computing the a_lm coefficients from the input temperature map after masking Galactic Plane and point sources.<br />
* computing the pseudo power spectrum from the alms.<br />
* estimating the bias due to the noise power spectrum of the map from noise-only Monte Carlo simulations based on detector noise properties<br />
* correcting for the effect of the adopted mask by computing the mode-mode coupling kernel corresponding to that mask<br />
* deconvolving the effect due to the finite angular resolution of the telescope by using the beam window function<br />
* deconvolving the effect due to the finite size of the pixel in the map by using a pixel window function<br />
* binning the power spectrum from individual multipoles into bandpowers<br />
* estimating error bars on bandpowers from signal plus noise Monte Carlo simulations, where signal simulations include only CMB anisotropies.<br />
<br />
===Inputs===<br />
<br />
The inputs are the following:<br />
<br />
* [[Frequency Maps| LFI Frequency Maps]]<br />
* Point source and galactic plane masks (the name being specified in the comment keyword in the header, see Note in ''Meta Data'' section below): <br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"! Mask Name || <br />
|-<br />
!colspan="4" | Point source masks<br />
|-<br />
|{{PLASingleFile|fileType=map|name=LFI_MASK_030-ps_2048_R1.00.fits|link=LFI_MASK_030-ps_2048_R1.00.fits}}<br />
|-<br />
|{{PLASingleFile|fileType=map|name=LFI_MASK_044-ps_2048_R1.00.fits|link=LFI_MASK_044-ps_2048_R1.00.fits}}<br />
|-<br />
|{{PLASingleFile|fileType=map|name=LFI_MASK_070-ps_2048_R1.00.fits|link=LFI_MASK_070-ps_2048_R1.00.fits}}<br />
|-<br />
!colspan="4" | Galactic plane masks<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_MASK_gal-06_2048_R1.00.fits|link=COM_MASK_gal-06_2048_R1.00.fits}}<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_MASK_gal-07_2048_R1.00.fits|link=COM_MASK_gal-07_2048_R1.00.fits}}<br />
|}<br />
* [[The RIMO#Beam_Window_Functions| Beam window functions]]<br />
* Monte Carlo simulations<br />
* binning scheme [[Media:Power_spectra_CTP_bin_tt.pdf]].<br />
<br />
===File Names===<br />
<br />
: {{PLASingleFile|fileType=cosmo|name=LFI_PowerSpect_030_R1.10.fits|link=LFI_PowerSpect_030_R1.10.fits}}<br />
: {{PLASingleFile|fileType=cosmo|name=LFI_PowerSpect_044_R1.10.fits|link=LFI_PowerSpect_044_R1.10.fits}}<br />
: {{PLASingleFile|fileType=cosmo|name=LFI_PowerSpect_070_R1.10.fits|link=LFI_PowerSpect_070_R1.10.fits}}<br />
<br />
===Meta Data ===<br />
<br />
The angular power spectra source list in each frequency is structured as a FITS binary table. <br />
The Fits extension is composed by the columns described below:<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|L || Integer*4 || || ell parameter<br />
|-<br />
|TEMP_CL || Real*8 || uK<math>_{CMB}^2</math> || <math>C_l</math> (temperature) <br />
|-<br />
|TEMP_CL_ERR || Real*8 || uK<math>_{CMB}^2</math> || <math>C_l</math> error<br />
|-<br />
|}<br />
<br />
<br />
'''Note.-''' in the comment keyword in the header, the galactic and point source maps used to generate the angular spectra are specified (LFI_MASK_030-ps_2048_R1.00.fits and COM_MASK_gal-06_2048_R1.00.fits in the example below). Note also that, due to an oversight, the mask description related to COM_MASK_gal-xxx is wrong and should refer to the galactic mask. <br />
<br />
Below an example of the header. <br />
<br />
<pre><br />
XTENSION= 'BINTABLE' /Written by IDL: Sat Feb 16 00:44:22 2013<br />
BITPIX = 8 /<br />
NAXIS = 2 /Binary table<br />
NAXIS1 = 20 /Number of bytes per row<br />
NAXIS2 = 130 /Number of rows<br />
PCOUNT = 0 /Random parameter count<br />
GCOUNT = 1 /Group count<br />
TFIELDS = 3 /Number of columns<br />
TFORM1 = '1J ' /Integer*4 (long integer)<br />
TTYPE1 = 'L ' /<br />
TFORM2 = '1D ' /Real*8 (double precision)<br />
TTYPE2 = 'TEMP_CL ' /<br />
TFORM3 = '1D ' /Real*8 (double precision)<br />
TTYPE3 = 'TEMP_CL_ERR' /<br />
EXTNAME = 'POW-SPEC' / Extension name<br />
EXTVER = 1 /Extension version<br />
DATE = '2013-02-15' /Creation date<br />
TUNIT2 = 'uK_CMB^2' /<br />
TUNIT3 = 'uK_CMB^2' /<br />
FILENAME= 'LFI_PowerSpect_030_R1.00.fits' /<br />
PROCVER = 'Dx9_delta' /<br />
COMMENT ---------------------------------------------<br />
COMMENT Original Inputs<br />
COMMENT ---------------------------------------------<br />
COMMENT TT_30GHz_maskCS0.60_PS30GHzdet_febecopWls<br />
COMMENT Used Point source Mask LFI_MASK_030-ps_2048_R1.00.fits<br />
COMMENT Used Point source Mask COM_MASK_gal-06_2048_R1.00.fits<br />
COMMENT Used FebeCoP 30 GHz wls<br />
END<br />
</pre><br />
<br />
Below an example of the header of two masks used as input: COM_MASK_gal-06_2048_R1.00.fits and LFI_MASK_030-ps_2048_R1.00.fits:<br />
<pre><br />
XTENSION= 'BINTABLE' / binary table extension<br />
BITPIX = 8 / 8-bit bytes<br />
NAXIS = 2 / 2-dimensional binary table<br />
NAXIS1 = 4 / width of table in bytes<br />
NAXIS2 = 50331648 / number of rows in table<br />
PCOUNT = 0 / size of special data area<br />
GCOUNT = 1 / one data group (required keyword)<br />
TFIELDS = 1 / number of fields in each row<br />
TTYPE1 = 'Mask ' / label for field 1<br />
TFORM1 = 'E ' / data format of field: 4-byte REAL<br />
TUNIT1 = 'none ' / physical unit of field<br />
EXTNAME = '06-GalMask'<br />
DATE = '2013-02-16T11:07:42' / file creation date (YYYY-MM-DDThh:mm:ss UT)<br />
CHECKSUM= 'NaGVNZGUNaGUNYGU' / HDU checksum updated 2013-02-16T11:07:43<br />
DATASUM = '2540860986' / data unit checksum updated 2013-02-16T11:07:43<br />
COMMENT<br />
COMMENT *** Planck params ***<br />
COMMENT<br />
PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation<br />
ORDERING= 'NESTED ' / Pixel ordering scheme, either RING or NESTED<br />
NSIDE = 2048 / Resolution parameter for HEALPIX<br />
FIRSTPIX= 0 / First pixel # (0 based)<br />
LASTPIX = 50331647 / Last pixel # (0 based)<br />
INDXSCHM= 'IMPLICIT' / Indexing: IMPLICIT or EXPLICIT<br />
OBJECT = 'FULLSKY ' / Sky coverage, either FULLSKY or PARTIAL<br />
BAD_DATA= -1.6375E+30<br />
COORDSYS= 'GALACTIC'<br />
FILENAME= 'COM_MASK_gal-06_2048_R1.00.fits'<br />
COMMENT ---------------------------------------------------------------------<br />
COMMENT Combined galactic mask 0.6 sky fraction<br />
COMMENT Objects used:<br />
COMMENT /sci_planck/lfi_dpc_test/ashdown/repository/masks/component_separation/d<br />
COMMENT x9/combined_mask_0.60_sky_fraction.fits<br />
COMMENT ---------------------------------------------------------------------<br />
END<br />
</pre><br />
<br />
<pre><br />
XTENSION= 'BINTABLE' / binary table extension<br />
BITPIX = 8 / 8-bit bytes<br />
NAXIS = 2 / 2-dimensional binary table<br />
NAXIS1 = 4 / width of table in bytes<br />
NAXIS2 = 50331648 / number of rows in table<br />
PCOUNT = 0 / size of special data area<br />
GCOUNT = 1 / one data group (required keyword)<br />
TFIELDS = 1 / number of fields in each row<br />
TTYPE1 = 'Mask ' / label for field 1<br />
TFORM1 = 'E ' / data format of field: 4-byte REAL<br />
TUNIT1 = 'none ' / physical unit of field<br />
EXTNAME = '030-PSMask'<br />
DATE = '2013-02-16T11:03:20' / file creation date (YYYY-MM-DDThh:mm:ss UT)<br />
CHECKSUM= 'fR7ThO7RfO7RfO7R' / HDU checksum updated 2013-02-16T11:03:21<br />
DATASUM = '3828742620' / data unit checksum updated 2013-02-16T11:03:21<br />
COMMENT<br />
COMMENT *** Planck params ***<br />
COMMENT<br />
PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation<br />
ORDERING= 'NESTED ' / Pixel ordering scheme, either RING or NESTED<br />
NSIDE = 2048 / Resolution parameter for HEALPIX<br />
FIRSTPIX= 0 / First pixel # (0 based)<br />
LASTPIX = 50331647 / Last pixel # (0 based)<br />
INDXSCHM= 'IMPLICIT' / Indexing: IMPLICIT or EXPLICIT<br />
OBJECT = 'FULLSKY ' / Sky coverage, either FULLSKY or PARTIAL<br />
BAD_DATA= -1.6375E+30<br />
COORDSYS= 'GALACTIC'<br />
FILENAME= 'LFI_MASK_030-ps_2048_R1.00.fits'<br />
COMMENT ---------------------------------------------------------------------<br />
COMMENT The radius of the holes is 3 times the sigma of the beam at the correspo<br />
COMMENT nding frequency and sigma is FWHM/(2*sqrt(2ln2))<br />
COMMENT FWHM at 30GHz used = 33.158 arcmin<br />
COMMENT Objects used:<br />
COMMENT /planck/sci_ops1/LFI_MAPs/DX9_Delta/MASKs/mask_ps_30GHz_beam33amin_nside<br />
COMMENT 2048.00_DX9_nonblind_holesize3.fits<br />
COMMENT ---------------------------------------------------------------------<br />
END<br />
</pre><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
[[Category:Mission products|006]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Frequency_maps_angular_power_spectra&diff=7707Frequency maps angular power spectra2013-06-19T10:02:12Z<p>Lvibert: /* HFI maps power spectra */</p>
<hr />
<div>{{DISPLAYTITLE:Sky temperature power spectra}}<br />
<span style="color:Red"><br />
<br />
== HFI maps power spectra ==<br />
-----------------------------<br />
<br />
Angular power spectra of cut sky CMB dominated maps are provided to allow independent cosmological analysis at high <math>\ell</math>.<br />
<br />
===Product description===<br />
<br />
The auto and cross-spectra of the 13 [[Frequency Maps#Types of maps | detector set ]] (detset) maps at 100, 143 and 217 GHz, all analyzed on the same 42.8% of the sky, are provided.<br />
The mask used is apodized to reduce the power leakage from large scale to small scale (see input section). Except for the removal of the most contaminated pixels through masking, no attempt at astrophysical components separation has been performed. <br />
<br />
For each pair of detectors <math>X</math> and <math>Y</math>, are provided,<br />
* the unbinned ''estimated'' power spectrum <math>\hat{C}^{XY}_\ell</math> for all <math>\ell</math> from 0 to 3508 (see [[#all_dscl|Figure 1]] below), as well as<br />
* the unbinned symmetric covariance matrix<br />
\begin{align}<br />
\hat{M}^{XY}_{\ell \ell'} \equiv \langle\Delta \hat{C}^{XY}_\ell\Delta \hat{C}^{XY}_{\ell'}\rangle<br />
\label{eq:covmatCl}<br />
\end{align}<br />
for all <math>\ell</math> on the same range. At the price of some extra hypotheses, that information can be used to build the likelihood of a given theoretical power spectrum <math>C_{\ell}</math> given the data, and therefore determine the best cosmological models fitting the data. Several examples of such high-<math>\ell</math> likelihoods are described, discussed and compared in <cite>#planck2013-p08</cite> {{p2013|8}}.<br />
<br />
$<br />
\newcommand{\bfE}{\boldsymbol{\mathrm{E}}}<br />
\newcommand{\bfM}{\boldsymbol{\mathrm{M}}}<br />
\newcommand{\bfx}{\boldsymbol{\mathrm{x}}}<br />
\newcommand{\lmax}{\ell_{\mathrm{max}}}<br />
$<br />
Note that <math>\hat{\bfM}</math> only describes the statistical covariance of the power spectrum<br />
induced by the signal and noise of the input map on the cut sky begin analyzed. <br />
Most sources of systematic effects (such as uncertainty on the beam modeling) as well as post-processing steps (such as foreground subtraction) will increase the covariance. In the particular case of the uncertainty on the beam window functions <math>B(l)</math>,<br />
the [[The RIMO|RIMO]] provides for each pair <math>XY</math> a set of eigen-vectors <math>E_{p}^{XY}(\ell)</math> of the relative error on <math>B^{XY}_{\ell}</math> (see "HFI time response and beams paper"<cite>planck2013-p03c</cite> {{P2013|7}}), defined for <math>p</math> in <math>[1,5]</math> and <math>\ell</math> in <math>[0, \lmax]</math> (with <math>\lmax</math> being 2500, 3000 or 4000 when the lowest of the nominal frequencies of the detectors <math>X</math> and <math>Y</math> is respectively 100, 143 or 217GHz). The extra contribution to the covariance of <math>C^{XY}_\ell</math> is then <br />
\begin{align}<br />
\hat{M}^{XY, \mathrm{beam}}_{\ell_1 \ell_2} = 4 \hat{C}^{XY}_{\ell_1} \hat{C}^{XY}_{\ell_2} \sum_{p=1}^{5} E^{XY}_p(\ell_1) E^{XY}_p(\ell_2).<br />
\label{eq:covmatBeam}<br />
\end{align}<br />
<br />
<!-- =================================================== --><br />
<div id="all_dscl"><br />
[[File:all_dscl.png | 500px | center | thumb | '''Figure 1:''' The 91 auto- (dotted lines) and cross- (solid lines) angular power spectra <math>\hat{C}_\ell</math>, shown here after a binning of <math>\Delta \ell = 31</math>, grouped by frequencies. For instance the top left panel, tagged ''100x100 (3)'', contains the three spectra 100-ds1x100-ds2, 100-ds1x100-ds1 and 100-ds1x100-ds2. The auto spectra are contaminated at high <math>\ell</math> by the instrumental noise, and all of them may be affected by foreground contamination. The grey circles show the best Planck CMB high-<math>\ell</math> power spectrum described in the [[CMB spectrum & Likelihood Code | CMB spectrum & Likelihood Code section]] ]]<br />
</div><br />
<!-- =================================================== --><br />
<br />
<br />
====Auto and Cross Power Spectra====<br />
<br />
The spectra computed up to <math>l=3508</math> using [http://prof.planck.fr/article141.html PolSpice] (<cite>Szapudi2001</cite>, <cite>Chon2004</cite>) <br />
are corrected from the effect of the cut sky, and from the nominal beam window function and average pixel function. The different steps of the calculation are<br />
* computation of the Spherical Harmonics coefficients of the masked input maps <math>\Delta T^X(p)</math> and of the input mask <math>w(p)</math>,<br />
\begin{align}<br />
\tilde{a}^X_{\ell m} = \sum_p \Omega_p\, \Delta T^X(p)\, w(p)\, Y^*_{\ell m}(p), \label{eq:almdef}<br />
\end{align}<br />
\begin{align}<br />
\tilde{w}^{(n)}_{\ell m} = \sum_p \Omega_p\ w^n(p)\, Y^*_{\ell m}(p); \label{eq:wlmdef}<br />
\end{align}<br />
where the sum is done over all sky pixels <math>p</math>, <math>\Omega_p</math> is the pixel area, and <math>n</math> is either 1 or 2;<br />
* the sky (cross or auto) pseudo-power spectrum and mask power spectrum are computed from the $\tilde{a}_{\ell m}$ and $\tilde{w}_{\ell m}$,<br />
\begin{align}<br />
\tilde{C}^{XY}_\ell = \sum_{\ell m} \tilde{a}^X_{ m} \tilde{a}^{Y^*}_{\ell m} / (2 \ell + 1), \label{eq:alm2cl}<br />
\end{align}<br />
\begin{align}<br />
\tilde{W}^{(n)}_\ell = \sum_{\ell m} \tilde{w}^{(n)}_{ m} {\tilde{w}^{(n)}}^*_{\ell m} / (2 \ell + 1); \label{eq:wlm2wl}<br />
\end{align}<br />
* the sky and mask angular correlation function are computed from the respective power spectra,<br />
\begin{align}<br />
\tilde{\xi}(\theta) = \sum_\ell \frac{2\ell+1}{4\pi} \tilde{C}_{\ell} P_\ell(\theta),\label{eq:cl2xi}<br />
\end{align}<br />
\begin{align}<br />
\tilde{\xi}_W(\theta) = \sum_\ell \frac{2\ell+1}{4\pi} \tilde{W}^{(1)}_{\ell} P_\ell(\theta),<br />
\end{align}<br />
where $P_\ell$ is the Legendre Polynomial of order $\ell$;<br />
* the ratio of the sky angular correlation by the mask correlation provides the cut sky corrected angular correlation,<br />
\begin{align}<br />
\xi(\theta) = \tilde{\xi}(\theta) / \tilde{\xi}_W(\theta); \label{eq:xi_deconv}<br />
\end{align}<br />
* the sky angular correlation function which is then turned into a angular power spectrum,<br />
\begin{align}<br />
{C'}_\ell = 2\pi \sum_i w_i \xi(\theta_i) P_\ell(\theta_i), \label{eq:xi2cl}<br />
\end{align}<br />
where $w_i$ are the weights of the Gauss-Legendre quadrature, for $\theta$ in $[0, \pi]$;<br />
* the resulting power spectrum is corrected from the nominal beam window function $B_\ell$ and average pixel window function $w_{\mathrm{pix}}(\ell)$, to provide the final Spice estimator $\hat{C}_\ell$,<br />
\begin{align}<br />
\hat{C}_\ell = {C'}_\ell / \left( B^2_\ell w^2_{\mathrm{pix}}(\ell) \right). \label{eq:clfinal}<br />
\end{align}<br />
<br />
====Covariance Matrices====<br />
The covariance matrix for the pair $XY$ is computed by PolSpice<br />
using the formalism described in <cite>Efstathiou2004</cite><!--[http://adsabs.harvard.edu/abs/2004MNRAS.349..603E Efstathiou (2004)]-->, also sketched in the appendix<br />
of "CMB power spectra and likelihood paper"<cite>planck2013-p08</cite>, assuming the instrumental noise to be white and uniform.<br />
<br />
$<br />
\newcommand{\hC}{\hat C}<br />
$<br />
One note that a good approximation of the covariance matrix $\tilde{M}$ of the pseudo $\tilde{C}_{\ell}$ is related to the underlying ''estimated'' auto- and cross-spectra $\hC_{\ell}$ through<br />
\begin{align}<br />
\tilde{M}_{\ell_1\ell_2} \equiv \langle\Delta \tilde{C}^{XY}_{\ell_1}\Delta \tilde{C}^{XY}_{\ell_2}\rangle = <br />
\left( \left(\hC^{XX}_{\ell_1} \hC^{YY}_{\ell_1} \hC^{XX}_{\ell_2} \hC^{YY}_{\ell_2}\right)^{1/2}<br />
+ \hC^{XY}_{\ell_1} \hC^{XY}_{\ell_2} \right) <br />
\sum_{\ell_3} \frac{2\ell_3+1}{4\pi} \tilde{W}^{(2)}_{\ell_3} \left( <br />
\begin{array}{ccc}<br />
\! \ell_1\! & \ell_2\! & \ell_3\! \\<br />
\! 0 \! & 0 \! & 0 \!<br />
\end{array}<br />
\right)^2,<br />
\label{eq:covpseudo}<br />
\end{align}<br />
where $\tilde{W}^{(2)}_{\ell}$ is the power spectrum of the square of the pixel mask (Eqs. \ref{eq:wlmdef} and \ref{eq:wlm2wl} for $n=2$). The covariance matrix $\hat{M}$<br />
of the Spice estimator is then computed by applying Eqs. \ref{eq:cl2xi}, \ref{eq:xi_deconv}, \ref{eq:xi2cl} and \ref{eq:clfinal} on each row and column of $\tilde{M}$.<br />
<br />
<br />
<!-- The products described here, spectra ${\hat C}_{\ell}$ and covariances ${\hat M}_{\ell \ell'}$ can be used to <br />
estimate the high-$\ell$ likelihood of a given theoretical model given the data available. --><br />
<br />
===Inputs===<br />
<br />
; Maps<br />
: The input maps are the 13 HFI detset (see [[Frequency_Maps#Types_of_maps | ''Type of maps'']] section for details) maps available at 100, 143 and 217 GHz. These are the same as the ones used for high-ell part of the [[CMB spectrum & Likelihood Code | likelihood code]], but that code applies different masks for each cross-spectra in order to minimize further the foreground contamination.<br />
; Sky mask<br />
: All maps were analyzed on the 42.8% of the sky defined by the apodized mask ''HFI_PowerSpect_Mask_2048_R1.10.fits'', which masks out Galactic Plane and point sources (see <cite>planck2013-p08</cite>), and which is shown in [[#mask_Cl|Figure 2]] below<br />
<br />
<div id="mask_Cl"><br />
[[File:mask_Cl.png | 500px | center | thumb | '''Figure 2:''' Apodized pixel mask used for HFI power spectrum estimation ]]<br />
</div><br />
<br />
; Beam Window Function<br />
: The beam window functions $B(l)$, and their uncertainties, are the ones used in the high-ell likelihood analysis, described in section 6.1 "Error Eigenmodes" of <cite>planck2013-p08</cite> and provided in the HFI [[The RIMO|RIMO]].<br />
<br />
===Related products===<br />
<br />
None<br />
<br />
===FITS file structure===<br />
<br />
Power spectra are provided for the auto and cross products built from the 13 detsets available at 100, 143 and 217 GHz, namely: <br />
* 100-ds1, 100-ds2,<br />
* 143-ds1, 143-ds2, 143-5, 143-6, 143-7, <br />
* 217-ds1, 217-ds2, 217-1, 217-2, 217-3, 217-4<br />
which makes 13*(13+1)/2 = 91 spectra. Filenames for the auto spectra are ''HFI_PowerSPect_{detset}_Relnum.fits'' and ''HFI_PowerSPect_{detset1}x{detset2}_Relnum.fits'' for the auto- and cross-spectra, respectively. The list of the 91 files is given below. Each files contains 2 BINTABLE extensions:<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Power spectrum file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'POW-SPEC' (BINTABLE)<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|TEMP_CL || Real*4 || $\mu$K<sub>cmb</sub><sup>2</sup> || the power spectrum<br />
|-<br />
|TEMP_CL_ERR || Real*4 || $\mu$K<sub>cmb</sub><sup>2</sup> || estimate of the uncertainty in the power spectrum<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|LMIN || Integer || 0 || First monopole<br />
|-<br />
|LMAX || Integer || value || Last monopole<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 2. EXTNAME = 'PSCOVMAT' (IMAGE)<br />
|-<br />
|COVMAT || Real*4 || $\mu$K<sub>cmb</sub><sup>4</sup> || the covariance matrix<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|NAXIS1 || Integer || dim1 || matrix first dimension<br />
|-<br />
|NAXIS2 || Integer || dim2 || matrix second dimension<br />
|}<br />
<br />
where LMAX is the same for both vectors, and dim1 = dim2 = LMAX+1 by construction.<br />
<br />
<br />
===List of filenames===<br />
<br />
{| align="center" style="text-align:left" border="1" cellpadding="2" cellspacing="0" width=400px<br />
|+ '''FITS filenames''' <br />
|- bgcolor="ffdead" <br />
! Auto power spectra<br />
|-<br />
| HFI_PowerSpect_100-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-ds2_R1.10.fits <br />
