Frequency maps in Temperature and Polarization

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General description[edit]

Sky maps give the best estimate of the intensity and polarization (Stokes Q and U components), if available, of the signal from the sky after removal, as far as possible, of known systematic effects (mostly instrumental, but including also the solar and Earth-motion dipoles, Galactic stray light, and the zodiacal light). The Planck Collaboration has made three releases of maps, in 2013, 2015 and 2018. This section describes the 2018 release. For descriptions of the other two releases, please go to the sections at the end of this chapter related to 2013 and 2015.

In the 2013, 2015 and 2018 releases, sky maps are provided for the full Planck mission using all valid detectors in each frequency channel, and also for various subsets obtained by splitting the mission into various time ranges or into subsets of the detectors in a given channel, or by considering only odd or even pointing periods. These products are especially interesting for characterization purposes (see also the data validation section), though some are also useful for the study of source variability. The details of the start and end of the time ranges are given in the table below.

For this (2018) release, HFI is providing a more limited subset of maps that include the full channel maps, the half-mission and the odd-even ring splits. Also, note that for the 353 GHz band, both full channel and PSBs only maps are provided, and that by default it is the PBS-only maps that are served.


Ranges for mission and surveys
Range ODs HFI rings pointing-IDs Comment
Nominal mission 91 - 563 240 - 14723 00004200 - 03180200
Full mission 91 - 974 240 - 27005 00004200 - 05322620 For HFI
Full mission 91 - 1543 n/a 00004200 - 06511160 For LFI
Survey 1 91 - 270 240 - 5720 00004200 - 01059820
Survey 2 270 - 456 5721 - 11194 01059830 - 02114520
Survey 3 456 - 636 11195 - 16691 02114530 - 03193660
Survey 4 636 - 807 16692 - 21720 03193670 - 04243900
Survey 5 807 - 974 21721 - 26050 05267180 - 05322590 End of mission for HFI
Survey 5 807 - 993 n/a 05267180 - 06344800 End of survey for LFI
Survey 6 993 - 1177 n/a 06344810 - 06398120 LFI only
Survey 7 1177 - 1358 n/a 06398130 - 06456410 LFI only
Survey 8 1358 - 1543 n/a 06456420 - 06511160 LFI only
HFI mission-half-1 91 - 531 240 - 13471 00004200 - 03155580
HFI mission-half-2 531 - 974 13472 - 27005 03155590 - 05322590
LFI Year 1 91 - 456 n/a 00004200 - 02114520
LFI Year 2 456 - 807 n/a 02114530 - 04243900
LFI Year 3 807 - 1177 n/a 05267180 - 06398120
LFI Year 4 1177 - 1543 n/a 06398130 - 06511160

To help in further processing, there are also masks of the Galactic plane and of point sources, each provided for several different depths.

All sky maps are in HEALPix format, with Nside=1024 (for LFI 30, 44, and 70GHz) and 2048 (for LFI 70GHz and HFI), in Galactic coordinates, and with nested ordering.

WARNING: The HEALPix convention for polarization is not the same as the IAU convention (Section 8 on this page).

The signal is given in units of KCMB for 30 to 353 GHz, and of MJy.sr-1 (for a constant νIν energy distribution) for 545 and 857 GHz. For each frequency channel, the intensity and polarization maps are packaged into a "BINTABLE" extension of a FITS file together with a hit-counts map (or "hits map", for short, giving the number of observation samples that are accumulated in a pixel, all detectors combined) and with the variance and covariance maps. Additional information is given in the FITS file header. The structure of the FITS file is given in the FITS file structure section below.

Production process[edit]

Sky maps are produced by appropriately combining the data from all working detectors in a frequency channel over some period of the mission. They give the best estimate of the signal from the sky (unpolarized) after removal, as far as possible, of known systematic effects and of the dipole signals induced by the motion of the solar system in the CMB and of the Planck satellite in the solar system. In particular, they include the zodiacal light emission ("zodi" for short) and also the scattering from the far sidelobes of the beams (FSL). More on this below.

HFI processing[edit]

The mapmaking and calibration process is described in detail in the mapmaking section and in the Planck-2016-XLVI[1] paper, where detailed references can be found. In brief, the timelines are cleaned and calibrated and converted into HealPix rings (HPRs), then SRoll is applied to destripe them in polarised space (removal of very low frequency noise by minimising differences at ring crossing points), to remove knows systematic effects (including the flux calibration), and to project them onto a HealPix map.

The processing yields maps of the signal, hit counts and auto- and cross-variance maps for the 6 full channel and for a pseudo-channel built from the 353 PSBs only. For each channel HFI provides

  • a map for the full mission
  • two maps for each half-mission
  • two maps for built from odd or even rings only

for a total of 35 maps.

PR3 HFI products[edit]

Healpix Pixel Rings (HPRs)[edit]

SRoll main products are the HFI frequency maps. Nevertheless, we also make available the Healpix Pixel Rings (HPRs) of those maps, ie. the data before projection. See description of those files.

Frequency maps[edit]

The 35 HFI frequency maps of the PR3 Legacy Release are the followings:

PR3 HFI frequency maps
100 GHz 143 GHz 217 GHz 353 GHz 353_PSB GHz 545 GHz 857 GHz
Full mission I, Q, U I, Q, U I, Q, U I, Q, U I, Q, U I I
Half mission 1 I, Q, U I, Q, U I, Q, U I, Q, U I, Q, U I I
Half mission 2 I, Q, U I, Q, U I, Q, U I, Q, U I, Q, U I I
Odd rings I, Q, U I, Q, U I, Q, U I, Q, U I, Q, U I I
Even rings I, Q, U I, Q, U I, Q, U I, Q, U I, Q, U I I

See description of those files. These maps are available on the [Planck Legacy Archive].


LFI processing[edit]

LFI maps were constructed with the MADAM mapmaking code, version 3.7.4. The code is based on a generalized destriping technique, where the correlated noise component is modelled as a sequence of constant offsets, called "baselines". A noise filter was used to constrain the baseline solution, allowing the use of 0.25-s and 1-s baselines for the 30 and 44GHz, and 70 GHz channels, respectively. See section 6 of Planck-2020-A2[2].


Radiometers were combined according to the horn-uniform weighting scheme to minimize systematics. The flagged samples were excluded from the analysis by setting their weights to Cw-1 = 0. The Galaxy region was masked out in the destriping phase, to reduce errors arising from strong signal gradients. The polarization component was included in the analysis.

Dipole and Far Side Lobe correction
Input timelines are cleaned by the 4π-convolved dipole and Galactic stray light, obtained as a convolution of the 4π in-band far sidelobes and Galactic simulations, as explained in Planck-2020-A2[2].

Scaling of the maps due to beam effects is taken into account in the LFI's beam functions (as provided in the RIMO) which should be used for analysis of diffuse components.

Bandpass leakage correction 
LFI high-resolution maps have been reseleased corrected for bandpass leakage or uncorrected. Further details about the procedure used to generate the bandpass correction maps can be found in section 7 of Planck-2020-A2[2].
Map zero-level 
The 30, 44 and 70 GHz, maps are corrected for a zero-level monopole by applying an offset correction (see the LFI Calibration paper, Planck-2015-A05[3]). Note that the offset applied is indicated in the header as a comment keyword.

A detailed description of the mapmaking procedure is given in Planck-2013-II[4], Planck-2015-A02[5], Planck-2015-A06[6] and in the Mapmaking section here, in Planck-2020-A2[2] only a summary is reported.

Types of map[edit]

Full-mission, full-channel maps (7 HFI, 4 LFI)[edit]

Full channel maps are built using all the valid detectors of a frequency channel and cover either the full or the nominal mission. For HFI, the 143-8 and 545-3 bolometers are rejected entirely, since they are seriously affected by RTS noise. HFI provides the Q and U components for the 100, 143, 217 and 353 GHz channels only. LFI provides the I, Q, and U maps for all the channels. Note that the HFI and LFI Q and U maps are corrected for bandpass leakage, version without correction for LFi is also provided. The I, Q, and U maps are displayed in the figures below. The colour range here is set using a histogram equalization scheme (from HEALPix) that is useful for these non-Gaussian data fields. For visualization purposes, the Q and U maps shown here have been smoothed with a 1° Gaussian kernel, otherwise they look like noise to the naked eye. The 70 GHz full map is also available at Nside=2048.

The high dynamic range colour scheme of the Planck maps is described here.



Full mission light maps, full channel maps (7 HFI, 7 LFI)[edit]

These maps are based on the Full mission maps but contain fewer columns, IQU from 30 to 353 GHz, and I only at 545 and 857 GHz. These maps have been produced to reduce the transfer time of the most downloaded frequency full mission maps.