|- bgcolor="ffdead" <br />
! Cross power spectra<br />
|-<br />
| HFI_PowerSpect_100-ds1x100-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds1x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_100-ds2x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-5x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-6x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-7x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x143-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds1x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x143-5_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x143-6_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x143-7_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_143-ds2x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-1x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-3_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-2x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3x217-4_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-3x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-4x217-ds1_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-4x217-ds2_R1.10.fits <br />
|-<br />
| HFI_PowerSpect_217-ds1x217-ds2_R1.10.fits <br />
|- bgcolor="ffdead" <br />
! Sky mask<br />
|-<br />
| {{PLASingleFile|fileType=map|name=HFI_PowerSpect_Mask_2048_R1.10.fits|link=HFI_PowerSpect_Mask_2048_R1.10.fits}}<br />
|}<br />
<br />
The full list of HFI power spectra with links to the files in the PLA can be found {{PLASpec|inst=HFI|link=here}}.<br />
<br />
== LFI maps power spectra ==<br />
---------------------------------<br />
<br />
===Product description===<br />
The angular power spectrum provides information about the distribution of power on the sky map at the various angular scales. It is especially important for CMB, because it is characterized by a number of features, most notably the acoustic peaks, that encode the dependence from cosmological parameters. Therefore, angular power spectra are the basic inputs for the [[CMB spectrum & Likelihood Code | Planck Likelihood Code]], and for estimation of cosmological parameters in general.<br />
<br />
For this release we have computed only temperature power spectra. Polarization is not included.<br />
<br />
Please note that these spectra come from frequency maps. No component separation has been applied, and we have only masked Galactic Plane and detected point sources. Units are <math> \rm{ \mu K^2_{CMB}} </math>.<br />
<br />
===Production process===<br />
Spectra are computed using cROMAster, a implementation of the pseudo-Cl method described in <cite>#master</cite>. In addition to the original approach, our implementation allows for estimation of cross-power spectra from two or more maps (see <cite>#polenta_CrossSpectra</cite> for details). The software package uses [http://healpix.sourceforge.net/ HEALPix] modules for spherical harmonic transform and Cl calculation. The schematic of the estimation process is as follows:<br />
<br />
* computing the a_lm coefficients from the input temperature map after masking Galactic Plane and point sources.<br />
* computing the pseudo power spectrum from the alms.<br />
* estimating the bias due to the noise power spectrum of the map from noise-only Monte Carlo simulations based on detector noise properties<br />
* correcting for the effect of the adopted mask by computing the mode-mode coupling kernel corresponding to that mask<br />
* deconvolving the effect due to the finite angular resolution of the telescope by using the beam window function<br />
* deconvolving the effect due to the finite size of the pixel in the map by using a pixel window function<br />
* binning the power spectrum from individual multipoles into bandpowers<br />
* estimating error bars on bandpowers from signal plus noise Monte Carlo simulations, where signal simulations include only CMB anisotropies.<br />
<br />
===Inputs===<br />
<br />
The inputs are the following:<br />
<br />
* [[Frequency Maps| LFI Frequency Maps]]<br />
* Point source and galactic plane masks (the name being specified in the comment keyword in the header, see Note in ''Meta Data'' section below): <br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"! Mask Name || <br />
|-<br />
!colspan="4" | Point source masks<br />
|-<br />
|{{PLASingleFile|fileType=map|name=LFI_MASK_030-ps_2048_R1.00.fits|link=LFI_MASK_030-ps_2048_R1.00.fits}}<br />
|-<br />
|{{PLASingleFile|fileType=map|name=LFI_MASK_044-ps_2048_R1.00.fits|link=LFI_MASK_044-ps_2048_R1.00.fits}}<br />
|-<br />
|{{PLASingleFile|fileType=map|name=LFI_MASK_070-ps_2048_R1.00.fits|link=LFI_MASK_070-ps_2048_R1.00.fits}}<br />
|-<br />
!colspan="4" | Galactic plane masks<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_MASK_gal-06_2048_R1.00.fits|link=COM_MASK_gal-06_2048_R1.00.fits}}<br />
|-<br />
|{{PLASingleFile|fileType=map|name=COM_MASK_gal-07_2048_R1.00.fits|link=COM_MASK_gal-07_2048_R1.00.fits}}<br />
|}<br />
* [[The RIMO#Beam_Window_Functions| Beam window functions]]<br />
* Monte Carlo simulations<br />
* binning scheme [[Media:Power_spectra_CTP_bin_tt.pdf]].<br />
<br />
===File Names===<br />
<br />
: {{PLASingleFile|fileType=cosmo|name=LFI_PowerSpect_030_R1.10.fits|link=LFI_PowerSpect_030_R1.10.fits}}<br />
: {{PLASingleFile|fileType=cosmo|name=LFI_PowerSpect_044_R1.10.fits|link=LFI_PowerSpect_044_R1.10.fits}}<br />
: {{PLASingleFile|fileType=cosmo|name=LFI_PowerSpect_070_R1.10.fits|link=LFI_PowerSpect_070_R1.10.fits}}<br />
<br />
===Meta Data ===<br />
<br />
The angular power spectra source list in each frequency is structured as a FITS binary table. <br />
The Fits extension is composed by the columns described below:<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|L || Integer*4 || || ell parameter<br />
|-<br />
|TEMP_CL || Real*8 || uK<math>_{CMB}^2</math> || <math>C_l</math> (temperature) <br />
|-<br />
|TEMP_CL_ERR || Real*8 || uK<math>_{CMB}^2</math> || <math>C_l</math> error<br />
|-<br />
|}<br />
<br />
<br />
'''Note.-''' in the comment keyword in the header, the galactic and point source maps used to generate the angular spectra are specified (LFI_MASK_030-ps_2048_R1.00.fits and COM_MASK_gal-06_2048_R1.00.fits in the example below). Note also that, due to an oversight, the mask description related to COM_MASK_gal-xxx is wrong and should refer to the galactic mask. <br />
<br />
Below an example of the header. <br />
<br />
<pre><br />
XTENSION= 'BINTABLE' /Written by IDL: Sat Feb 16 00:44:22 2013<br />
BITPIX = 8 /<br />
NAXIS = 2 /Binary table<br />
NAXIS1 = 20 /Number of bytes per row<br />
NAXIS2 = 130 /Number of rows<br />
PCOUNT = 0 /Random parameter count<br />
GCOUNT = 1 /Group count<br />
TFIELDS = 3 /Number of columns<br />
TFORM1 = '1J ' /Integer*4 (long integer)<br />
TTYPE1 = 'L ' /<br />
TFORM2 = '1D ' /Real*8 (double precision)<br />
TTYPE2 = 'TEMP_CL ' /<br />
TFORM3 = '1D ' /Real*8 (double precision)<br />
TTYPE3 = 'TEMP_CL_ERR' /<br />
EXTNAME = 'POW-SPEC' / Extension name<br />
EXTVER = 1 /Extension version<br />
DATE = '2013-02-15' /Creation date<br />
TUNIT2 = 'uK_CMB^2' /<br />
TUNIT3 = 'uK_CMB^2' /<br />
FILENAME= 'LFI_PowerSpect_030_R1.00.fits' /<br />
PROCVER = 'Dx9_delta' /<br />
COMMENT ---------------------------------------------<br />
COMMENT Original Inputs<br />
COMMENT ---------------------------------------------<br />
COMMENT TT_30GHz_maskCS0.60_PS30GHzdet_febecopWls<br />
COMMENT Used Point source Mask LFI_MASK_030-ps_2048_R1.00.fits<br />
COMMENT Used Point source Mask COM_MASK_gal-06_2048_R1.00.fits<br />
COMMENT Used FebeCoP 30 GHz wls<br />
END<br />
</pre><br />
<br />
Below an example of the header of two masks used as input: COM_MASK_gal-06_2048_R1.00.fits and LFI_MASK_030-ps_2048_R1.00.fits:<br />
<pre><br />
XTENSION= 'BINTABLE' / binary table extension<br />
BITPIX = 8 / 8-bit bytes<br />
NAXIS = 2 / 2-dimensional binary table<br />
NAXIS1 = 4 / width of table in bytes<br />
NAXIS2 = 50331648 / number of rows in table<br />
PCOUNT = 0 / size of special data area<br />
GCOUNT = 1 / one data group (required keyword)<br />
TFIELDS = 1 / number of fields in each row<br />
TTYPE1 = 'Mask ' / label for field 1<br />
TFORM1 = 'E ' / data format of field: 4-byte REAL<br />
TUNIT1 = 'none ' / physical unit of field<br />
EXTNAME = '06-GalMask'<br />
DATE = '2013-02-16T11:07:42' / file creation date (YYYY-MM-DDThh:mm:ss UT)<br />
CHECKSUM= 'NaGVNZGUNaGUNYGU' / HDU checksum updated 2013-02-16T11:07:43<br />
DATASUM = '2540860986' / data unit checksum updated 2013-02-16T11:07:43<br />
COMMENT<br />
COMMENT *** Planck params ***<br />
COMMENT<br />
PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation<br />
ORDERING= 'NESTED ' / Pixel ordering scheme, either RING or NESTED<br />
NSIDE = 2048 / Resolution parameter for HEALPIX<br />
FIRSTPIX= 0 / First pixel # (0 based)<br />
LASTPIX = 50331647 / Last pixel # (0 based)<br />
INDXSCHM= 'IMPLICIT' / Indexing: IMPLICIT or EXPLICIT<br />
OBJECT = 'FULLSKY ' / Sky coverage, either FULLSKY or PARTIAL<br />
BAD_DATA= -1.6375E+30<br />
COORDSYS= 'GALACTIC'<br />
FILENAME= 'COM_MASK_gal-06_2048_R1.00.fits'<br />
COMMENT ---------------------------------------------------------------------<br />
COMMENT Combined galactic mask 0.6 sky fraction<br />
COMMENT Objects used:<br />
COMMENT /sci_planck/lfi_dpc_test/ashdown/repository/masks/component_separation/d<br />
COMMENT x9/combined_mask_0.60_sky_fraction.fits<br />
COMMENT ---------------------------------------------------------------------<br />
END<br />
</pre><br />
<br />
<pre><br />
XTENSION= 'BINTABLE' / binary table extension<br />
BITPIX = 8 / 8-bit bytes<br />
NAXIS = 2 / 2-dimensional binary table<br />
NAXIS1 = 4 / width of table in bytes<br />
NAXIS2 = 50331648 / number of rows in table<br />
PCOUNT = 0 / size of special data area<br />
GCOUNT = 1 / one data group (required keyword)<br />
TFIELDS = 1 / number of fields in each row<br />
TTYPE1 = 'Mask ' / label for field 1<br />
TFORM1 = 'E ' / data format of field: 4-byte REAL<br />
TUNIT1 = 'none ' / physical unit of field<br />
EXTNAME = '030-PSMask'<br />
DATE = '2013-02-16T11:03:20' / file creation date (YYYY-MM-DDThh:mm:ss UT)<br />
CHECKSUM= 'fR7ThO7RfO7RfO7R' / HDU checksum updated 2013-02-16T11:03:21<br />
DATASUM = '3828742620' / data unit checksum updated 2013-02-16T11:03:21<br />
COMMENT<br />
COMMENT *** Planck params ***<br />
COMMENT<br />
PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation<br />
ORDERING= 'NESTED ' / Pixel ordering scheme, either RING or NESTED<br />
NSIDE = 2048 / Resolution parameter for HEALPIX<br />
FIRSTPIX= 0 / First pixel # (0 based)<br />
LASTPIX = 50331647 / Last pixel # (0 based)<br />
INDXSCHM= 'IMPLICIT' / Indexing: IMPLICIT or EXPLICIT<br />
OBJECT = 'FULLSKY ' / Sky coverage, either FULLSKY or PARTIAL<br />
BAD_DATA= -1.6375E+30<br />
COORDSYS= 'GALACTIC'<br />
FILENAME= 'LFI_MASK_030-ps_2048_R1.00.fits'<br />
COMMENT ---------------------------------------------------------------------<br />
COMMENT The radius of the holes is 3 times the sigma of the beam at the correspo<br />
COMMENT nding frequency and sigma is FWHM/(2*sqrt(2ln2))<br />
COMMENT FWHM at 30GHz used = 33.158 arcmin<br />
COMMENT Objects used:<br />
COMMENT /planck/sci_ops1/LFI_MAPs/DX9_Delta/MASKs/mask_ps_30GHz_beam33amin_nside<br />
COMMENT 2048.00_DX9_nonblind_holesize3.fits<br />
COMMENT ---------------------------------------------------------------------<br />
END<br />
</pre><br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
[[Category:Mission products|006]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Unit_conversion_and_Color_correction&diff=7704Unit conversion and Color correction2013-06-19T09:53:41Z<p>Lvibert: </p>
<hr />
<div>==Unit conversion and colour correction==<br />
---------------------------<br />
The unit conversion and colour correction software (UC_CC) consists of a set of IDL procedures and functions that read the band transmission from the DPC RIMOs and perform the requested conversions. The package is delivered as a tarfile and contains a detailed instruction manual. The data and software file requirements are provided below along with basic use instructions and some simple examples. The full list of its contents is:<br />
<br />
UC_CC_v102/get_hfibolo_list.pro<br />
UC_CC_v102/hfi_co_correction.pro<br />
UC_CC_v102/hfi_colour_correction.pro<br />
UC_CC_v102/hfi_lfi_test_script.pro<br />
UC_CC_v102/hfi_lfi_test_script_PLA_RIMO.pro<br />
UC_CC_v102/hfi_read_avg_bandpass.pro<br />
UC_CC_v102/hfi_read_bandpass.pro<br />
UC_CC_v102/hfi_unit_conversion.pro<br />
UC_CC_v102/lfi_read_avg_bandpass.pro<br />
UC_CC_v102/lfi_read_bandpass.pro<br />
UC_CC_v102/LFI_fastcc.pro<br />
UC_CC_v102/LFI_fastcc_test.pro<br />
UC_CC_v102/README.txt<br />
UC_CC_v102/Instructions.pdf<br />
<br />
The package is currently available on [[http://externaltools.planck.fr]]<br />
<br />
== Relevant documentation ==<br />
<br />
Please refer to the Spectral Response sections of the Explanatory Supplement (i.e. 2.2.1.2, 4.4.5, and 4.6), as well as the Spectral Response Paper <cite>#planck2013-p03d</cite> for details of the derivation of the detector spectra and band-average spectra included in the RIMO files, as well as additional details on the unit conversion and colour correction methodology, philosophy, and implementation. This section concentrates on the use of the provided UC_CC software itself, leaving the other sections to provide the basis for it. <br />
<br />
== Tarfile distribution package ==<br />
<br />
This section provides a brief explanation of each file included in the UC_CC distribution.<br />
<br />
# <tt>get_hfibolo_list.pro</tt>: used to provide basic detector information (i.e. names) within subsequent routines.<br />
# <tt>hfi_read_bandpass.pro</tt>: a routine to get the desired detector level spectral transmission data (HFI) and output in a structure format used by the other routines.<br />
# <tt>hfi_read_avg_bandpass.pro</tt>: a routine to get the desired HFI band-average spectral transmission data and output in a structure format used by the other routines.<br />
# <tt>hfi_unit_conversion.pro</tt>: a routine that accepts spectral response information and outputs unit conversion coefficients.<br />
# <tt>hfi_colour_correction.pro</tt>: a routine that accepts spectral response information and outputs colour correction coefficients.<br />
# <tt>hfi_co_correction.pro</tt>: a routine that accepts spectral response information and outputs CO conversion coefficients.<br />
# <tt>lfi_read_bandpass.pro</tt>: a routine to get the desired detector level spectral transmission data (LFI) and output in a structure format used by the other routines.<br />
# <tt>lfi_read_avg_bandpass.pro</tt>: a routine to get the desired LFI band-average spectral transmission data and output in a structure format used by the other routines.<br />
# <tt>hfi_lfi_test_script.pro</tt>: a sample script providing examples of calling the various routines.<br />
# <tt>hfi_lfi_test_script_PLA_RIMO.pro</tt>: a sample script providing examples of calling the various routines using the PLA RIMO file (without detector-level spectra).<br />
# <tt>LFI_fastcc.pro</tt>: a routine to calculate LFI colour corrections using quadratic approximations (faster than integrating each time).<br />
# <tt>LFI_fastcc_test.pro</tt>: a sample script providing examples of calling the LFI_fastcc routine.<br />
# <tt>README.txt</tt>: a text file providing basic instructions and expected output for the hfi_lfi_test_script.pro file (basic introduction and precursor to this document).<br />
<br />
== Required input data ==<br />
<br />
<div id="sec:input"></div><br />
The UC_CC routines require access to the Planck spectral response data. This is nominally provided in the RIMO files included in the same location as this package. The ingestion routines are written in such a way as to accept updated RIMO files (provided the <tt>.fits</tt> header structure uses the same naming conventions as currently / previously implemented). For users with access to the HFI databases on magique3 (i.e. members of the HFI Core-team), the software is also able to access the spectral response data directly from the HFI IMO (see examples below for details). The software is written to allow use of the PLA RIMO file which includes only band-average spectra, as well as the full RIMO (with detector level spectra) which will be made available through the PLA in a future release.<br />
<br />
A user may provide a unique model spectrum about which to generate colour correction coefficients specific to the model input (see §[[#sec:CC|2.6.5]]), however this is not required for standard colour correction coefficients based on power-law spectral indices and/or modified blackbody spectra.<br />
<br />
== Required software packages ==<br />
<br />
<div id="sec:soft"></div><br />
This software has been tested on IDL versions 6.4, 7.1, 8.0, 8.1, and 8.2. It requires use of the <tt>mrdfits.pro</tt> file, and related sub-routines, from ''the IDL Astronomy User’s Library'' to read the RIMO <tt>.fits</tt> files. This library should be included with most IDL Healpix distributions, and is otherwise freely available online (http://idlastro.gsfc.nasa.gov/). The UC_CC routines will not work with the RIMO <tt>.fits</tt> files without routines from this library! The routines provided will work with either the full (internal) RIMO files containing detector level spectra, or the PLA (external) RIMO files with only frequency-band level spectra. To date the software has not been tested on the PLA RIMO files (this should change soon, and needs to prior to the data release).<br />
<br />
== Software initialization ==<br />
<br />
<div id="sec:init"></div><br />
No installation is required. It is recommended to add the UC_CC scripts to a directory within your IDL path, or add the UC_CC directory to your IDL path. As some of the UC_CC files contain multiple functions/procedures, it is also recommended to compile each of the UC_CC <tt>.pro</tt> files prior to running scripts using the respective routines; <tt>get_hfibolo_list.pro</tt> should be compiled before any of the other routines.<br />
<br />
== Software use ==<br />
<br />
<div id="sec:use"></div><br />
The following section outlines basic use of the UC_CC IDL scripts and provides examples.<br />
<br />
=== Spectral input ===<br />
<br />
<div id="sec:getSpec"></div><br />
The UC_CC routines accept individual detector and band-average spectra structures as input. The<br /><br />
<tt>hfi_read_bandpass.pro</tt> and <tt>hfi_read_avg_bandpass.pro</tt> routines are used to obtain this data for HFI, and the <tt>lfi_read_bandpass.pro</tt> and <tt>lfi_read_avg_bandpass.pro</tt> routines are used to obtain this data for LFI. The spectra can be restored from either a RIMO file, or an IMO database (if access to such is available). The routines return the transmission spectra by default, but are also configured to return the spectral uncertainty and interpolation flag as additional output parameters. Here are some example IDL commands using these routines:<br />
<br />
<tt>hfi_bp = hfi_read_bandpass(/RIMO, PATH_RIMO='/path/to/RIMO/file/', $</tt><br /><br />
<tt> NAME_RIMO='Name_of_RIMO_file.fits', FLG_INFO=flg, ER_INFO=er, /FLAG)</tt><br />
<tt>hfi_bp_withCO = hfi_read_bandpass(/RIMO, PATH_RIMO='/path/to/file', $</tt><br /><br />
<tt> NAME_RIMO='Name_of_RIMO_file.fits', FLG_INFO=flg_withCO, $</tt><br /><br />
<tt> ER_INFO=er_withCO, FLAG = 0)</tt><br />
<tt>hfi_avg = hfi_read_avg_bandpass(/RIMO, PATH_RIMO='/path/to/RIMO/file/', $</tt><br /><br />
<tt> NAME_RIMO='Name_of_RIMO_file.fits', FLG_INFO=flg_avg, ER_INFO=er_avg, /FLAG)</tt><br />
<tt>hfi_avg_withCO = hfi_read_avg_bandpass(/RIMO, PATH_RIMO='/path/to/file', $</tt><br /><br />
<tt> NAME_RIMO='Name_of_RIMO_file.fits', FLG_INFO=flg_avg_withCO, $</tt><br /><br />
<tt> ER_INFO=er_avg_withCO, FLAG = 0)</tt><br />
<tt>lfi_bp = lfi_read_bandpass(/RIMO, PATH_RIMO='/path/to/RIMO/file/', $</tt><br /><br />
<tt> NAME_RIMO='Name_of_LFI_RIMO_file.fits', ER_INFO=er)</tt><br />
<tt>lfi_avg = lfi_read_avg_bandpass(/RIMO, PATH_RIMO='/path/to/RIMO/file/', $</tt><br /><br />
<tt> NAME_RIMO='Name_of_LFI_RIMO_file.fits', ER_INFO=er_avg)</tt><br />
<br />