Single-survey, full-channel maps (35 LFI)[edit]

Single-survey maps are built using all valid detectors of a frequency channel; they separately cover the different sky surveys. The surveys are defined as the times over which the satellite spin axis rotates by 180°, which, due to the position of the detectors in the focal plane does not cover the full sky, but a fraction between about 80% and 90%, depending on detector position. During adjacent surveys the sky is scanned in opposite directions (more precisely it is the ecliptic equator that is scanned in opposite directions). While these are useful to investigate variable sources, they are also used to study the systematics of the time-response of the detectors as they scan bright sources, like the Galactic Plane, in different directions during different survey. Note that the HFI and LFI missions cover five and eight surveys, respectively, and in the case of HFI the last survey in incomplete. The 70 GHz survey maps are available also at Nside=2048. Note that LFI provides a special survey-map combination used in the low-ℓ analysis; this maps, available at the three LFI frequencies, 30, 44, and 70 GHz, was built using the combination of Surveys 1, 3, 5, 6, 7, and 8.

Year maps, full-channel maps (16 LFI)[edit]

These maps are built using the data of Surveys 1+2, Surveys 3+4, and so forth. They are used to study long-term systematic effects. The 70 GHz years maps are available also at Nside=2048.

Half-mission maps, full-channel maps (14 HFI, 12 LFI)[edit]

For HFI, the half mission is defined after eliminating those rings that are discarded for all bolometers, many of which occurred during the 5th survey when the "End-of-Life" tests were performed. The remaining rings are divided in half to define the two halves of the mission. This exercise is done for the full mission only.

For LFI, instead of the half-mission maps, the following year combinations have been created: Year 1+2, Year 1+3, Year 2+4, Year 3+4,

Full mission, single-detector maps (22 LFI)[edit]

For LFI, all the 22 Radiometers maps are available, and (obviously) only in Stokes I.

Full-mission, detector-set or detector-pairs maps (8 LFI)[edit]

The objective here is to build independent temperature (I) and polarization (Q and U) maps using the two pairs of polarization-sensitive detectors of each channel where they are available, i.e., for the 44-353 GHz channels. The table below indicates which detectors were used to build each detector set (detset).

Definition of LFI detector pairs
Frequency Horn pair Comment
44 GHz 24 This map is only in temperature
44 GHz 25 and 26
70 GHz 18 and 23 Available also at Nside=2048
70 GHz 19 and 22 Available also at Nside=2048
70 GHz 20 and 21 Available also at Nside=2048

Half-ring maps (62 LFI)[edit]

These maps are similar to the ones described above, but are built using only the first or the second halves of each ring (or pointing period). The HFI provides half-ring maps for the full mission only, as well as for the full channel, the detsets, and the single bolometers. The LFI provides half-ring maps for the full mission in each channel (70 GHz also at Nside=2048), for the full-mission radiometers, and for the full-mission horn pairs.

=== Odd and even rings maps (14 HFI)

As the name indicates, these are generated by using only the odd or only the even rings.

Caveats and known issues[edit]

HFI frequency maps[edit]

Some imperfections have shown up in the tests of the HFI PR3 maps that were previously hidden by higher-level systematics in the previous PR2 data. These lead to guidelines for the proper use of the HFI PR3 data. See Planck-2020-A3[7] for a detailed description of all these issues.

Update 12 Sep 2018: Covariance matrices in PR3.00 frequency maps FITS files were not correctly computed and contained wrong values. They must not be used for any purpose. These maps have been removed from the PLA. Version 3.01 must be used instead. Intensity, polarization and hit count maps have not changed.

Monopoles[edit]

Monopoles, which cannot be extracted from Planck data alone, are adjusted at each frequency (as was done in the previous PR2 release). For component separation, this provides maps that can be used directly in combination with other tracers. See Planck-2020-A3[7] for a detailed discussion. In the 2018 maps, three monopoles have been adjusted:

  • during production of the HFI frequency maps, an HI correlation analysis is carried out to adjust the overall monopole of the map to be consistent with the intensity of the Galactic dust foreground at high galactic latitudes (this adjustment was also done in the 2016 maps)
  • a monopole corresponding to the zero-level of the CIB (Cosmic Infrared Background) estimated from a galaxy evolution model has been added to the maps (as for the 2016 maps)
  • a monopole corresponding to the zero-level of zodiacal emission, representative of the high ecliptic latitude emission regions, has been added to the maps (note that this was not done in the 2016 maps).

It is recommended that for work separating CMB and diffuse Galactic components from HFI frequency maps, the CIB and Zodiacal emission monopoles should first be removed. Furthermore, especially for applications at low intensity, it is critical to appreciate that there are significant uncertainties in the zero levels in the Galactic maps. It is therefore also recommended that the maps be correlated with the HI map at high latitude, following the detailed methodology set out in Planck-2013-VIII[8] and [9]. Consideration should also be given to the possible effect of dust in the warm ionized medium, as discussed and quantified in [9].

Solar dipole residual[edit]

The Planck 2015 Solar dipole is removed from the PR3 HFI maps to be consistent with LFI maps and to facilitate comparison with the previous PR2 ones. The best Solar dipole determination from HFI PR3 data shows a small shift in direction of about 1', but a 1.8 μK lower amplitude. Removal of the Planck 2015 Solar dipole thus leaves a small but non-negligible dipole residual in the HFI PR3 maps. To correct for this, and adjust maps at the best photometric calibration, users of the HFI PR3 maps should:

  1. put back into the maps the Planck 2015 Solar dipole (d,l,b)= (3364.5 ± 2.0 μK, 264.00 ± 0.03°, 48.24 ± 0.02°),
  2. include the absolute calibration frequency bias, i.e., multiply by 1 minus the calibration bias,
  3. lastly, remove the HFI 2018 Solar dipole.
Use of the 353 GHz SWBs[edit]

In 2018, two types of maps at 353 GHz are provided, one including only PSBs and one including both PSBs and SWBs. For reasons detailed in Planck-2020-A3[7], it is recommended to use the former (i.e. only including PSBs). The alternative one including the 353 GHz SWBs should be used only for specific uses such as, for example, increasing the signal to noise level at high multipoles.

Color correction and component separation[edit]

In 2018 the SRoll algorithm has been used to produce the frequency maps. This algorithms adjusts by construction all single bolometer maps to the band average response. For this reason, it becomes impossible to use the different individual bolometer responses to extract foreground component maps, and the individual bolometer maps are not provided as part of the release. See Planck-2020-A3[7] for a detailed description. Note also that for the same reason, the effective bandpass response of the 2018 maps is not the same as for the 2015 maps. The new bandpass response is established in the 2018 RIMO.

Sub-pixel effects in very bright regions[edit]

The bandpass corrections have been optimized for high latitude regions which implied to reduce the noise of the CO and dust bandpass templates to avoid the introduction of significant correlated noise. The effect is negligible for dust but not for CO in very bright regions. As a consequence, some systematic effects (which appear as striping) appear in some of the maps in the brightest galactic emission regions. See detailed description.

LFI Frequency maps[edit]

TBD

Inputs[edit]

HFI inputs[edit]

The HFI mapmaking takes as input:

  • the cleaned TOIs of the signal from each detector, together with their flags, produced by the TOI processing pipeline;
  • the TOIs of pointing (quaternions), described in Detector pointing;
  • bolometer-level characterization data, from the DPC's internal IMO (not distributed);
  • Planck orbit data, used to compute and remove the Earth's dipole;
  • Planck solar dipole information, used to calibrate the CMB channels;
  • planet models used to calibrate the Galactic channels.

LFI inputs[edit]

The MADAM mapmaker takes as input:

  • the calibrated timelines (for details see TOI Processing);
  • the detector pointings (for details see Detector pointing);
  • the noise information in the form of 3-parameter (white noise level σ, slope, and knee frequency fknee) noise model (for details see RIMO).

Related products[edit]

Masks[edit]

This section presents the "general purpose" masks. Other masks specific to certain products are packaged with those products.

Note that for this release, HFI has not produced any new masks.

Point source masks[edit]

For HFI and LFI two sets of point-source masks are provided.

  • Intensity masks, which remove sources detected with S/N > 5.
  • Polarisation masks, which remove sources that have polarization detection significance levels of 99.97 % or greater at the position of a source detected in intensity. They were derived from the polarization maps with dust foreground bandpass mismatch leakage corrections applied. The area excised around each source has a radius of 3σ (width) of the beam, i.e., 1.27 FWHM (for LFI the cut around each source has a radius of 32 arcmin at 30GHz, 27 arcmin at 44 GHz, and 13 arcmin at 70 GHz).

Both sets of masks are found in the files HFI_Mask_PointSrc_2048_R2.00.fits and LFI_Mask_PointSrc_2048_R2.00.fits, in which the first extension contains the intensity masks, and the second contains the polarization masks.