In the above examples, <tt>hfi_bp</tt>, <tt>hfi_bp_withCO</tt>, and <tt>lfi_bp</tt> represent IDL structures containing individual detector spectra. The variables <tt>er</tt> and <tt>er_avg</tt> containt the spectral uncertainty within a structure similar to that of the spectra. The <tt>flg</tt> and <tt>flg_avg</tt> structures contain the CO interpolation flag indiciating if a spectral data point is uniquely measured from the calibration data (i.e. <tt>flg[i] = 0</tt>), or interpolated (i.e. <tt>flg[i] = 1</tt>, see Ex. Supp. for more details). No such flag exists for LFI. If the <tt>FLAG</tt> keyword is set, flagged data points are removed from the spectral structures prior to being output; i.e. <tt>FLAG=0</tt> outputs all data and <tt>FLAG=1</tt> outputs only un-flagged data points, the default setting if FLAG is not input is the <tt>FLAG=1</tt> setting. With the <tt>RIMO</tt> keyword set, there must be a <tt>RIMO.fits</tt> file in the <tt>PATH_RIMO</tt> directory of the <tt>NAME_RIMO</tt> keyword value. The routines may also get the spectra from an IMO database (this requires the user to have access to an IMO data base with details available within the Planck collaboration). <br />
<br />
The output of the ...read_bandpass.pro routines is an array of IDL structures. The other UC_CC routines are written in such a way as to accept these structures as input. The software has been modularized such that the subroutines within the scripts can accept input spectra in other formats. This level of use of the UC_CC routines is beyond this introduction, however. Those interested are directed to look through the original source code of the subroutines, paying particular attention to the subroutines without the hfi_ prefix within each script; these routines may be called externally. Further queries may be directed towards the authors (esp. Spencer).<br />
<br />
The LFI RIMO files follow a different convention than that of HFI, so the ingestion routine also accounts for this. The LFI RIMO file frequency bins represent the bin start frequency rather than the bin centre frequency, and the convention is such that the transmission data need to be scaled by <math>\lambda^2</math> to be consistent with the HFI spectra. Both of these modifications are performed within the <tt>lfi_read_bandpass</tt> and <tt>lfi_read_avg bandpass</tt> routines, so their output structures are in the format expected by the remaining UC_CC routines.<br />
<br />
The UC_CC routines follow HFI unit conversion and colour correction conventions, and have been developed primarily for use with HFI data processing. Functionality has also been included for the LFI spectra. The UC_CC routines LFI output has been verified against internal LFI coefficients for the combined case of K<math>_{\mbox{CMB}}</math> to T<math>_{\mbox{b}}</math> unit conversion and colour correction for spectral indices ranging from <math>-2</math> to <math>+4</math>. This validation confirmed that the UC_CC code treats the LFI spectra in the same way as in other LFI data processing, and thus all of the UC_CC LFI output is expected to conform with official LFI data processing.<br />
<br />
=== UC_CC output ===<br />
<br />
<div id="sec:output"></div><br />
The UC_CC routines output conversion coefficients as arrays of IDL structures. This ensures that the detector name and coefficient are paired, and any additional information may also be provided, e.g. the CO rotational transition line in the case of a CO coefficient. It is important to note that the output for the 143-8 and 545-3 detector coefficients is intentionally set to <math>-10^{9}</math> in all cases. These two detectors have been excluded from HFI data processing due to their noise characteristics, and thus do not contribute to the band-average spectra or band-average coefficients. Ground measurements for these detectors do exist, and it is possible to determine these coefficients if needed, but they have been intentionally hidden from standard use.<br />
<br />
=== Coefficient uncertainty estimate ===<br />
<br />
An optional function of this software is to output an uncertainty for every unit conversion and colour correction coefficient<br />
determined. This requires spectral uncertainty as input (HFI only at present), and has uncertainty of other parameters<br />
as optional depending on the colour correction (e.g. CO radial velocity, dust temperature or emissivity, spectral<br />
index uncertainty, user-supplied spectral profile uncertainty (see §6.5), etc.). The GETERR keyword instructs the<br />
routines to calculate the coefficient uncertainty via NITER (another keyword) iterations of a Monte-Carlo uncertainty<br />
simulation. This requires the BP_ERR keyword to be set to the detector uncertainty (output from the hfi_read_bandpass<br />
routine), and/or the band-average spectral uncertainty to be set via the EABP (Error in Average Band-Pass) keyword<br />
(output from the hfi_read_avg_bandpass routine). Please refer to the test scripts for details on how these routine calls<br />
are performed. In principle it is possible to determine uncertainties for the LFI colour corrections, based on errors in<br />
the spectral index, dust temperature, etc. without spectral uncertainty; this is beyond the scope of this introduction and<br />
is left as an exercise (contact the authors for assistance if needed).<br />
The colour correction routine accepts various error keywords for use in the GETERR uncertainty estimate. These<br />
include ER_ALPHA, ER_TBD, ER_BETABD, ER_INU, associated with the ALPHA, TBD, BETABD, and INU input<br />
keywords. The default setting is zero to allow the uncertainty estimate to be strictly based on the spectral uncertainty. If<br />
any of the additional error keywords are set, then this additional uncertainty is combined with the spectral uncertainty<br />
in the simulation run.<br />
The defualt number of itereations is 2. Obviously this will not provide an accurate estimate, but not task processing<br />
time if accidentally set. The example routines use 100 iterations. Published uncertainty results typically use 10000<br />
iterations (but this obviously takes longer to compute).<br />
<br />
=== Unit conversion ===<br />
<br />
<div id="sec:Uc"></div><br />
The hfi_unit_conversion.pro routine will yield a structure of unit conversion coefficients for the provided spectral input, on a frequency channel and individual detector level for both LFI and HFI. It accepts an IDL structure containing individual detector spectra as input. It also accepts a band-average structure array as an additional keyword input, and outputs coefficients derived from the provided detector average spectrum. If this ABP optional keyword input is not provided, then the optional AVG_UC keyword output is not returned, and the main output returned by the function is set to zero (the individual bolometer coefficients are still returned via the keyword outputs).<br />
<br />
<tt>hfi_100_uc = hfi_unit_conversion(BP_INFO=hfi_bp, '100',hfibolo_100_uc, $</tt><br /><br />
<tt> ABP=hfi_avg, AVG_UC=AVG_100_UC, CH_UC=ch_100_uc)</tt><br /><br />
<tt>help, hfibolo_100_uc, /STRUCT ; Displays details of the structure contents.</tt><br /><br />
<tt>uc_KCMB2MJy_100_1a = hfibolo_100_uc[0].KCMB2MJYSR</tt><br /><br />
<tt>uc_KCMB2YSZ_100_2b = hfibolo_100_uc[3].KCMB2YSZ</tt><br /><br />
<tt>uc_MJY2TB_100_avg = avg_100_uc.MJY2TB</tt><br /><br />
<tt>lfi_44_uc = hfi_unit_conversion(BP_INFO=lfi_bp, '44', lfibolo_44_uc, $</tt><br /><br />
<tt> /lfi, ABP=lfi_avg, AVG_UC=AVG_44_UC)</tt><br />
<br />
In the above expressions, both the <tt>hfi_100_uc</tt> and <tt>avg_100_uc</tt> variables contain the coefficients determined using the band-average spectrum, and the <tt>ch_100_uc</tt> variable contains the average of the individual detector coefficients; these two variable sets may be similar but are not expected to be identical. The hfibolo_100_uc variable contains the individual detector values. The UC_CC unit conversion script accepts both LFI and HFI spectra in the format output by the corresponding read_..._bandpass routine. Details of the unit conversion equations are available in <cite>planck2013-p03d</cite>.<br />
<br />
=== Colour correction ===<br />
<br />
<div id="sec:CC"></div><br />
The colour correction routine works in much the same way as the unit conversion. It requires individual detector spectra as input, and band-average spectral input is optional, with the same caveats as above (§[[#sec:Uc|2.8]]). The colour correction routine has three distinct modes of operation. The first mode is a powerlaw spectral index where the output is a multiplicative coefficient for conversion ''from'' a spectral index of <math>-1</math> ''to'' a user-supplied spectral index, <math>\alpha</math>. The second is a modified blackbody where the conversion is ''from'' a <math>-1</math> spectral index ''to'' a Planck function of temperature, <math>T</math>, and emissivity <math>\propto\nu^\beta</math> (normalized by a <math>\nu_c^\beta B_\nu(\nu_c,T)</math> factor). The third is ''from'' a <math>-1</math> spectral index ''to'' a user supplied spectral profile. One example of this use is in the provision of colour correction coefficients for Mars, Jupiter, Saturn, Uranus, and Neptune where planet model spectra is provided as the user-specified spectral profile. Details of the colour correction equations are available in the Ex. Supp. An additional set of keywords have been added to the colour correction routines to provide the relevant effective frequency for a given spectral index, modified blackbody profile, or user-specified spectral profile. Examples of this use are included in the hfi_lfi_test_script.pro file. It is stressed that the use of effective frequencies is not within the official data processing philosophy of Planck; these outputs are provided strictly to allow comparison with other experiments that have adopted the effective frequency approach.<br />
<br />
<tt> ; Determine a powerlaw colour correction for 100 GHz detectors.</tt><br /><br />
<tt>hfi_100_cc = hfi_color_correction(BP_INFO=hfi_bp, '100', hfibolo_100_cc, $</tt><br /><br />
<tt> /POWERLAW, ALPHA=2.0, ABP=hfi_avg, AVG_CC=AVG_100_cc)</tt><br /><br />
<tt>help, hfibolo_100_cc, /struct ; Print info about the detector output.</tt><br /><br />
<tt> ; Determine a modified blackbody colour correction for Beta = 1.8 and T = 18 K.</tt><br /><br />
<tt>hfi_545_cc = hfi_color_correction(BP_INFO=hfi_bp, '545', hfibolo_545_cc, /MODBLACKBODY, $</tt><br /><br />
<tt> TBD = 18d, BETABD = 1.8d, ABP=hfi_avg, CH_CC=CH_545_CC, AVG_CC=AVG_545_CC)</tt><br /><br />
<tt> print, hfibolo_545_cc.BOLONAME</tt><br /><br />
<tt> print, hfibolo_545_cc.CC</tt><br />
* Note that 545-3 is set to <math>-10^9</math> as this detector is not included in flight data products due to excessive noise.<br />
<tt> ; Try to use a user-input spectrum</tt><br /><br />
<tt>nu = (hfi_avg[5].freq) ; in Hz</tt><br /><br />
<tt>Inu = COS((hfi_avg[5].trans)) ; some arb. profile</tt><br /><br />
<tt>hfi_857_cc = hfi_color_correction(BP_INFO=hfi_bp, '857', nu, Inu, hfibolo_857_cc, $</tt><br /><br />
<tt> ABP=hfi_avg, CH_CC=CH_857_CC, AVG_CC=AVG_857_CC)</tt><br /><br />
<tt>print, hfibolo_857_cc.BOLONAME</tt><br /><br />
<tt> print, hfibolo_857_cc.CC</tt><br />
<br />
<tt> ; Try to use another user-input spectrum</tt><br /><br />
<tt>nu = (hfi_avg[5].freq) ; in Hz</tt><br /><br />
<tt>Inu = LOG((hfi_avg[5].trans)) ; some arb. profile</tt><br /><br />
<tt>hfi_857_cc = hfi_color_correction(BP_INFO=hfi_bp, '857', nu, Inu, hfibolo_857_cc, $</tt><br /><br />
<tt> ABP=hfi_avg, CH_CC=CH_857_CC, AVG_CC=AVG_857_CC)</tt><br /><br />
<tt>print, hfibolo_857_cc.BOLONAME</tt><br /><br />
<tt> print, hfibolo_857_cc.CC</tt><br />
<br />
<br />
<br />
<br />
The variable CH_CC represents the average of the individual detector coefficients. The AVG_CC keyword and the function return value are both the output variable for the colour correction based on the band-average spectrum (i.e. the spectra are averaged and single coefficients are determined, not the averaging of multiple coefficients). The hfibolo_... variable is the output for the individual detector coefficients. For the user specified spectral profile, i.e. nu and Inu provided by the user, the frequency sampling of nu and Inu must match that of the corresponding transmission spectra. This was demonstrated above by setting nu = (hfi_avg[5].freq) from the transmission structure array.<br />
<br />
=== CO correction ===<br />
<br />
<div id="sec:CO"></div><br />
<br />
The CO correction routine provides conversion for CO emission from units of K<math>_{\mbox{CMB}}</math> to units of K km/s. The input and output formats are similar to the other UC_CC routines as described above. It is advised to use the <tt>FLAG=0</tt> setting in obtaining the detector and band-average spectra for the CO coefficients whereas it is recommended to use the <tt>FLAG=1</tt> or <tt>/FLAG</tt> setting for generation of any of the other coefficients (§[[#sec:getSpec|2.6.1]]).<br />
<br />
<nowiki><br />
<br />
; Determine CO coefficients for 100 GHz detectors, COJ1-0 transition.<br />
vrad = 0d ; radial velocity of 0 km/s.<br />
hfi_100_co = hfi_co_correction( BP_INFO=hfi_bp_withCO, ’100’, hfibolo_100_co, $<br />
hfibolo_100_13co, vrad=vrad, ABP=hfi_avg_withCO, AVG_CO=AVG_100_CO, $<br />
AVG_13CO=AVG_100_13CO, CH_CO=CH_100_CO, CH_13CO=CH_100_13CO, $<br />
BP_FLG=flg_withCO, FABP=flg_avg_withCO)<br />
<br />
print, hfibolo_100_co.BOLONAME ; print the detector names<br />
print, hfibolo_100_co.COLINE ; print the lower J value of the CO transition<br />
print, hfibolo_100_co.CC ; print the CO coefficients<br />
print, hfibolo_100_13co.CC ; print the 13CO coefficients<br />
<br />
; Repeat the above while also getting an uncertainty estimate.<br />
hfi_100_co_wEr = hfi_co_correction( BP_INFO=hfi_bp_withCO, ’100’, hfibolo_100_co_wEr, $<br />
hfibolo_100_13co_wEr, vrad=vrad, ABP=hfi_avg_withCO, AVG_CO=AVG_100_CO_wEr, $<br />
AVG_13CO=AVG_100_13CO_wEr, CH_CO=CH_100_CO_wEr, CH_13CO=CH_100_13CO_wEr, $<br />
BP_FLG=flg_withCO, FABP=flg_avg_withCO, BP_ERR=hfi_er_withCO, EABP=hfi_er_avg_withCO, $<br />
/GETERR, NITER=100)<br />
<br />
print, hfibolo_100_co.BOLONAME ; print the detector names<br />
print, hfibolo_100_co.COLINE ; print the lower J value of the CO transition<br />
print, hfibolo_100_co.CC ; print the CO coefficients<br />
print, hfibolo_100_co.ER ; print the CO coefficient uncertainties<br />
print, hfibolo_100_13co.CC ; print the 13CO coefficients<br />
print, hfibolo_100_13co.ER ; print the 13CO coefficient uncertainties<br />
<br />
; Use a different vrad and get the coefficients for the 143 GHz detectors.<br />
; You do not have to set the BP_FLG and FABP keywords, but the result is more accurate if you do.<br />
<br />
vrad = -30d ; radial velocity of -30 km/s (towards viewer).<br />
hfi_143_co = hfi_co_correction( BP_INFO=hfi_bp_withCO, ’143’, hfibolo_143_co, $<br />
hfibolo_143_13co, vrad=vrad, ABP=hfi_avg_withCO, AVG_CO=AVG_143_CO, $<br />
AVG_13CO=AVG_143_13CO, CH_CO=CH_143_CO, CH_13CO=CH_143_13CO)<br />
<br />
print, hfibolo_143_co.BOLONAME ; print the detector names<br />
print, hfibolo_143_co.COLINE ; There are two 143 GHz lines inc. (both coeffs. very small)<br />
print, hfibolo_143_co.CC ; print the CO coefficients<br />
<br />
; Use another vrad and get the coefficients for the 857 GHz detectors.<br />
vrad = 60d ; radial velocity of 60 km/s (away from viewer).<br />
hfi_857_co = hfi_co_correction( BP_INFO=hfi_bp_withCO, ’857’, hfibolo_857_co, $<br />
hfibolo_857_13co, vrad=vrad, ABP=hfi_avg_withCO, AVG_CO=AVG_857_CO, $<br />
AVG_13CO=AVG_857_13CO, CH_CO=CH_857_CO, CH_13CO=CH_857_13CO)<br />
<br />
print, hfibolo_857_co.BOLONAME ; print the detector names<br />
print, hfibolo_857_co.COLINE ; There are four 857 GHz lines<br />
print, hfibolo_857_co.CC ; print the CO coefficients<br />
</nowiki><br />
<br />
Although it is possible to determine CO coefficients for all 9 of the lowest rotational transitions for each HFI channel, the UC_CC routine only outputs those within, or nearly within the relevant spectral band. The two out-of-band 143 GHz coefficients are included as a confirmation of the CO rejection within this band.<br />
<br />
=== Nested correction ===<br />
<div id="sec:nest"></div><br />
Combinations of the above coefficients may be used to obtain additional correction factors. A few illustrative examples are included below.<br />
<br />
==== Colour correction from <math>\alpha = -2</math> to <math>\alpha = 4 </math> ====<br />
<br />
The colour correction from a spectral index of <math>-2</math> to <math>4</math> is done by first computing the conversion from both indices to <math>-1</math>, and then producing the correct ratio of the two.<br />
<br />
<tt> ; Determine the -2 to -1 correction, and the 4 to -1 correction</tt><br /><br />
<tt>alpha1 = -2d ; the first CC spectral index</tt><br /><br />
<tt>alpha2 = 4d ; the second CC spectral index</tt><br /><br />
<tt>hfi_100_a1_cc = hfi_colour_correction(BP_INFO=hfi_bp, '100', hfibolo_100_a1_cc, $</tt><br /><br />
<tt> /POWERLAW, ALPHA=alpha1, ABP=hfi_avg, AVG_CC=AVG_100_a1_cc)</tt><br /><br />
<tt> ; The above converts from -1 to alpha1</tt><br /><br />
<tt>hfi_100_a2_cc = hfi_colour_correction(BP_INFO=hfi_bp, '100', hfibolo_100_a2_cc, $</tt><br /><br />
<tt> /POWERLAW, ALPHA=alpha2, ABP=hfi_avg, AVG_CC=AVG_100_a2_cc)</tt><br /><br />
<tt> ; The above converts from -1 to alpha2</tt><br /><br />
<tt>hfibolo_100_m2_to_4_cc = hfibolo_100_a1_cc ; Use this as a placeholder.</tt><br /><br />
<tt>cc_m1_to_m2 = hfibolo_100_a1_cc.CC ; Coeffs. for -1 to -2</tt><br /><br />
<tt>cc_m1_to_4 = hfibolo_100_a2_cc.CC ; Coeffs. for -1 to 4</tt><br /><br />
<tt>cc_m2_to_4 = cc_m1_to_4/cc_m1_to_m2 ; ratio the coeffs.</tt><br /><br />
<tt>hfibolo_100_m2_to_4_cc.CC = cc_m2_to_4 ; Set the structure values to the coeff. ratios.</tt><br /><br />
<tt>print, cc_m1_to_m2 ; the -1 -&gt; -2 coeffs.</tt><br /><br />
<tt>print, cc_m1_to_4 ; the -1 -&gt; 4 coeffs.</tt><br /><br />
<tt>print, cc_m2_to_4 ; the -2 -&gt; 4 coeffs.</tt><br />
<br />
It is important to get the correct numerator and denominator when determining nested/combined unit conversion and colour correction ratios. Colour correction coefficients are from spectral index <math>-1</math> ''to'' spectral index <math>\alpha</math> by definition. The units of the unit conversion coefficients should be clear. The IRAS convention implies a spectral index of <math>-1</math>, so the unit conversion coefficients yielding results in units of MJy/sr are expected to have an associated spectral index of <math>-1</math>.<br />
<br />
==== Unit conversion / colour correction from K<math>_{\mbox{CMB}}</math> to <math>\alpha = 2</math> ====<br />
<br />
In order to convert between units of K<math>_{\mbox{CMB}}</math> to MJy/sr with an effective spectral index of <math>\alpha = 2</math> requires both a unit conversion and a colour correction.<br />
<br />
<tt> ; Determine the K_CMB to MJy/sr conversion (alpha=-1)</tt><br /><br />
<tt>hfi_100_uc = hfi_unit_conversion(BP_INFO=hfi_bp, '100',hfibolo_100_uc, $</tt><br /><br />
<tt> ABP=hfi_avg, AVG_UC=AVG_100_UC)</tt><br /><br />
<tt>uc_100_KCMB2MJy = hfibolo_100_uc.KCMB2MJYSR ; The UC Coeffs.</tt><br /><br />
<tt> ; Determine the -1 to 2 colour correction.</tt><br /><br />
<tt>hfi_100_cc = hfi_color_correction(BP_INFO=hfi_bp, '100', hfibolo_100_cc, $</tt><br /><br />
<tt> /POWERLAW, ALPHA=2.0, ABP=hfi_avg, AVG_CC=AVG_100_cc)</tt><br /><br />
<tt>cc_100_m1_to_2 = hfibolo_100_cc.CC ; The CC coeffs.</tt><br /><br />
<tt>uccc_100_Kcmb_to_2 = uc_100_KCMB2MJy*cc_100_m1_to_2 ; Units are still MJy/sr/Kcmb</tt><br /><br />
<tt>print, uccc_100_Kcmb_to_2 ; Print the UC/CC Coeffs.</tt><br />
<br />
The above examples should demonstrate the basic idea. Users are welcome to experiment with various combinations of data conversion.<br />
<br />
== LFI quadratic (fast) colour correction ==<br />
<br />
The IDL routine 'LFI_fastcc' provides a quick and easy method of calculating the colour corrections that should be applied to Planck LFI data depending on the source spectra. It uses quadratic fits of the form <math>cc=A + B\times\alpha + C\times\alpha^2</math> to the tabulated values in section 2 of <cite>#planck2013-p02b</cite>{{P2013|5}}. It does not have any external dependencies.<br />
<br />
The routine can be called for the band averaged maps as<br />
LFI_fastcc(freq,spectra)<br />
where ''freq'' is one of 28.4, 44.1 or 70.4; or for individual RCA as<br />
LFI_fastcc(70.4,spectra,detector=18)<br />
(for the 70GHz RCA number 18).<br />
<br />
Also included is the LFI_fastcc_test.pro script. This reproduces the tabulated values using the quadratic fits, and demonstrates that the values from the quadratic fit agree with those in the table to an accuracy of ~0.1%.<br />
<br />
The conventions for the spectra and corrections are the same as in the paper, i.e. the measured values should be ''multiplied'' by the colour corrections to obtain the colour-corrected value.<br />
<br />
== Conclusions ==<br />
<div id="sec:concl"></div><br />
<br />
The basic function and structure of the UC_CC routines has been described with command-line examples provided. Further details on the derivation of the equations used within the routines is found in the references cited above, i.e. <cite>#planck2013-p03d</cite>.<br />
<br />
<br />
== References ==<br />
<biblio force=false><br />
#[[References]] <br />
#[[References2]] <br />
</biblio><br />
<br />
<br />
[[Category:Software utilities|001]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Specially_processed_maps&diff=7696Specially processed maps2013-06-19T09:27:48Z<p>Lvibert: </p>
<hr />
<div>{{DISPLAYTITLE:Additional maps}}<br />
==Overview==<br />
<br />
This section describes products that require special processing. Only one such product is available at this time; this section will be expanded with time as more products are added.<br />
<br />
== Lensing map ==<br />
=== Description ===<br />
<br />
Here we present the minimum-variance (MV) lens reconstruction which forms the basis for the main results of <cite>#planck2013-p12</cite>. This map is produced using a combination of the 143 and 217 GHz Planck maps on approximately 70% of the sky, and is the same map on which the Planck lensing likelihood is based.<br />
<br />
We distribute:<br />
<br />
; PHIBAR : A (transfer-function convolved) map of the lensing potential, in NSIDE 2048 HEALPix RING format. It is obtained by convolving the lensing potential estimate <math>\hat{\phi}</math> with the lensing response function <math>R_L^{\phi\phi}</math>. This map has been band-limited between multipoles <math>10 \le L \le 2048</math>.<br />
; MASK : This is a NSIDE = 2048 HEALPix map, containing the analysis mask used in the lens reconstruction. ''Note'': the lensing map PHIBAR may take small but non-zero values inside the masked regions because it has been bandlimited.<br />
; RLPP : This column contains the response function <math>R_L^{\phi\phi}</math>.<br />
; NLPP : This column contains a sky-averaged estimate of the noise power spectrum of PHIBAR, <math>N_L^{\phi\phi}</math>. The noise is highly coloured. There is a dependence of the noise power spectrum on the local noise level of the map, discussed in Appendix A of <cite>#planck2013-p12</cite>. Note that the noise power spectrum estimate here is not sufficiently accurate for a power spectrum analysis.<br />
<br />
=== Production process ===<br />
<br />
The construction PHIBAR, RLPP and NLPP are described in detail in Sec. 2.1 of <cite>#planck2013-p12</cite>. The response function <math>R_L^{\phi\phi}</math> here is analogous to the the beam transfer function in a CMB temperature or polarization map. We have chosen to distribute this transfer-function convolved map rather than the normalized lens reconstruction as it is a significantly more localized function of the CMB temperature map from which it is derived, and therefore more useful for cross-correlation studies.<br />
<br />
===Inputs===<br />
<br />
This product is built from the 143 and 217 GHz Planck [[Frequency Maps|frequency maps]], with 857GHz projected out as a dust template.<br />
The analysis mask is constructed from a combination of thresholding in the 857GHz map (to remove the regions which are most contaminated by Galactic dust) and the [[CMB_and_astrophysical_component_maps#CO_emission_maps | Type2 CO map]] (to reduce contamination from CO lines at 217GHz). This is joined with a compact object mask synthesized from several Planck source [[Catalogues | catalogues]], including the [[ Catalogues#ERCSC | ERCSC]], [[ Catalogues#SZ | SZ ]] and [[ Catalogues#The Catalogue of Compact Sources | PCCS ]]. The reconstruction was performed using the fiducial beam window functions B(l) from the [[ The RIMO | HFI RIMO ]]. Details of the procedure used to produce a lensing estimate from these inputs are given in <cite>#planck2013-p12</cite>.<br />
<br />
===File names and format===<br />
<br />
A single file named <br />
*''{{PLASingleFile|fileType=map|name=COM_CompMap_Lensing_2048_R1.10.fits|link=COM_CompMap_Lensing_2048_R1.10.fits}}'' <br />
with two BINTABLE extensions containing the items described below. <br />
<br />
For illustration, we show in the figures below the maps of the Wiener-filtered CMB lensing potential in Galactic coordinates using orthographic projection. The reconstruction was bandpass filtered to <math>L \in [10, 2048]</math>. Note that the lensing reconstruction, while highly statistically significant, is still noise dominated for every individual mode, and is at best <math>S/N \simeq 0.7</math> around <math>L = 30</math>.<br />
<br />
<center><br />
<gallery perrow=3 widths=260px heights=170px> <br />
File: analysis_lens_pub_map_orth_north_dat_p.png | Galactic north<br />
File: analysis_lens_pub_map_orth_south_dat_p.png | Galactic south<br />
</gallery></center><br />
<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left"<br />
|+ '''FITS file structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = ''LENS-MAP''<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|PHIBAR || Real*4 || none || Map of the lensing potential estimate, convolved with RLPP<br />
|-<br />
|MASK || Int || none || Region over which the lensing potential is reconstructed<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|PIXTYPE || string || HEALPIX || colspan="2"| <br />
|-<br />
|COORDSYS || string || GALACTIC || Coordinate system <br />
|-<br />
|ORDERING || string || NESTED || Healpix ordering<br />
|-<br />
|NSIDE || Int*4 || 2048 ||colspan="2"| Healpix Nside<br />
|-<br />
|FIRSTPIX || Int*4 || 0 || <br />
|-<br />
|LASTPIX || Int*4 || 50331647 ||<br />
|- bgcolor="ffdead" <br />
!colspan="4"| 2. EXTNAME = ''TransFun''<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|RLPP || Real*4 || none || Response function<br />
|-<br />
|NLPP || Real*4 || none || Sky-averaged noise power spectrum estimate<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|L_MIN || Int*4 || 0 || First multipole<br />
|-<br />
|L_MAX || Int*4 || 2048 || Last multipole<br />
|}<br />
<br />
==References==<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|010]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Cosmological_Parameters&diff=7695Cosmological Parameters2013-06-19T09:23:59Z<p>Lvibert: /* File formats */</p>
<hr />
<div>== Description ==<br />
<br />
The cosmological parameter results explore a variety of cosmological models with combinations of Planck and other data. We provide results from MCMC exploration chains, as well as best fits, and sets of parameter tables. Definitions, conventions and reference are contained in <cite>#planck2013-p11</cite>. <br />
<br />
==Production process==<br />
<br />
Parameter chains are produced using CosmoMC, a sampling package available from [http://cosmologist.info/cosmomc]. This includes the sample analysis package GetDist, and the scripts for managing, analysing, and plotting results from the full grid or runs. Chain products provided here have had burn in removed. Some results with additional data are produced by importance sampling.<br />
<br />
Note that the baseline model includes one massive neutrino (0.06eV). Grid outputs include WMAP 9 results for consistent assumptions.<br />
<br />
== Caveats and known issues ==<br />
<br />
# Confidence intervals are derived from the MCMC samples, and assume the input likelihoods are exactly correct, so there is no quantification for systematic errors other than via the covariance, foreground and beam error models assumed in the likelihood codes. We had some issues producing reliable results from the minimizer used to produce the best fits, so in some cases the quoted fits may be significantly improved. The chain outputs contain some parameters that are not used, for example the beam mode ranges for all but the first mode (the beam modes are marginalised over anlaytically internally to the likelihood).<br />
# Where determined from BBN consistency, the <math>Y_P</math> parameter uses an interpolation table from <cite>#Hamann2007sb</cite> based on the 2008 version of the Parthenope BBN code. More recent updates to the neutron lifetime suggest that the <math>Y_P</math> values reported in the tables may be in error by around 0.0005. This has a negligible impact on the predicted CMB power spectrum or any of the parameter results reported in this series of papers. However, the difference should be taken into account when comparing with BBN results reported in Sect. 6.4. of <cite>#planck2013-p11</cite>, which use an updated version for the neutron lifetime (and several other nuclear reaction rates that have negligible impact). Note also that the error on <math>Y_P</math> quoted in the tables here does not include theoretical errors in the BBN prediction.<br />
<br />
== Related products ==<br />
<br />
Results of the parameter exploration runs should be reproducible using CosmoMC with the Planck likelihood code.<br />
<br />
== Parameter Tables ==<br />
<br />
These list paramter constraints for each considered model and data combination separately<br />
<br />
* PDF tables with 68% limits [[File:grid_limit68.pdf]]<br />
* PDF tables with 95% limits [[File:grid_limit95.pdf]]<br />
<br />
There are also summary comparison tables, showing how constraints for selected models vary with data used to constrain them:<br />
<br />
* Comparison tables with 68% limits [[File:comparetables_limit68.pdf | bla]]<br />
* Comparison tables with 95% limits [[File:comparetables_limit95.pdf]]<br />
<br />
<br />
Data combination tags used to label results are as follows (see <cite>#planck2013-p11</cite> for full description and references):<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:left" border="1" cellpadding="3" cellspacing="0" width=800px<br />
|+ <br />
|- bgcolor="ffdead" <br />
! Tag|| Data<br />
|-<br />
| '''planck''' || high-L Planck temperature (CamSpec, 50 <= l <= 2500)<br />
|-<br />
| '''lowl''' || low-L: Planck temperature (2 <= l <= 49)<br />
|-<br />
| '''lensing''' || Planck lensing power spectrum reconstruction<br />
|-<br />
| '''lowLike''' || low-L WMAP 9 polarization (WP)<br />
|-<br />
| '''tauprior''' || A Gaussian prior on the optical depth, tau = 0.09 +- 0.013<br />
|-<br />
| '''BAO''' || Baryon oscillation data from DR7, DR9 and and 6DF<br />
|-<br />
| '''SNLS''' || Supernova data from the Supernova Legacy Survey<br />
|-<br />
| '''Union2''' || Supernova data from the Union compilation<br />
|-<br />
| '''HST''' || Hubble parameter constraint from HST (Riess et al) <br />
|-<br />
| '''WMAP''' || The full WMAP (temperature and polarization) 9 year data <br />
|}<br />
<br />
<br />
Tags used to identify the model paramters that are varied are described in [[File:parameter_tag_definitions.pdf]]. Note that alpha1 results are not used in the parameter paper, and are separate from the isocurvature results in the inflation paper.<br />
<br />
== Parameter Chains ==<br />
<br />
We provide the full chains and getdist outputs for our parameter results. The entire grid of results is available from as a 2.8GB compressed file:<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_FullGrid_R1.10.tar.gz|link=Full Grid Download}}<br />
<br />
You can also download key chains for the baseline LCDM model here:<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_post_lensing_R1.10.tar.gz|link=Planck+lensing}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_lowLike_R1.10.tar.gz|link=Planck+WP}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_lowLike_post_lensing_R1.10.tar.gz|link=Planck+WP+lensing}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_lowLike_highL_R1.10.tar.gz|link=Planck+WP+highL}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_lowLike_highL_post_lensing_R1.10.tar.gz|link=Planck+WP+highL+lensing}}<br />
<br />
The download contains a hierarchy of directories, with each separate chain in a separate directory. The structure for the directories is<br />
<br />
: '' base_AAA_BBB/XXX_YYY_.../''<br />
<br />
where AAA and BBB are any additional parameters that are varied in addition to the six parameters of the baseline model. XXX, YYY, etc encode the data combinations used. These follow the naming conventions described above under Parameter Tables. Each directory contains the main chains, 4-8 text files with one chain in each, and various other files all with names of the form<br />
<br />
: ''base_AAA_BBB_XXX_YYY.ext''<br />
<br />
where ''ext'' describes the type of file, and the possible values or ''ext'' are<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:left" border="1" cellpadding="3" cellspacing="0" width=800px<br />
|+ <br />
|- bgcolor="ffdead" <br />
! Extension || Data<br />
|-<br />
| '''.txt''' || parameter chain file with burn in removed<br />
|-<br />
| '''.paramnames''' || File that describes the parameters included in the chains<br />
|-<br />
| '''.minimum''' || Best-fit parameter values, -log likelihoods and chi-square<br />
|-<br />
| '''.bestfit_cl''' || The best-fit temperature and polarization power spectra and lensing potential (see below)<br />
|-<br />
| '''.inputparams''' || Input parameters used when generating the chain<br />
|-<br />
| '''.minimum.inputparams''' || Input parameters used when generating the best fit<br />
|-<br />
| '''.ranges''' || prior ranges assumed for each parameter<br />
|}<br />
<br />
<br />
In addition each directory contains any importanced sampled outputs with additional data. These have names of the form<br />
<br />
: ''base_AAA_BBB_XXX_YYY_post_ZZZ.ext''<br />
<br />
where ZZZ is the data likelihood that is added by importance sampling. Finally, each directory contains a ''dist'' subdirectory, containing results of chain analysis. File names follow the above convntions, with the following extensions<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:left" border="1" cellpadding="3" cellspacing="0" width=800px<br />
|+ <br />
|- bgcolor="ffdead" <br />
! Extension || Data<br />
|-<br />
| '''.margestats''' || mean, variance and 68, 95 and 99% limits for each parameter (see below)<br />
|-<br />
| '''.likestats''' || parameters of best-fitting sample in the chain (generally different from the .minmum global best-fit)<br />
|-<br />
| '''.covmat''' || Covariance matrix for the MCMC parameters<br />
|-<br />
| '''.corr''' || Correlation matrix for the parameters<br />
|-<br />
| '''.converge''' || A summary of various convergence diagnostics<br />
|}<br />
<br />
<br />
Python scripts for reading in chains and calculating new derived parameter constraints are available as part of CosmoMC, see the readme for details [http://cosmologist.info/cosmomc/readme_planck.html].<br />
<br />
== File formats ==<br />
<br />
The file formats are standard March 2013 CosmoMC outputs. CosmoMC includes python scripts for generating tables, 1D, 2D and 3D plots using the provided data. The formats are summarised here:<br />
<br />
; Chain files<br />
: Each chain file is ASCII and contains one sample on each line. Each line is of the format<br />
<br />
: '' weight like param1 param2 param3 …''<br />
<br />
: Here ''weight'' is the importance weight or multiplicity count, and ''like'' is the total -log Likelihood. ''param1'',''param2'', etc are the parameter values for the sample, where the numbering is defined by the position in the accompanying.paramnames files.<br />
<br />
: Note that burn in has been removed from the cosmomc outputs, so full chains provided can be used for analysis. Importance sampled results (with ''_post'') in the name have been thinned by a factor of 10 compared to the original chains, so the files are smaller, but this does not significantly affect the effective number of samples. Note that due to the way MCMC works, the samples in the chain outputs are not independent, but it is safe to use all the samples for estimating posterior averages.<br />
<br />
;.margestats files<br />
: Each row contains the marginalized constraint on individual parameters. The format is fairly self explanatory given the text description in the file, with each line of the form<br />
<br />
: '' parameter mean sddev lower1 upper1 limit1 lower2 upper2 limit2 lower3 upper3 limit3''<br />
<br />
: where sddev is the standard deviation, and the limits are 1: 68%, 2: 95%, 3: 99%. The limit tags specify whether a given limit is one tail, two tail or none (if no constraint within the assumed prior boundary). <br />
<br />
;.bestfit_cl files<br />
: They contain the best-fit theoretical power spectra (without foregrounds) for each model. The columns are: <math>l</math>, <math>D^{TT}_l</math>, <math>D^{TE}_l</math>, <math>D^{EE}_l</math>, <math>D^{BB}_l</math>, and <math>D^{dd}_l</math>, were <math>D_l \equiv l(l+1) C_l / (2\pi)</math> in <math>\mu{\rm K}^2</math>. Also <math>D^{dd}_l= [l(l+1)]^2 C^{\phi\phi}_l/(2\pi)</math> is the power spectrum of the lensing deflection angle, where <math>C^{\phi\phi}_l</math> is the lensing potential power spectrum. For results not including the lensing likelihood, this is the prediction from linear theory; for lensing outputs this includes corrections due to non-linear structure growth. The <math>D_l</math> are output to high <math>l</math>, but not actually computed above <math>l_{\rm max}=2500</math> (Planck), <math>l_{\rm max}=4500</math> (Planck+highL) or <math>l_{\rm max}=1500</math> (WMAP), and <math>l</math> values above these are fixed to a scaled fiducial template.<br />
<br />
== References ==<br />
<br />
<br />
<biblio force=false><br />
#[[References]]<br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|009]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Cosmological_Parameters&diff=7694Cosmological Parameters2013-06-19T09:19:22Z<p>Lvibert: /* Caveats and known issues */</p>
<hr />
<div>== Description ==<br />
<br />
The cosmological parameter results explore a variety of cosmological models with combinations of Planck and other data. We provide results from MCMC exploration chains, as well as best fits, and sets of parameter tables. Definitions, conventions and reference are contained in <cite>#planck2013-p11</cite>. <br />
<br />
==Production process==<br />
<br />
Parameter chains are produced using CosmoMC, a sampling package available from [http://cosmologist.info/cosmomc]. This includes the sample analysis package GetDist, and the scripts for managing, analysing, and plotting results from the full grid or runs. Chain products provided here have had burn in removed. Some results with additional data are produced by importance sampling.<br />
<br />
Note that the baseline model includes one massive neutrino (0.06eV). Grid outputs include WMAP 9 results for consistent assumptions.<br />
<br />
== Caveats and known issues ==<br />
<br />
# Confidence intervals are derived from the MCMC samples, and assume the input likelihoods are exactly correct, so there is no quantification for systematic errors other than via the covariance, foreground and beam error models assumed in the likelihood codes. We had some issues producing reliable results from the minimizer used to produce the best fits, so in some cases the quoted fits may be significantly improved. The chain outputs contain some parameters that are not used, for example the beam mode ranges for all but the first mode (the beam modes are marginalised over anlaytically internally to the likelihood).<br />
# Where determined from BBN consistency, the <math>Y_P</math> parameter uses an interpolation table from <cite>#Hamann2007sb</cite> based on the 2008 version of the Parthenope BBN code. More recent updates to the neutron lifetime suggest that the <math>Y_P</math> values reported in the tables may be in error by around 0.0005. This has a negligible impact on the predicted CMB power spectrum or any of the parameter results reported in this series of papers. However, the difference should be taken into account when comparing with BBN results reported in Sect. 6.4. of <cite>#planck2013-p11</cite>, which use an updated version for the neutron lifetime (and several other nuclear reaction rates that have negligible impact). Note also that the error on <math>Y_P</math> quoted in the tables here does not include theoretical errors in the BBN prediction.<br />
<br />
== Related products ==<br />
<br />
Results of the parameter exploration runs should be reproducible using CosmoMC with the Planck likelihood code.<br />
<br />
== Parameter Tables ==<br />
<br />
These list paramter constraints for each considered model and data combination separately<br />
<br />
* PDF tables with 68% limits [[File:grid_limit68.pdf]]<br />
* PDF tables with 95% limits [[File:grid_limit95.pdf]]<br />
<br />
There are also summary comparison tables, showing how constraints for selected models vary with data used to constrain them:<br />
<br />
* Comparison tables with 68% limits [[File:comparetables_limit68.pdf | bla]]<br />
* Comparison tables with 95% limits [[File:comparetables_limit95.pdf]]<br />
<br />
<br />
Data combination tags used to label results are as follows (see <cite>#planck2013-p11</cite> for full description and references):<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:left" border="1" cellpadding="3" cellspacing="0" width=800px<br />
|+ <br />
|- bgcolor="ffdead" <br />
! Tag|| Data<br />
|-<br />
| '''planck''' || high-L Planck temperature (CamSpec, 50 <= l <= 2500)<br />
|-<br />
| '''lowl''' || low-L: Planck temperature (2 <= l <= 49)<br />
|-<br />
| '''lensing''' || Planck lensing power spectrum reconstruction<br />
|-<br />
| '''lowLike''' || low-L WMAP 9 polarization (WP)<br />
|-<br />
| '''tauprior''' || A Gaussian prior on the optical depth, tau = 0.09 +- 0.013<br />
|-<br />
| '''BAO''' || Baryon oscillation data from DR7, DR9 and and 6DF<br />
|-<br />
| '''SNLS''' || Supernova data from the Supernova Legacy Survey<br />
|-<br />
| '''Union2''' || Supernova data from the Union compilation<br />
|-<br />
| '''HST''' || Hubble parameter constraint from HST (Riess et al) <br />
|-<br />
| '''WMAP''' || The full WMAP (temperature and polarization) 9 year data <br />
|}<br />
<br />
<br />
Tags used to identify the model paramters that are varied are described in [[File:parameter_tag_definitions.pdf]]. Note that alpha1 results are not used in the parameter paper, and are separate from the isocurvature results in the inflation paper.<br />
<br />
== Parameter Chains ==<br />
<br />
We provide the full chains and getdist outputs for our parameter results. The entire grid of results is available from as a 2.8GB compressed file:<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_FullGrid_R1.10.tar.gz|link=Full Grid Download}}<br />
<br />
You can also download key chains for the baseline LCDM model here:<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_post_lensing_R1.10.tar.gz|link=Planck+lensing}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_lowLike_R1.10.tar.gz|link=Planck+WP}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_lowLike_post_lensing_R1.10.tar.gz|link=Planck+WP+lensing}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_lowLike_highL_R1.10.tar.gz|link=Planck+WP+highL}}<br />
* {{PLASingleFile|fileType=cosmo|name=COM_CosmoParams_base_planck_lowl_lowLike_highL_post_lensing_R1.10.tar.gz|link=Planck+WP+highL+lensing}}<br />
<br />
The download contains a hierarchy of directories, with each separate chain in a separate directory. The structure for the directories is<br />
<br />
: '' base_AAA_BBB/XXX_YYY_.../''<br />
<br />
where AAA and BBB are any additional parameters that are varied in addition to the six parameters of the baseline model. XXX, YYY, etc encode the data combinations used. These follow the naming conventions described above under Parameter Tables. Each directory contains the main chains, 4-8 text files with one chain in each, and various other files all with names of the form<br />
<br />
: ''base_AAA_BBB_XXX_YYY.ext''<br />
<br />
where ''ext'' describes the type of file, and the possible values or ''ext'' are<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:left" border="1" cellpadding="3" cellspacing="0" width=800px<br />
|+ <br />
|- bgcolor="ffdead" <br />
! Extension || Data<br />
|-<br />
| '''.txt''' || parameter chain file with burn in removed<br />
|-<br />
| '''.paramnames''' || File that describes the parameters included in the chains<br />
|-<br />
| '''.minimum''' || Best-fit parameter values, -log likelihoods and chi-square<br />
|-<br />
| '''.bestfit_cl''' || The best-fit temperature and polarization power spectra and lensing potential (see below)<br />
|-<br />
| '''.inputparams''' || Input parameters used when generating the chain<br />
|-<br />
| '''.minimum.inputparams''' || Input parameters used when generating the best fit<br />
|-<br />
| '''.ranges''' || prior ranges assumed for each parameter<br />
|}<br />
<br />
<br />
In addition each directory contains any importanced sampled outputs with additional data. These have names of the form<br />
<br />
: ''base_AAA_BBB_XXX_YYY_post_ZZZ.ext''<br />
<br />
where ZZZ is the data likelihood that is added by importance sampling. Finally, each directory contains a ''dist'' subdirectory, containing results of chain analysis. File names follow the above convntions, with the following extensions<br />
<br />
<br />
{| class="wikitable" align="center" style="text-align:left" border="1" cellpadding="3" cellspacing="0" width=800px<br />
|+ <br />
|- bgcolor="ffdead" <br />
! Extension || Data<br />
|-<br />
| '''.margestats''' || mean, variance and 68, 95 and 99% limits for each parameter (see below)<br />
|-<br />
| '''.likestats''' || parameters of best-fitting sample in the chain (generally different from the .minmum global best-fit)<br />
|-<br />
| '''.covmat''' || Covariance matrix for the MCMC parameters<br />
|-<br />
| '''.corr''' || Correlation matrix for the parameters<br />
|-<br />
| '''.converge''' || A summary of various convergence diagnostics<br />
|}<br />
<br />
<br />
Python scripts for reading in chains and calculating new derived parameter constraints are available as part of CosmoMC, see the readme for details [http://cosmologist.info/cosmomc/readme_planck.html].<br />
<br />
== File formats ==<br />
<br />
The file formats are standard March 2013 CosmoMC outputs. CosmoMC includes python scripts for generating tables, 1D, 2D and 3D plots using the provided data. The formats are summarised here:<br />
<br />
; Chain files<br />
: Each chain file is ASCII and contains one sample on each line. Each line is of the format<br />
<br />
: '' weight like param1 param2 param3 …''<br />
<br />
: Here ''weight'' is the importance weight or multiplicity count, and ''like'' is the total -log Likelihood. ''param1'',''param2'', etc are the parameter values for the sample, where the numbering is defined by the position in the accompanying.paramnames files.<br />
<br />
: Note that burn in has been removed from the cosmomc outputs, so full chains provided can be used for analysis. Importance sampled results (with ''_post'') in the name have been thinned by a factor of 10 compared to the original chains, so the files are smaller, but this does not significantly affect the effective number of samples. Note that due to the way MCMC works, the samples in the chain outputs are not independent, but it is safe to use all the samples for estimating posterior averages.<br />
<br />
;.margestats files<br />
: Each row contains the marginalized constraint on individual parameters. The format is fairly self explanatory given the text description in the file, with each line of the form<br />
<br />
: '' parameter mean sddev lower1 upper1 limit1 lower2 upper2 limit2 lower3 upper3 limit3''<br />
<br />
: where sddev is the standard deviation, and the limits are 1: 68%, 2: 95%, 3: 99%. The limit tags specify whether a given limit is one tail, two tail or none (if no constraint within the assumed prior boundary). <br />
<br />
;.bestfit_cl files<br />
: They contain the best-fit theoretical power spectra (without foregrounds) for each model. The columns are: $l$, $D^{TT}_l$, $D^{TE}_l$, $D^{EE}_l$, $D^{BB}_l$, and $D^{dd}_l$, were $D_l \equiv l(l+1) C_l / (2\pi)$ in $\mu{\rm K}^2$. Also $D^{dd}_l= [l(l+1)]^2 C^{\phi\phi}_l/(2\pi)$ is the power spectrum of the lensing deflection angle, where $C^{\phi\phi}_l$ is the lensing potential power spectrum. For results not including the lensing likelihood, this is the prediction from linear theory; for lensing outputs this includes corrections due to non-linear structure growth. The $D_l$ are output to high $l$, but not actually computed above $l_{\rm max}=2500$ (Planck), $l_{\rm max}=4500$ (Planck+highL) or $l_{\rm max}=1500$ (WMAP), and $l$ values above these are fixed to a scaled fiducial template.<br />
<br />
== References ==<br />
<br />
<br />
<biblio force=false><br />
#[[References]]<br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|009]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=7693CMB spectrum & Likelihood Code2013-06-19T08:50:59Z<p>Lvibert: /* Likelihood */</p>
<hr />
<div>{{DISPLAYTITLE:CMB spectrum and likelihood code}}<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 =2-2479</math>. Over the multipole range <math> \ell =2–49</math>, 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 <cite>#planck2013-p06</cite>. 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 <cite>#planck2013-p08</cite> 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. <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 <cite>#planck2013-p11</cite>).''']]<br />
<br />
===Likelihood===<br />
<br />
The likelihood code and data allow to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum and foreground and some instrumental parameters. The data file are built from the Planck mission results, as well as the some ancillary data from the wmap9 data release. The data file are in a specific internal format and can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code allows to read the data files, and provided model power spectra and nuisance parameters to compute the log likelihood of the model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes six data files: five for the CMB likelihoods and one for the lensing likelihood.<br />
All of the likelihood delivered are described full in the Power spectrum & Likelihood Paper <cite>#planck2013-p08</cite> (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) <cite>#planck2013-p12</cite>.<br />
<br />
The CMB full likelihood has been cut in 3 different part to allow using selectively different range of multipoles. It also reflects the fact that the mathematical approximation used for those different part are very different, as well as the underlying data. In details, we are distributing one low-<math>\ell</math> Temperature only likelihood (commander), one low-<math>\ell</math> Temperature and Polarisation likelihood (lowlike) and one higl-<math>\ell</math> likelihood CAMspec.<br />
<br />
The commander likelihood is covering 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 do the likelihood computation in the code. See <cite>#planck2013-p08</cite> section 8.1 for more details.<br />
<br />
The lowlike likelihood is covering the multipole 2 to 32 for Temperature and Polarization data. Planck is not releasing any polarisation data in this release. We are using here the WMAP9 polarization map which are included in the data package. A temperature map is needed to perform the computation nevertheless, and we are using 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 is essentially providing 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 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 <cite>#planck2013-p08</cite> section 8.3 for more details. Note that the version of the WMAP code we are currently using (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrix, 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 is covering the multipoles 50 to 2500 for Temperature. 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 217Ghz channels. Doing so it must model the foreground in each of those frequency using a 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. Detailled description of the different nuisance parameter names and meaning is given below. Priors are included in the likelihood on the cib spectral index, relative calibration factors and beam error eigenmodes. See <cite>#planck2013-p08</cite> section 2.1 for more details.<br />
<br />
The actspt likelihood covers the multipole 1500 to 10000 for Temperature. It is described in <cite>#dun2013,#Keis2011,#Reic2012</cite><!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012]-->. It uses the code and data that can be retrieved [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]. It has been slightly modified to use a thermal and kinetci SZ model that matches the one used in CAMspec. As stated in <cite>#dun2013</cite>, the dust parameters a_ge and a_gs must be explored witht he 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 />
<br />
The lensing likelihood is covering the multipoles 40 to 400. It uses 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 one 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 <cite>#planck2013-p12</cite> section 6.1 for more details.<br />
<br />
==Production process==<br />
----------------------<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 <cite>#planck2013-p06</cite>. 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% CL <cite>#planck2013-p08</cite>. <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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p11</cite>). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of <cite>#planck2013-p08</cite> and Sec. 4 of <cite>#planck2013-p11</cite>. 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 upon some basic routine 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 <cite>#dun2013,#Keis2011,#Reic2012</cite> <!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012] --> for the actspt 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 <cite>#planck2013-p08</cite> (section 2 and 8) and in the lensing paper <cite>#planck2013-p12</cite> (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 />
<br />
* frequency maps from 30–353 GHz;<br />
* common mask <cite>#planck2013-p06</cite>;<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 <cite>#planck2013-p08</cite>);<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of <cite>#planck2013-p11</cite>);<br />
* Beam transfer function uncertainties <cite>#planck2013-p03c</cite>;<br />
<br />
===Likelihood===<br />
<br />
;commander : All Planck channels maps, compact source catalogs, common masks, beam transfer functions for all channels.<br />
<br />
;lowlike : WMAP9 likelihood data. Low-ell commander map.<br />
<br />
;CAMspec : 100,143 & 217GHz detector and detests maps. 857GHz chanel Map. compact source catalog. Common masks (0,1 & 3). beam transfer function and error eigenmodes and covariance for 100,143 and 217Ghz detectors & detsets. Theoretical templates for the tSZ and kSZ contributions. Color corrections for the CIB emission for the 143GHz and 217GHz detectors & detsets. Fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 & 217GHz. <br />
<br />
;lensing : the lensing map, beam error eigenmodes and covariance for the 143GHz and 217GHz chanel maps. Fiducial CMB model (from Planck cosmological parameter best fit).<br />
<br />
;act/spt : The data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]. The TSZ and KSZ 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 is distributed in a single FITS file named ''COM_PowerSpect_CMB_R1.10.fits'' 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 $\langle l \rangle = 47-2419$ in bins of width $l=31$ (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 {{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 />
: ''COM_Data_Likelihood-commander_R1.10.tar.gz'' (low-ell TT likelihood)<br />
: ''COM_Data_Likelihood-lowlike_R1.10.tar.gz'' (low-ell TE,EE,BB likelihood)<br />
: ''COM_Data_Likelihood-CAMspec_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''COM_Data_Likelihood-actspt_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''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 of the package comes with a README file describing the full package. 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 modelling granted 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 into 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.<br />
<br />
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 <cite>#planck2013-p08</cite> are found in<br />
: ''COM_Mask_Likelihood_2048_R1.10.fits''<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 />
=== Retrieval from the Planck Legacy Archive ===<br />
<br />
The CMB spectra and likelihood files can be retrieved from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive| Planck Legacy Archive]. One should select "Cosmology products" and look at the "CMB angular power spectra" and "Likelihood" sections.<br />
The files can be downloaded directly or through the "Shopping Basket".<br />
<br />
== References ==<br />
<br />
<biblio force=false><br />
#[[References]]<br />
#[[References2]]<br />
</biblio><br />
[[Category:Mission products|008]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=7691CMB spectrum & Likelihood Code2013-06-19T08:17:15Z<p>Lvibert: /* Retrieval from the Planck Legacy Archive */</p>
<hr />
<div>{{DISPLAYTITLE:CMB spectrum and likelihood code}}<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 =2-2479</math>. Over the multipole range <math> \ell =2–49</math>, 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 <cite>#planck2013-p06</cite>. 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 <cite>#planck2013-p08</cite> 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. <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 <cite>#planck2013-p11</cite>).''']]<br />
<br />
===Likelihood===<br />
<br />
The likelihood code and data allow to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum and foreground and some instrumental parameters. The data file are built from the Planck mission results, as well as the some ancillary data from the wmap9 data release. The data file are in a specific internal format and can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code allows to read the data files, and provided model power spectra and nuisance parameters to compute the log likelihood of the model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes six data files: five for the CMB likelihoods and one for the lensing likelihood.<br />
All of the likelihood delivered are described full in the Power spectrum & Likelihood Paper <cite>#planck2013-p08</cite> (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) <cite>#planck2013-p12</cite>.<br />
<br />
The CMB full likelihood has been cut in 3 different part to allow using selectively different range of multipoles. It also reflects the fact that the mathematical approximation used for those different part are very different, as well as the underlying data. In details, we are distributing one low-<math>\ell</math> Temperature only likelihood (commander), one low-<math>\ell</math> Temperature and Polarisation likelihood (lowlike) and one higl-<math>\ell</math> likelihood CAMspec.<br />
<br />
The commander likelihood is covering 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 do the likelihood computation in the code. See <cite>#planck2013-p08</cite> section 8.1 for more details.<br />
<br />
The lowlike likelihood is covering the multipole 2 to 32 for Temperature and Polarization data. Planck is not releasing any polarisation data in this release. We are using here the WMAP9 polarization map which are included in the data package. A temperature map is needed to perform the computation nevertheless, and we are using 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 is essentially providing 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 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 <cite>#planck2013-p08</cite> section 8.3 for more details. Note that the version of the WMAP code we are currently using (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrix, 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 is covering the multipoles 50 to 2500 for Temperature. 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 217Ghz channels. Doing so it must model the foreground in each of those frequency using a 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. Detailled description of the different nuisance parameter names and meaning is given below. Priors are included in the likelihood on the cib spectral index, relative calibration factors and beam error eigenmodes. See <cite>#planck2013-p08</cite> section 2.1 for more details.<br />
<br />
The actspt likelihood covers the multipole 1500 to 10000 for Temperature. It is described in <cite>#dun2013,#Keis2011,#Reic2012</cite><!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012]-->. It uses the code and data that can be retrieved [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]. It has been slightly modified to use a thermal and kinetci SZ model that matches the one used in CAMspec. As stated in <cite>#dun2013</cite>, the dust parameters a_ge and a_gs must be explored witht he 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 />
<br />
The lensing likelihood is covering the multipoles 40 to 400. It uses 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 one 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 <cite>#planck2013-p12</cite> section 6.1 for more details.<br />
<br />
==Production process==<br />
----------------------<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 <cite>#planck2013-p06</cite>. 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% CL <cite>#planck2013-p08</cite>. <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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p11</cite>). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of <cite>#planck2013-p08</cite> and Sec. 4 of <cite>#planck2013-p11</cite>. 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 upon some basic routine 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 <cite>#dun2013,#Keis2011,#Reic2012</cite> <!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012] --> for the actspt 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 <cite>#planck2013-p08</cite> (section 2 and 8) and in the lensing paper <cite>#planck2013-p12</cite> (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 />
<br />
* frequency maps from 30–353 GHz;<br />
* common mask <cite>#planck2013-p06</cite>;<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 <cite>#planck2013-p08</cite>);<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of <cite>#planck2013-p11</cite>);<br />
* Beam transfer function uncertainties <cite>#planck2013-p03c</cite>;<br />
<br />
===Likelihood===<br />
<br />
;commander : All Planck channels maps, compact source catalogs, common masks, beam transfer functions for all channels.<br />
<br />
;lowlike : WMAP9 likelihood data. Low-ell commander map.<br />
<br />
;CAMspec : 100,143 & 217GHz detector and detests maps. 857GHz chanel Map. compact source catalog. Common masks (0,1 & 3). beam transfer function and error eigenmodes and covariance for 100,143 and 217Ghz detectors & detsets. Theoretical templates for the tSZ and kSZ contributions. Color corrections for the CIB emission for the 143GHz and 217GHz detectors & detsets. Fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 & 217GHz. <br />
<br />
;lensing : the lensing map, beam error eigenmodes and covariance for the 143GHz and 217GHz chanel maps. Fiducial CMB model (from Planck cosmological parameter best fit).<br />
<br />
;act/spt : The data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]. The TSZ and KSZ 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 is distributed in a single FITS file named ''COM_PowerSpect_CMB_R1.10.fits'' 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 $\langle l \rangle = 47-2419$ in bins of width $l=31$ (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 />
; 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 />
; the {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''COM_Data_Likelihood-commander_R1.10.tar.gz'' (low-ell TT likelihood)<br />
: ''COM_Data_Likelihood-lowlike_R1.10.tar.gz'' (low-ell TE,EE,BB likelihood)<br />
: ''COM_Data_Likelihood-CAMspec_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''COM_Data_Likelihood-actspt_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''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 of the package comes with a README file describing the full package. 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 modelling granted 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 into 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.<br />
<br />
Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
; The masks used in the Likelihood paper <cite>#planck2013-p08</cite> are found in<br />
: ''COM_Mask_Likelihood_2048_R1.10.fits''<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 />
=== Retrieval from the Planck Legacy Archive ===<br />
<br />
The CMB spectra and likelihood files can be retrieved from the [http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive| Planck Legacy Archive]. One should select "Cosmology products" and look at the "CMB angular power spectra" and "Likelihood" sections.<br />
The files can be downloaded directly or through the "Shopping Basket".<br />
<br />
== References ==<br />
<br />
<biblio force=false><br />
#[[References]]<br />
#[[References2]]<br />
</biblio><br />
[[Category:Mission products|008]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_spectrum_%26_Likelihood_Code&diff=7690CMB spectrum & Likelihood Code2013-06-19T08:13:31Z<p>Lvibert: /* CMB spectra */</p>
<hr />
<div>{{DISPLAYTITLE:CMB spectrum and likelihood code}}<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 =2-2479</math>. Over the multipole range <math> \ell =2–49</math>, 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 <cite>#planck2013-p06</cite>. 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 <cite>#planck2013-p08</cite> 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. <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 <cite>#planck2013-p11</cite>).''']]<br />
<br />
===Likelihood===<br />
<br />
The likelihood code and data allow to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum and foreground and some instrumental parameters. The data file are built from the Planck mission results, as well as the some ancillary data from the wmap9 data release. The data file are in a specific internal format and can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code allows to read the data files, and provided model power spectra and nuisance parameters to compute the log likelihood of the model. <br />
<br />
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes six data files: five for the CMB likelihoods and one for the lensing likelihood.<br />
All of the likelihood delivered are described full in the Power spectrum & Likelihood Paper <cite>#planck2013-p08</cite> (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) <cite>#planck2013-p12</cite>.<br />
<br />
The CMB full likelihood has been cut in 3 different part to allow using selectively different range of multipoles. It also reflects the fact that the mathematical approximation used for those different part are very different, as well as the underlying data. In details, we are distributing one low-<math>\ell</math> Temperature only likelihood (commander), one low-<math>\ell</math> Temperature and Polarisation likelihood (lowlike) and one higl-<math>\ell</math> likelihood CAMspec.<br />
<br />
The commander likelihood is covering 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 do the likelihood computation in the code. See <cite>#planck2013-p08</cite> section 8.1 for more details.<br />
<br />
The lowlike likelihood is covering the multipole 2 to 32 for Temperature and Polarization data. Planck is not releasing any polarisation data in this release. We are using here the WMAP9 polarization map which are included in the data package. A temperature map is needed to perform the computation nevertheless, and we are using 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 is essentially providing 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 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 <cite>#planck2013-p08</cite> section 8.3 for more details. Note that the version of the WMAP code we are currently using (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrix, 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 is covering the multipoles 50 to 2500 for Temperature. 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 217Ghz channels. Doing so it must model the foreground in each of those frequency using a 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. Detailled description of the different nuisance parameter names and meaning is given below. Priors are included in the likelihood on the cib spectral index, relative calibration factors and beam error eigenmodes. See <cite>#planck2013-p08</cite> section 2.1 for more details.<br />
<br />
The actspt likelihood covers the multipole 1500 to 10000 for Temperature. It is described in <cite>#dun2013,#Keis2011,#Reic2012</cite><!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012]-->. It uses the code and data that can be retrieved [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]. It has been slightly modified to use a thermal and kinetci SZ model that matches the one used in CAMspec. As stated in <cite>#dun2013</cite>, the dust parameters a_ge and a_gs must be explored witht he 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 />
<br />
The lensing likelihood is covering the multipoles 40 to 400. It uses 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 one 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 <cite>#planck2013-p12</cite> section 6.1 for more details.<br />
<br />
==Production process==<br />
----------------------<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 <cite>#planck2013-p06</cite>. 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% CL <cite>#planck2013-p08</cite>. <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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p08</cite>. 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 <cite>#planck2013-p11</cite>). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of <cite>#planck2013-p08</cite> and Sec. 4 of <cite>#planck2013-p11</cite>. 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 upon some basic routine 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 <cite>#dun2013,#Keis2011,#Reic2012</cite> <!---[http://adsabs.harvard.edu/abs/2013arXiv1301.0776D dun2013], [http://adsabs.harvard.edu/abs/2011ApJ...743...28K Keis2011] [http://adsabs.harvard.edu/abs/2012ApJ...755...70R Reic2012] --> for the actspt 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 <cite>#planck2013-p08</cite> (section 2 and 8) and in the lensing paper <cite>#planck2013-p12</cite> (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 />
<br />
* frequency maps from 30–353 GHz;<br />
* common mask <cite>#planck2013-p06</cite>;<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 <cite>#planck2013-p08</cite>);<br />
* best-fit foreground templates and inter-frequency calibration factors (Table 5 of <cite>#planck2013-p11</cite>);<br />
* Beam transfer function uncertainties <cite>#planck2013-p03c</cite>;<br />
<br />
===Likelihood===<br />
<br />
;commander : All Planck channels maps, compact source catalogs, common masks, beam transfer functions for all channels.<br />
<br />
;lowlike : WMAP9 likelihood data. Low-ell commander map.<br />
<br />
;CAMspec : 100,143 & 217GHz detector and detests maps. 857GHz chanel Map. compact source catalog. Common masks (0,1 & 3). beam transfer function and error eigenmodes and covariance for 100,143 and 217Ghz detectors & detsets. Theoretical templates for the tSZ and kSZ contributions. Color corrections for the CIB emission for the 143GHz and 217GHz detectors & detsets. Fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 & 217GHz. <br />
<br />
;lensing : the lensing map, beam error eigenmodes and covariance for the 143GHz and 217GHz chanel maps. Fiducial CMB model (from Planck cosmological parameter best fit).<br />
<br />
;act/spt : The data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here]. The TSZ and KSZ 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 is distributed in a single FITS file named ''COM_PowerSpect_CMB_R1.10.fits'' 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 $\langle l \rangle = 47-2419$ in bins of width $l=31$ (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 />
; 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 />
; the {{PLALikelihood|type=Data|link=data packages}} are<br />
: ''COM_Data_Likelihood-commander_R1.10.tar.gz'' (low-ell TT likelihood)<br />
: ''COM_Data_Likelihood-lowlike_R1.10.tar.gz'' (low-ell TE,EE,BB likelihood)<br />
: ''COM_Data_Likelihood-CAMspec_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''COM_Data_Likelihood-actspt_R1.10.tar.gz'' (high-ell TT likelihood)<br />
: ''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 of the package comes with a README file describing the full package. 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 modelling granted 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 into 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.<br />
<br />
Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.<br />
<br />
; The masks used in the Likelihood paper <cite>#planck2013-p08</cite> are found in<br />
: ''COM_Mask_Likelihood_2048_R1.10.fits''<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 />
=== Retrieval from the Planck Legacy Archive ===<br />
<br />
The Planck Legacy Archive can be accessed here:<br />
<br />
http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive<br />
<br />
In order to retrieve the CMB spectra and likelihood files, one should select "Cosmology products" and look at the "CMB angular power spectra" and "Likelihood" sections.<br />
The files can be downloaded directly or through the "Shopping Basket".<br />
<br />
== References ==<br />
<br />
<biblio force=false><br />
#[[References]]<br />
#[[References2]]<br />
</biblio><br />
[[Category:Mission products|008]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7689CMB and astrophysical component maps2013-06-19T08:06:46Z<p>Lvibert: /* Dust optical depth products */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
=== Model of thermal dust emission ===<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
=== The <math>E(B-V)</math> map ===<br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
=== Dust optical depth products ===<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5', no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5', units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5', units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35', no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7688CMB and astrophysical component maps2013-06-19T08:05:25Z<p>Lvibert: /* Dust optical depth map and model */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
=== Model of thermal dust emission ===<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
=== The <math>E(B-V)</math> map ===<br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
=== Dust optical depth products ===<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5 arcmin, no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5 arcmin, units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5 arcmin, units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35 arcmin, no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7687CMB and astrophysical component maps2013-06-19T08:02:27Z<p>Lvibert: /* Sky mask */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
; Model of thermal dust emission<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
; The <math>E(B-V)</math> map <br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
; Dust optical depth products<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5 arcmin, no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5 arcmin, units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5 arcmin, units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35 arcmin, no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7686CMB and astrophysical component maps2013-06-19T08:01:45Z<p>Lvibert: /* Thermal dust component at N$_\rm{side}$=2048 */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
; Model of thermal dust emission<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
; The <math>E(B-V)</math> map <br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
; Dust optical depth products<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5 arcmin, no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5 arcmin, units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5 arcmin, units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35 arcmin, no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7685CMB and astrophysical component maps2013-06-19T08:01:02Z<p>Lvibert: /* Thermal dust component at N$_\rm{side}$=256 */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
; Model of thermal dust emission<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
; The <math>E(B-V)</math> map <br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
; Dust optical depth products<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5 arcmin, no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5 arcmin, units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5 arcmin, units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35 arcmin, no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7684CMB and astrophysical component maps2013-06-19T08:00:10Z<p>Lvibert: /* Low frequency component at N$_\rm{side}$ = 2048 */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
; Model of thermal dust emission<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
; The <math>E(B-V)</math> map <br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
; Dust optical depth products<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5 arcmin, no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5 arcmin, units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5 arcmin, units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35 arcmin, no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7683CMB and astrophysical component maps2013-06-19T07:59:30Z<p>Lvibert: /* Low frequency component at N$_\rm{side}$ = 2048 */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
; Model of thermal dust emission<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
; The <math>E(B-V)</math> map <br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
; Dust optical depth products<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5 arcmin, no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5 arcmin, units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5 arcmin, units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35 arcmin, no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7682CMB and astrophysical component maps2013-06-19T07:58:49Z<p>Lvibert: /* Low frequency component at N$_\rm{side}$ = 256 */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
; Model of thermal dust emission<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
; The <math>E(B-V)</math> map <br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
; Dust optical depth products<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5 arcmin, no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5 arcmin, units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5 arcmin, units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35 arcmin, no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7681CMB and astrophysical component maps2013-06-19T07:57:12Z<p>Lvibert: /* Low frequency component at N$_\rm{side}$ 2048 */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
; Model of thermal dust emission<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
; The <math>E(B-V)</math> map <br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
; Dust optical depth products<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5 arcmin, no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5 arcmin, units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5 arcmin, units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35 arcmin, no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=CMB_and_astrophysical_component_maps&diff=7680CMB and astrophysical component maps2013-06-19T07:56:39Z<p>Lvibert: /* Low frequency component at N$_\rm{side}$ 256 */</p>
<hr />
<div>== Overview ==<br />
--------------<br />
<br />
This section describes the maps of astrophysical components produced from the Planck data. These products are derived from some or all of the nine frequency channel maps described above using different techniques and, in some cases, using other constraints from external data sets. Here we give a brief description of the 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 <cite>#planck2013-p06</cite>.<br />
<br />
<br />
==CMB maps==<br />
-----------------<br />
<br />
CMB maps have been produced by the SMICA, NILC, and SEVEM 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 each 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 />
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=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 />
| Raw CMB anisotropy map. These are the maps used in the component separation paper <cite>#planck2013-p06</cite> {{P2013|12}}.<br />
|-<br />
| 2: NOISE<br />
| [[File: CMBnoise-smica.png|200px]]<br />
| [[File: CMBnoise-nilc.png|200px]]<br />
| [[File: CMBnoise-sevem.png|200px]]<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 />
| 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 />
| 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 />
| 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 />
| 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 <cite>#planck2013-p06</cite> {{P2013|12}} 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 Leach et al., 2008 <cite>#leach2008</cite> and to WMAP polarisation data Fernandez-Cobos et al., 2012 <cite>xx</cite>. In the cleaning process, no assumptions about the foregrounds or noise levels are needed, rendering the technique very robust.<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 <cite>#planck2013-p06</cite>.<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; Casaponsa et al. 2011 <cite>#Casaponsa2011</cite>) 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 <cite>#planck2013-p09</cite> {{P2013|23}} and <cite>#planck2013-p14</cite> {{P2013|19}}. In particular, clean maps from 44 to 353 GHz have been used for the stacking analysis presented in <cite>#planck2013-p14</cite>, while frequencies from 70 to 217 GHz were used for consistency tests in <cite>#planck2013-p09</cite>.<br />
<br />
The method has been successfully applied to Planck simulations <cite>#leach2008</cite> and to WMAP polarisation data <cite>#Fernandez-Cobos2012</cite>.<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.<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_R1.11.fits|link=COM_CompMap_CMB-sevem_2048_R1.11.fits}}<br />
* {{PLASingleFile|fileType=map|name=COM_CompMap_CMB-smica_2048_R1.20.fits|link=COM_CompMap_CMB-smica_2048_R1.20.fits}}<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 />
|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)<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)<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)<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 product file.<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.<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 />
<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 />
===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 />
== Astrophysical foregrounds from parametric component separation ==<br />
--------------------------<br />
<br />
We describe diffuse foreground products for the Planck 2013 release. See Planck Component Separation paper <cite>#planck2013-p06</cite> {{P2013|12}} for a detailed description and astrophysical discussion of those.<br />
<br />
===Product description===<br />
<br />
; Low frequency foreground component<br />
: The products below contain the result of the fitting for one foreground component at low frequencies in Planck bands,along with its spectral behavior parametrized by a power law spectral index. Amplitude and spectral indeces are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on both. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is also provided as a secondary Extension in the N$_\rm{side}$ 2048 product.<br />
<br />
; Thermal dust<br />
: The products below contain the result of the fitting for one foreground component at high frequencies in Planck bands, along with its spectral behavior parametrized by temperature and emissivity. Amplitude, temperature and emissivity are evaluated at N$_\rm{side}$ 256 (see below in the production process), along with standard deviation from sampling and instrumental noise on all of them. An amplitude solution at N$_\rm{side}$=2048 is also given, along with standard deviation from sampling and instrumental noise as well as solutions on halfrings. The beam profile associated to this component is provided. <br />
<br />
; Sky mask<br />
: The delivered mask is defined as the sky region where the fitting procedure was conducted and the solutions presented here were obtained. It is made by masking a region where the Galactic emission is too intense to perform the fitting, plus the masking of brightest point sources.<br />
<br />
===Production process===<br />
<br />
CODE: COMMANDER-RULER. The code exploits a parametrization of CMB and main diffuse foreground observables. The naive resolution of input <br />
frequency channels is reduced to N$_\rm{side}$=256 first. Parameters related to the foreground scaling with frequency are estimated at that resolution <br />
by using Markov Chain Monte Carlo analysis using Gibbs sampling. The foreground parameters make the foreground mixing matrix which is <br />
applied to the data at full resolution in order to obtain the provided products at N$_\rm{side}$=2048. In the Planck Component Separation paper <cite>#planck2013-p06</cite> {{p2013|12}}additional material is discussed, specifically concerning the sky region where the solutions are reliable, in terms of chi2 maps.<br />
<br />
===Inputs===<br />
<br />
Nominal frequency maps at 30, 44, 70, 100, 143, 217, 353 GHz ({{PLAFreqMaps|inst=LFI|freq=30|period=Nominal|link=LFI 30 GHz frequency maps}}, {{PLAMaps|inst=LFI|freq=44|period=Nominal|link=LFI 44 GHz frequency maps}} and {{PLAMaps|inst=LFI|freq=70|period=Nominal|link=LFI 70 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=100|period=Nominal|zodi=uncorr|link=HFI 100 GHz frequency maps}}, {{PLAMaps|inst=HFI|freq=143|period=Nominal|zodi=uncorr|link=HFI 143 GHz frequency maps}},{{PLAMaps|inst=HFI|freq=217|period=Nominal|zodi=uncorr|link=HFI 217 GHz frequency maps}} and {{PLAMaps|inst=HFI|freq=353|period=Nominal|zodi=uncorr|link=HFI 353 GHz frequency maps}}) and their II column corresponding to the noise covariance matrix. <br />
Halfrings at the same frequencies. Beam window functions as reported in the [[The RIMO#Beam Window Functions|LFI and HFI RIMO]].<br />
<br />
===Related products===<br />
<br />
None. <br />
<br />
===File names===<br />
<br />
* Low frequency component at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits}}<br />
* Low frequency component at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits|link=COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 256: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_0256_R1.00.fits|link=COM_CompMap_dust-commrul_0256_R1.00.fits}}<br />
* Thermal dust at N$_\rm{side}$ 2048: {{PLASingleFile|fileType=map|name=COM_CompMap_dust-commrul_2048_R1.00.fits|link=COM_CompMap_dust-commrul_2048_R1.00.fits}}<br />
* Mask: {{PLASingleFile|fileType=map|name=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits|link=COM_CompMap_Mask-rulerminimal_2048_R1.00.fits}}<br />
<br />
===Meta Data===<br />
<br />
====Low frequency foreground component====<br />
<br />
=====Low frequency component at N$_\rm{side}$ = 256=====<br />
<br />
File name: COM_CompMap_Lfreqfor-commrul_0256_R1.00.fits<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|Beta || Real*4 || || effective spectral index <br />
|-<br />
|B_stdev || Real*4 || || standard deviation on the effective spectral index <br />
|}<br />
<br />
; Notes:<br />
: Comment: The Intensity is normalized at 30 GHz<br />
: Comment: The intensity was estimated during mixing matrix estimation<br />
<br />
=====Low frequency component at N$_\rm{side}$ 2048=====<br />
<br />
: File name: COM_CompMap_Lfreqfor-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || uK<math>_{CMB}</math>|| Intensity <br />
|-<br />
|I_stdev || Real*8 || uK<math>_{CMB}</math> || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || uK<math>_{CMB}</math> || Intensity on half ring 2 <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity was computed after mixing matrix application<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
<br />
====Thermal dust====<br />
<br />
=====Thermal dust component at N$_\rm{side}$=256=====<br />
<br />
: File name: COM_CompMap_dust-commrul_0256_R1.00.fits<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*4 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*4 || MJy/sr || standard deviation of intensity <br />
|-<br />
|Em || Real*4 || || emissivity <br />
|-<br />
|Em_stdev || Real*4 || || standard deviation on emissivity <br />
|-<br />
|T || Real*4 || uK<math>_{CMB}</math> || temperature <br />
|-<br />
|T_stdev || Real*4 || uK<math>_{CMB}</math> || standard deviation on temerature <br />
|}<br />
<br />
; Notes:<br />
: Comment: The intensity is normalized at 353 GHz<br />
<br />
=====Thermal dust component at N$_\rm{side}$=2048=====<br />
<br />
File name: COM_CompMap_dust-commrul_2048_R1.00.fits<br />
<br />
<br />
: '''Name HDU -- COMP-MAP'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I || Real*8 || MJy/sr || Intensity <br />
|-<br />
|I_stdev || Real*8 || MJy/sr || standard deviation of intensity <br />
|-<br />
|I_hr1 || Real*8 || MJy/sr || Intensity on half ring 1 <br />
|-<br />
|I_hr2 || Real*8 || MJy/sr || Intensity on half ring 2 <br />
|}<br />
<br />
<br />
: '''Name HDU -- BeamWF'''<br />
<br />
The Fits second extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|BeamWF || Real*4 || || beam profile <br />
|}<br />
<br />
; Notes:<br />
: Comment: Beam window function used in the Component separation process<br />
<br />
====Sky mask====<br />
<br />
File name: COM_CompMap_Mask-rulerminimal_2048.fits<br />
<br />
; '''Name HDU -- COMP-MASK'''<br />
<br />
The Fits extension is composed by the columns described below:<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ FITS header<br />
|-<br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|Mask || Real*4 || || Mask <br />
|}<br />
<br />
<br />
== Dust optical depth map and model ==<br />
-------------------------------------<br />
<br />
Thermal emission from interstellar dust is captured by Planck-HFI over the whole sky, at all frequencies from 100 to 857 GHz. This emission is well modelled by a modified black body in the far-infrared to millimeter range. It is produced by the biggest interstellar dust grain that are in thermal equilibrium with the radiation field from stars. The grains emission properties in the sub-millimeter are therefore directly linked to their absorption properties in the UV-visible range. By modelling the thermal dust emission in the sub-millimeter, a map of dust reddening in the visible can then be constructed. <br />
<br />
; Model of thermal dust emission<br />
<br />
The model of the thermal dust emission is based on a modify black body fit to the data <math>I_\nu</math><br />
<br />
: <math>I_\nu = A\, B_\nu(T)\, \nu^\beta</math><br />
<br />
where B_nu(T) is the Planck function for dust equilibirum temperature T, A is the amplitude of the MBB and beta the dust spectral index. The dust optical depth at frequency nu is<br />
<br />
: <math>\tau_\nu = I_\nu / B_\nu(T) = A\, \nu^\beta</math><br />
<br />
The dust parameters provided are <math>T</math>, beta and <math>\tau_{353}</math>. They were obtained by fitting the Planck data at 353, 545 and 857 GHz together with the IRAS (IRIS) 100 micron data. All maps (in Healpix Nside=2048 were smoothed to a common resolution of 5 arcmin. The CMB anisotropies, clearly visible at 353 GHz, were removed from all the HFI maps using the SMICA map. An offset was removed from each map to obtained a meaningful Galactic zero level, using a correlation with the LAB 21 cm data in diffuse areas of the sky (<math>N_{HI} < 2\times10^{20} cm^{-2}</math>). Because the dust emission is so well correlated between frequencies in the Rayleigh-Jeans part of the dust spectrum, the zero level of the 545 and 353 GHz were improved by correlating with the 857 GHz over a larger mask (<math>N_{HI} < 3\times10^{20} cm^{-2}</math>). Faint residual dipole structures, identified in the 353 and 545 GHz maps, were removed prior to the fit.<br />
<br />
The MBB fit was performed using a chi-square minimization, assuming errors for each data point that include instrumental noise, calibration uncertainties (on both the dust emission and the CMB anisotropies) and uncertainties on the zero level. Because of the known degeneracy between <math>T</math> and <math>\beta</math> in the presence of noise, we produced a model of dust emission using data smoothed to 35 arcmin; at such resolution no systematic bias of the parameters is observed. The map of the spectral index <math>\beta</math> at 35 arcmin was than used to fit the data for <math>T</math> and <math>\tau_{353}</math> at 5 arcmin. <br />
<br />
; The <math>E(B-V)</math> map <br />
For the production of the <math>E(B-V)</math> map, we used Planck and IRAS data from which point sources in diffuse areas were removed to avoid contamination by galaxies. In the hypothesis of constant dust emission cross-section, the optical depth map <math>\tau_{353}</math> is proportional to dust column density. It can then be used to estimate E(B-V), also proportional to dust column density in the hypothesis of a constant differential absorption cross-section between the B and V bands. Given those assumptions, <math>E(B-V) = q\, \tau_{353}</math>.<br />
<br />
To estimate the calibration factor q, we followed a method similar to <cite>#mortsell2013</cite> based on SDSS reddening measurements (<math>E(g-r)</math> which corresponds closely to <math>E(B-V)</math>) of 77 429 Quasars <cite>#schneider2007</cite>. The interstellar HI column densities covered on the lines of sight of this sample ranges from <math>0.5</math> to <math>10\times10^{20}\,cm^{-2}</math>. Therefore this sample allows to estimate q in the diffuse ISM where dust properties are expected to vary less than in denser clouds where coagulation and grain growth might modify dust emission and absorption cross sections. <br />
<br />
; Dust optical depth products<br />
<br />
The characteristics of the dust model maps are the following.<br />
* Dust optical depth at 353 GHz : Nside=2048, fwhm=5 arcmin, no units<br />
* Dust reddening E(B-V) : Nside=2048, fwhm=5 arcmin, units=magnitude, obtained with data from which point sources were removed.<br />
* Dust temperature : Nside 2048, fwhm=5 arcmin, units=Kelvin<br />
* Dust spectral index : Nside=2048, fwhm=35 arcmin, no units<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Dust opacity file data structure'''<br />
|- bgcolor="ffdead" <br />
! colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
| TAU353 || Real*4 || none || The opacity at 353GHz<br />
|-<br />
| TAU353ERR || Real*4 || none || Error in the opacity<br />
|-<br />
| EBV || Real*4 || mag || E(B-V)<br />
|-<br />
| EBV_ERR || Real*4 || mag || Error in E(B-V)<br />
|-<br />
|T_HF || Real*4 || K || Temperature for the high frequency correction<br />
|-<br />
|T_HF_ERR || Real*4 || K || Error on the temperature<br />
|-<br />
| BETAHF || Real*4 || none || Beta for the high frequency correction<br />
|-<br />
| BETAHFERR || Real*4 || none || Error on beta<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
| AST-COMP || String || DUST-OPA|| 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 for LFI and HFI, respectively<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 />
== CO emission maps ==<br />
-------------------<br />
<br />
CO rotational transition line emission is present in all HFI bands but for the 143 GHz channel. It is especially significant in the 100, 217 and 353 GHz channels (due to the 115 (1-0), 230 (2-1) and 345 GHz (3-2) CO transitions). This emission comes essentially from the Galactic interstellar medium and is mainly located at low and intermediate Galactic latitudes. Three approaches (summarised below) have been used to extract CO velocity-integrated emission maps from HFI maps and to make three types of CO products. A full description of how these products were producedis given in <cite>#planck2013-p03a</cite>.<br />
<br />
* Type 1 product: it is based on a single channel approach using the fact that each CO line has a slightly different transmission in each bolometer at a given frequency channel. These transmissions can be evaluated from bandpass measurements that were performed on the ground or empirically determined from the sky using existing ground-based CO surveys. From these, the J=1-0, J=2-1 and J=3-2 CO lines can be extracted independently. As this approach is based on individual bolometer maps of a single channel, the resulting Signal-to-Noise ratio (SNR) is relatively low. The benefit, however, is that these maps do not suffer from contamination from other HFI channels (as is the case for the other approaches) and are more reliable, especially in the Galactic Plane.<br />
* Type 2 product: this product is obtained using a multi frequency approach. Three frequency channel maps are combined to extract the J=1-0 (using the 100, 143 and 353 GHz channels) and J=2-1 (using the 143, 217 and 353 GHz channels) CO maps. Because frequency channels are combined, the spectral behaviour of other foregrounds influences the result. The two type 2 CO maps produced in this way have a higher SNR than the type 1 maps at the cost of a larger possible residual contamination from other diffuse foregrounds.<br />
* Type 3 product: using prior information on CO line ratios and a multi-frequency component separation method, we construct a combined CO emission map with the largest possible SNR. This type 3 product can be used as a sensitive finder chart for low-intensity diffuse CO emission over the whole sky.<br />
<br />
The released Type 1 CO maps have been produced using the MILCA-b algorithm, Type 2 maps using a specific implementation of the Commander algorithm, and the Type 3 map using the full Commander-Ruler component separation pipeline (see [[CMB_and _astrophysical_component_maps#Maps_of_astrophysical_foregrounds | above]]).<br />
<br />
Characteristics of the released maps are the following. We provide Healpix maps with Nside=2048. For one transition, the CO velocity-integrated line signal map is given in K_RJ.km/s units. A conversion factor from this unit to the native unit of HFI maps (K_CMB) is provided in the header of the data files and in the RIMO. Four maps are given per transition and per type:<br />
* The signal map<br />
* The standard deviation map (same unit as the signal), <br />
* A null test noise map (same unit as the signal) with similar statistical properties. It is made out of half the difference of half-ring maps.<br />
* A mask map (0B or 1B) giving the regions (1B) where the CO measurement is not reliable because of some severe identified foreground contamination.<br />
<br />
All products of a given type belong to a single file.<br />
Type 1 products have the native HFI resolution i.e. approximately 10, 5 and 5 arcminutes for the CO 1-0, 2-1, 3-2 transitions respectively.<br />
Type 2 products have a 15 arcminute resolution<br />
The Type 3 product has a 5.5 arcminute resolution.<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-1 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|I32 || Real*4 || K_RJ km/sec || The CO(3-2) intensity map<br />
|-<br />
|E32 || Real*4 || K_RJ km/sec || Uncertainty in the CO(3-2) intensity<br />
|-<br />
|N32 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M32 || Byte || none || Region over which the CO(3-2) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || string || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 3-2 || Real*4 || value || Factor to convert CO(3-2) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-2 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|I10 || Real*4 || K_RJ km/sec || The CO(1-0) intensity map<br />
|-<br />
|E10 || Real*4 || K_RJ km/sec || Uncertainty in the CO(1-0) intensity<br />
|-<br />
|N10 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M10 || Byte || none || Region over which the CO(1-0) intensity is considered reliable<br />
|-<br />
|-<br />
|I21 || Real*4 || K_RJ km/sec || The CO(2-1) intensity map<br />
|-<br />
|E21 || Real*4 || K_RJ km/sec || Uncertainty in the CO(2-1) intensity<br />
|-<br />
|N21 || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|M21 || Byte || none || Region over which the CO(2-1) intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE2 || 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 for LFI and HFI, respectively<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 />
|CNV 1-0 || Real*4 || value || Factor to convert CO(1-0) intensity to Kcmb (units Kcmb/(Krj*km/s)) <br />
|-<br />
|CNV 2-1 || Real*4 || value || Factor to convert CO(2-1) intensityto Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px<br />
|+ '''Type-3 CO map file data structure'''<br />
|- bgcolor="ffdead" <br />
!colspan="4" | 1. EXTNAME = 'COMP-MAP' <br />
|- bgcolor="ffdead" <br />
! Column Name || Data Type || Units || Description<br />
|-<br />
|INTEN || Real*4 || K_RJ km/sec || The CO intensity map<br />
|-<br />
|ERR || Real*4 || K_RJ km/sec || Uncertainty in the intensity<br />
|-<br />
|NUL || Real*4 || K_RJ km/sec || Map built from the half-ring difference maps<br />
|-<br />
|MASK || Byte || none || Region over which the intensity is considered reliable<br />
|-<br />
|- bgcolor="ffdead" <br />
! Keyword || Data Type || Value || Description<br />
|-<br />
|AST-COMP || String || CO-TYPE1 || 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 for LFI and HFI, respectively<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 />
|CNV || Real*4 || value || Factor to convert to Kcmb (units Kcmb/(Krj*km/s)) <br />
|}<br />
<br />
<br />
== References ==<br />
----------------<br />
<br />
<biblio force=false><br />
#[[References]] <br />
</biblio><br />
<br />
<br />
<br />
[[Category:Mission products|007]]</div>Lviberthttps://wiki.cosmos.esa.int/planckpla2015/index.php?title=Effective_Beams&diff=7679Effective Beams2013-06-19T07:49:49Z<p>Lvibert: /* Retrieval of effective beam information from the PLA interface */</p>
<hr />
<div><span style="color:red"></span><br />
<br />
==Product description==<br />
----------------------<br />
<br />
The '''effective beam''' is the average of all scanning beams pointing at a certain direction within a given pixel of the sky map for a given scan strategy. It takes into account the coupling between azimuthal asymmetry of the beam and the uneven distribution of scanning angles across the sky.<br />
It captures the complete information about the difference between the true and observed image of the sky. They are, by definition, the objects whose convolution with the true CMB sky produce the observed sky map. <br />
<br />
Details of the beam processing are given in the respective pages for [[Beams|HFI]] and [[Beams_LFI|LFI]].<br />
<br />
The full algebra involving the effective beams for temperature and polarisation was presented in [[http://arxiv.org/pdf/1005.1929| Mitra, Rocha, Gorski et al.]] <cite>#mitra2010</cite>, and a discussion of its application to Planck data is given in the appropriate LFI <cite>#planck2013-p02d</cite> and HFI <cite>#planck2013-p03c</cite> papers. Relevant details of the processing steps are given in the [[Beams|Effective Beams]] section of this document.<br />
<br />
<!-- Everything from here down to the "Production Process" section should eventually be moved to a new section the Joint Processing pages --><br />
<br />
===Comparison of the images of compact sources observed by Planck with FEBeCoP products===<br />
<br />
<br />
We show here a comparison of the FEBeCoP derived effective beams, and associated point spread functions, PSF (the transpose of the beam matrix), to the actual images of a few compact sources observed by Planck, for all LFI and HFI frequency channels, as an example. We show below a few panels of source images organized as follows:<br />
* Row #1- DX9 images of four ERCSC objects with their galactic (l,b) coordinates shown under the color bar<br />
* Row #2- linear scale FEBeCoP PSFs computed using input scanning beams, Grasp Beams, GB, for LFI and B-Spline beams,BS, Mars12 apodized for the CMB channels and the BS Mars12 for the sub-mm channels, for HFI (see section Inputs below).<br />
* Row #3- log scale of #2; PSF iso-contours shown in solid line, elliptical Gaussian fit iso-contours shown in broken line<br />
<br />
<center><br />
<br />
<gallery widths=400px heights=400px perrow=2 caption="Comparison images of compact sources and effective beams, PSFs"><br />
File:30.png| '''30GHz'''<br />
File:44.png| '''44GHz'''<br />
File:70.png| '''70GHz'''<br />
File:100.png| '''100GHz'''<br />
File:143.png| '''143GHz'''<br />
File:217.png| '''217GHz'''<br />
File:353.png| '''353GHz'''<br />
File:545.png| '''545GHz'''<br />
File:857.png| '''857GHz'''<br />
</gallery><br />
</center><br />
<br />
===Histograms of the effective beam parameters===<br />
<br />
Here we present histograms of the three fit parameters - beam FWHM, ellipticity, and orientation with respect to the local meridian and of the beam solid angle. The shy is sampled (pretty sparsely) at 3072 directions which were chosen as HEALpix nside=16 pixel centers for HFI and at 768 directions which were chosen as HEALpix nside=8 pixel centers for LFI to uniformly sample the sky.<br />
<br />
Where beam solid angle is estimated according to the definition: '''<math> 4 \pi \sum</math>(effbeam)/max(effbeam)'''<br />
i.e., <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math><br />
<br />
<br />
[[File:ist_GB.png | 800px| thumb | center| '''Histograms for LFI effective beam parameters''' ]] <br />
[[File:ist_BS_Mars12.png | 800px| thumb | center| '''Histograms for HFI effective beam parameters''' ]]<br />
<br />
===Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian===<br />
<br />
<br />
* The discontinuities at the Healpix domain edges in the maps are a visual artifact due to the interplay of the discretized effective beam and the Healpix pixel grid.<br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky variation of effective beams ellipticity of the best-fit Gaussian"><br />
File:e_030_GB.png| '''ellipticity - 30GHz'''<br />
File:e_044_GB.png| '''ellipticity - 44GHz'''<br />
File:e_070_GB.png| '''ellipticity - 70GHz'''<br />
File:e_100_BS_Mars12.png| '''ellipticity - 100GHz'''<br />
File:e_143_BS_Mars12.png| '''ellipticity - 143GHz'''<br />
File:e_217_BS_Mars12.png| '''ellipticity - 217GHz'''<br />
File:e_353_BS_Mars12.png| '''ellipticity - 353GHz'''<br />
File:e_545_BS_Mars12.png| '''ellipticity - 545GHz'''<br />
File:e_857_BS_Mars12.png| '''ellipticity - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky (relative) variation of effective beams solid angle of the best-fit Gaussian"><br />
File:solidarc_030_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 30GHz'''<br />
File:solidarc_044_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 44GHz'''<br />
File:solidarc_070_GB.png| '''beam solid angle (relative) variations wrt scanning beam - 70GHz'''<br />
File:solidarc_100_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 100GHz'''<br />
File:solidarc_143_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 143GHz'''<br />
File:solidarc_217_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 217GHz'''<br />
File:solidarc_353_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 353GHz'''<br />
File:solidarc_545_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 545GHz'''<br />
File:solidarc_857_BS_Mars12.png| '''beam solid angle (relative) variations wrt scanning beam - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky (relative) variation of effective beams fwhm of the best-fit Gaussian"><br />
File:fwhm_030_GB.png| '''fwhm (relative) variations wrt scanning beam - 30GHz'''<br />
File:fwhm_044_GB.png| '''fwhm (relative) variations wrt scanning beam - 44GHz'''<br />
File:fwhm_070_GB.png| '''fwhm (relative) variations wrt scanning beam - 70GHz'''<br />
File:fwhm_100_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 100GHz'''<br />
File:fwhm_143_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 143GHz'''<br />
File:fwhm_217_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 217GHz'''<br />
File:fwhm_353_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 353GHz'''<br />
File:fwhm_545_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 545GHz'''<br />
File:fwhm_857_BS_Mars12.png| '''fwhm (relative) variations wrt scanning beam - 857GHz'''<br />
</gallery><br />
<br />
<br />
<gallery widths=300px heights=220px perrow=3 caption="Sky variation of effective beams $\psi$ angle of the best-fit Gaussian"><br />
File:psi_030_GB.png| '''$\psi$ - 30GHz'''<br />
File:psi_044_GB.png| '''$\psi$ - 44GHz'''<br />
File:psi_070_GB.png| '''$\psi$ - 70GHz'''<br />
File:psi_100_BS_Mars12.png| '''$\psi$ - 100GHz'''<br />
File:psi_143_BS_Mars12.png| '''$\psi$ - 143GHz'''<br />
File:psi_217_BS_Mars12.png| '''$\psi$ - 217GHz'''<br />
File:psi_353_BS_Mars12.png| '''$\psi$ - 353GHz'''<br />
File:psi_545_BS_Mars12.png| '''$\psi$ - 545GHz'''<br />
File:psi_857_BS_Mars12.png| '''$\psi$ - 857GHz'''<br />
</gallery><br />
<br />
<!--<br />
<gallery widths=500px heights=500px perrow=2 caption="Sky variation of effective beams solid angle and ellipticity of the best-fit Gaussian"><br />
File:e_030_GB.png| '''ellipticity - 30GHz'''<br />
File:solidarc_030_GB.png| '''beam solid angle (relative variations wrt scanning beam - 30GHz'''<br />
File:e_100_BS_Mars12.png| '''ellipticity - 100GHz'''<br />
File:solidarc_100_BS_Mars12.png| '''beam solid angle (relative variations wrt scanning beam - 100GHz'''<br />
</gallery><br />
--><br />
<br />
===Statistics of the effective beams computed using FEBeCoP===<br />
<br />
We tabulate the simple statistics of FWHM, ellipticity (e), orientation (<math> \psi</math>) and beam solid angle, (<math> \Omega </math>), for a sample of 3072 and 768 directions on the sky for HFI and LFI data respectively. Statistics shown in the Table are derived from the histograms shown above.<br />
<br />
* The derived beam parameters are representative of the DPC NSIDE 1024 and 2048 healpix maps (they include the pixel window function).<br />
* The reported FWHM_eff are derived from the beam solid angles, under a Gaussian approximation. These are best used for flux determination while the the Gaussian fits to the effective beam maps are more suited for source identification.<br />
<br />
<br />
<br />
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Statistics of the FEBeCoP Effective Beams Computed with the BS Mars12 apodized for the CMB channels and oversampled'''<br />
|-<br />
! '''frequency''' || '''mean(fwhm)''' [arcmin] || '''sd(fwhm)''' [arcmin] || '''mean(e)''' || '''sd(e)''' || '''mean(<math> \psi</math>)''' [degree] || '''sd(<math> \psi</math>)''' [degree] || '''mean(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''sd(<math> \Omega </math>)''' [arcmin<math>^{2}</math>] || '''FWHM_eff''' [arcmin] <br />
|-<br />
| 030 || 32.239 || 0.013 || 1.320 || 0.031 || -0.304 || 55.349 || 1189.513 || 0.842 || 32.34<br />
|-<br />
| 044 || 27.005 || 0.552 || 1.034 || 0.033 || 0.059 || 53.767 || 832.946 || 31.774 || 27.12<br />
|-<br />
| 070 || 13.252 || 0.033 || 1.223 || 0.026 || 0.587 || 55.066 || 200.742 || 1.027 || 13.31 <br />
|-<br />
| 100 || 9.651 || 0.014 || 1.186 || 0.023 || -0.024 || 55.400 || 105.778 || 0.311 || 9.66 <br />
|-<br />
| 143 || 7.248 || 0.015 || 1.036 || 0.009 || 0.383 || 54.130 || 59.954 || 0.246 || 7.27 <br />
|-<br />
| 217 || 4.990 || 0.025 || 1.177 || 0.030 || 0.836 || 54.999 || 28.447 || 0.271 || 5.01<br />
|-<br />
| 353 || 4.818 || 0.024 || 1.147 || 0.028 || 0.655 || 54.745 || 26.714 || 0.250 || 4.86<br />
|- <br />
| 545 || 4.682 || 0.044 || 1.161 || 0.036 || 0.544 || 54.876 || 26.535 || 0.339 || 4.84 <br />
|-<br />
| 857 || 4.325 || 0.055 || 1.393 || 0.076 || 0.876 || 54.779 || 24.244 || 0.193 || 4.63 <br />
|}<br />
<br />
<br />
<br />
<br />
====Beam solid angles for the PCCS====<br />
<br />
* <math>\Omega_{eff}</math> - is the mean beam solid angle of the effective beam, where beam solid angle is estimated according to the definition: '''<math>4 \pi \sum </math>(effbeam)/max(effbeam)''', i.e. as an integral over the full extent of the effective beam, i.e. <math> 4 \pi \sum(B_{ij}) / max(B_{ij}) </math>.<br />
<br />
* from <math>\Omega_{eff}</math> we estimate the <math>fwhm_{eff}</math>, under a Gaussian approximation - these are tabulated above<br />
** <math>\Omega^{(1)}_{eff}</math> is the beam solid angle estimated up to a radius equal to one <math>fwhm_{eff}</math> and <math>\Omega^{(2)}_{eff}</math> up to a radius equal to twice the <math>fwhm_{eff}</math>.<br />
*** These were estimated according to the procedure followed in the aperture photometry code for the PCCS: if the pixel centre does not lie within the given radius it is not included (so inclusive=0 in query disc).<br />
<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Band averaged beam solid angles'''<br />
| '''Band''' || '''<math>\Omega_{eff}</math>'''[arcmin<math>^{2}</math>] || '''spatial variation''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(1)}_{eff}</math>''' [arcmin<math>^{2}</math>]|| '''spatial variation-1''' [arcmin<math>^{2}</math>] || '''<math>\Omega^{(2)}_{eff}</math>''' [arcmin<math>^{2}</math>] || '''spatial variation-2''' [arcmin<math>^{2}</math>] <br />
|-<br />
|30 || 1189.513 || 0.842 || 1116.494 || 2.274 || 1188.945 || 0.847 <br />
|-<br />
| 44 || 832.946 || 31.774 || 758.684 || 29.701 || 832.168 || 31.811 <br />
|-<br />
| 70 || 200.742 || 1.027 || 186.260 || 2.300 || 200.591 || 1.027 <br />
|-<br />
| 100 || 105.778 || 0.311 || 100.830 || 0.410 || 105.777 || 0.311 <br />
|-<br />
| 143 || 59.954 || 0.246 || 56.811 || 0.419 || 59.952 || 0.246 <br />
|-<br />
| 217 || 28.447 || 0.271 || 26.442 || 0.537 || 28.426 || 0.271 <br />
|-<br />
| 353 || 26.714 || 0.250 || 24.827 || 0.435 || 26.653 || 0.250 <br />
|-<br />
| 545 || 26.535 || 0.339 || 24.287 || 0.455 || 26.302 || 0.337 <br />
|-<br />
| 857 || 24.244 || 0.193 || 22.646 || 0.263 || 23.985 || 0.191 <br />
|}<br />
<br />
==Production process==<br />
------------------------<br />
<br />
<br />
FEBeCoP, or Fast Effective Beam Convolution in Pixel space [[http://arxiv.org/pdf/1005.1929| Mitra, Rocha, Gorski et al.]] <cite>#mitra2010</cite>, is an approach to representing and computing effective beams (including both intrinsic beam shapes and the effects of scanning) that comprises the following steps:<br />
* identify the individual detectors' instantaneous optical response function (presently we use elliptical Gaussian fits of Planck beams from observations of planets; eventually, an arbitrary mathematical representation of the beam can be used on input)<br />
* follow exactly the Planck scanning, and project the intrinsic beam on the sky at each actual sampling position<br />
* project instantaneous beams onto the pixelized map over a small region (typically <2.5 FWHM diameter)<br />
* add up all beams that cross the same pixel and its vicinity over the observing period of interest<br />
*create a data object of all beams pointed at all N'_pix_' directions of pixels in the map at a resolution at which this precomputation was executed (dimension N'_pix_' x a few hundred)<br />
*use the resulting beam object for very fast convolution of all sky signals with the effective optical response of the observing mission<br />
<br />
<br />
Computation of the effective beams at each pixel for every detector is a challenging task for high resolution experiments. FEBeCoP is an efficient algorithm and implementation which enabled us to compute the pixel based effective beams using moderate computational resources. The algorithm used different mathematical and computational techniques to bring down the computation cost to a practical level, whereby several estimations of the effective beams were possible for all Planck detectors for different scanbeam models and different lengths of datasets. <br />
<br />
<br />
===Pixel Ordered Detector Angles (PODA)===<br />
<br />
The main challenge in computing the effective beams is to go through the trillion samples, which gets severely limited by I/O. In the first stage, for a given dataset, ordered lists of pointing angles for each pixels - the Pixel Ordered Detector Angles (PODA) are made. This is an one-time process for each dataset. We used computers with large memory and used tedious memory management bookkeeping to make this step efficient.<br />
<br />
===effBeam===<br />
<br />
The effBeam part makes use of the precomputed PODA and unsynchronized reading from the disk to compute the beam. Here we tried to made sure that no repetition occurs in evaluating a trigonometric quantity.<br />
<br />
<br />
One important reason for separating the two steps is that they use different schemes of parallel computing. The PODA part requires parallelisation over time-order-data samples, while the effBeam part requires distribution of pixels among different computers.<br />
<br />
<br />
===Computational Cost===<br />
<br />
The computation of the effective beams has been performed at the NERSC Supercomputing Center. The table below shows the computation cost for FEBeCoP processing of the nominal mission.<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+ '''Computational cost for PODA, Effective Beam and single map convolution. Wall-clock time is given as a guide, as found on the NERSC supercomputers.'''<br />
|-<br />
|Channel ||030 || 044 || 070 || 100 || 143 || 217 || 353 || 545 || 857<br />
|-<br />
|PODA/Detector Computation time (CPU hrs) || 85 || 100 || 250 || 500 || 500 || 500 || 500 || 500 || 500 <br />
|-<br />
|PODA/Detector Computation time (wall clock hrs) || 7 || 10 || 20 || 20 || 20 || 20 || 20 || 20 || 20<br />
|- <br />
|Beam/Channel Computation time (CPU hrs) || 900 || 2000 || 2300 || 2800 || 3800 || 3200 || 3000 || 900 || 1100<br />
|-<br />
|Beam/Channel Computation time (wall clock hrs) || 0.5 || 0.8 || 1 || 1.5 || 2 || 1.2 || 1 || 0.5 || 0.5<br />
|-<br />
|Convolution Computation time (CPU hr) || 1 || 1.2 || 1.3 || 3.6 || 4.8 || 4.0 || 4.1 || 4.1 || 3.7 <br />
|-<br />
|Convolution Computation time (wall clock sec) || 1 || 1 || 1 || 4 || 4 || 4 || 4 || 4 || 4 <br />
|-<br />
|Effective Beam Size (GB) || 173 || 123 || 28 || 187 || 182 || 146 || 132 || 139 || 124<br />
|}<br />
<br />
<br />
The computation cost, especially for PODA and Convolution, is heavily limited by the I/O capacity of the disc and so it depends on the overall usage of the cluster done by other users.<br />
<br />
==Inputs==<br />
------------<br />
<br />
In order to fix the convention of presentation of the scanning and effective beams, we show the classic view of the Planck focal plane as seen by the incoming CMB photon. The scan direction is marked, and the toward the center of the focal plane is at the 85 deg angle w.r.t spin axis pointing upward in the picture. <br />
<br />
<br />
[[File:PlanckFocalPlane.png | 500px| thumb | center|'''Planck Focal Plane''']]<br />
<br />
<br />
===The Focal Plane DataBase (FPDB)===<br />
<br />
The FPDB contains information on each detector, e.g., the orientation of the polarisation axis, different weight factors, (see the instrument [[The RIMO|RIMOs]]):<br />
<br />
*HFI - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
<br />
<!--<br />
*HFI - LFI_RIMO_DX9_PTCOR6 - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - HFI-RIMO-3_16_detilt_t2_ptcor6.fits - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
<br />
{{PLADoc|fileType=rimo|link=The Plank RIMOS}}<br />
--><br />
<br />
===The scanning strategy===<br />
<br />
The scanning strategy, the three pointing angle for each detector for each sample: Detector pointings for the nominal mission covers about 15 months of observation from Operational Day (OD) 91 to OD 563 covering 3 surveys and half.<br />
<br />
===The scanbeam===<br />
<br />
The scanbeam modeled for each detector through the observation of planets. Which was assumed to be constant over the whole mission, though FEBeCoP could be used for a few sets of scanbeams too.<br />
<br />
* LFI: [[Beams LFI#Main beams and Focalplane calibration|GRASP scanning beam]] - the scanning beams used are based on Radio Frequency Tuned Model (RFTM) smeared to simulate the in-flight optical response. <br />
* HFI: [[Beams#Scanning beams|B-Spline, BS]] based on 2 observations of Mars.<br />
<br />
(see the instrument [[The RIMO|RIMOs]]).<br />
<br />
<!--<br />
<br />
*HFI - LFI_RIMO_DX9_PTCOR6 - {{PLASingleFile|fileType=rimo|name=HFI_RIMO_R1.00.fits|link=The HFI RIMO}}<br />
*LFI - HFI-RIMO-3_16_detilt_t2_ptcor6.fits - {{PLASingleFile|fileType=rimo|name=LFI_RIMO_R1.12.fits|link=The LFI RIMO}}<br />
[[Beams LFI#Effective beams|LFI effective beams]]<br />
--><br />
<br />
===Beam cutoff radii===<br />
<br />
N times geometric mean of FWHM of all detectors in a channel, where N<br />
<br />
{|border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"<br />
|+'''Beam cut off radius'''<br />
| '''channel''' || '''Cutoff Radii in units of fwhm''' || '''fwhm of full beam extent''' <br />
|-<br />
|30 - 44 - 70 || 2.5 ||<br />
|-<br />
|100 || 2.25 || 23.703699<br />
|-<br />
|143 || 3 || 21.057402<br />
|-<br />
|217-353 || 4 || 18.782754<br />
|-<br />
|sub-mm || 4 || 18.327635(545GHz) ; 17.0937