Galactic plane masks[edit]

Eight Galactic emission masks are provided, giving 20, 40, 60, 70, 80, 90, 97, and 99% sky coverage, derived from the 353 GHz map after CMB subtraction. These are independent of frequency channel. Three versions are given: not apodized; and apodized by 2° and 5°. The filenames are HFI_Mask_GalPlane-apoN_2048_R2.00.fits, where N = 0, 2, and 5.

The masks are shown below. The eight "GalPlane" masks are combined (added together) and shown in a single figure for each of the three apodizations. While the result is quite clear for the case of no apodization, it is less so for the apodized case. The "PointSrc" masks are shown separately for the intensity case.

File names[edit]

The FITS filenames are of the form {H|L}FI_SkyMap_fff{-tag}_Nside_R3.nn_{coverage}-{type}.fits, where "fff" are three digits to indicate the Planck frequency band, "tag" indicates the single detector or the detset (no "tag" indicates full channel), "Nside" is the HEALPix Nside value of the map, "coverage" indicates which part of the mission is covered (full, half mission, survey, year, etc.), and the optional "type" indicates the subset of input data used. The table below lists the products by type, with the appropriate unix wildcards that form the full filename.

HFI FITS filenames
Coverage Filename
Full channel, full mission HFI_SkyMap_fff{-tag}_2048_R3.??_full.fits
Full channel, half mission HFI_SkyMap_fff{-tag}_2048_R3.??_halfmission-{1/2}.fits
Full channel, full mission, odd/even ring HFI_SkyMap_fff{-tag}_2048_R3.??_{odd/even}ring.fits
LFI FITS filenames
Coverage Filename Half-ring filename Comment
Full channel, full mission LFI_SkyMap_???_1024_R3.??_full.fits LFI_SkyMap_???_1024_R3.??_full-ringhalf-?.fits 70GHz is corrected for Template
Full channel, full mission BandPass corrected LFI_SkyMap_???-BPassCorrected_1024_R3.??_full.fits LFI_SkyMap_???-BPassCorrected_???_1024_R3.??_full-ringhalf-?.fits 70GHz is corrected for Template
Full channel, single survey LFI_SkyMap_???_1024_R3.??_survey-?.fits n/a n/a
Full channel, survey combination LFI_SkyMap_???_1024_R3.??_survey-1-3-5-6-7-8.fits n/a n/a
Full channel, survey combination BandPass corrected LFI_SkyMap_???_1024_R3.??-BPassCorrected_survey-1-3-5-6-7-8.fits n/a n/a
Full channel, single year LFI_SkyMap_???_1024_R3.??_year-?.fits n/a n/a
Full channel, single year BandPass corrected LFI_SkyMap_???-BPassCorrected_1024_R3.??_year-?.fits n/a n/a
Full channel, year combination LFI_SkyMap_???_1024_R3.??_year?-?.fits n/a n/a
Full channel, year combination BandPass corrected LFI_SkyMap_???-BPassCorrected_1024_R3.??_year?-?.fits n/a n/a
Horn pair, full mission LFI_SkyMap_???-??-??_1024_R3.??_full.fits LFI_SkyMap_???_??-??_1024_R3.??_full-ringhalf-?.fits n/a
Single radiometer, full mission LFI_SkyMap_???-???_1024_R3.??_full.fits LFI_SkyMap_???-???_1024_R3.??_full-ringhalf-?.fits n/a

For the benefit of users who are only looking for the frequency maps with no additional information, we also provide a file combining the nine frequency maps as separate columns in a single extension. The nine columns in this file contain the intensity maps only and no other information (hits maps or variance maps) is provided.

FITS file structure[edit]

The FITS files for the sky maps contain a minimal primary header with no data, and a BINTABLE extension (EXTENSION 1, EXTNAME = FREQ-MAP) containing the data. The structure is shown schematically in the figure below. The FREQ-MAP extension contains a 3- or 10-column table that contain the signal, hit-count, and variance maps, all in HEALPix format. The 3-column case is for intensity only maps, while the 10-column case is for polarization. The number of rows is the number of map pixels, which is Npix = 12 Nside2 for HEALPix maps, where Nside = 1024 or 2048 for most the maps presented in this section.

FITS file structure.

Note that file sizes are approximately 0.6 GB for I-only maps and 1.9 GB for IQU maps at Nside=2048, but about 0.14 GB for I-only maps and 0.45 GB for IQU maps at Npix=1024 .

Keywords indicate the coordinate system ("GALACTIC"), the HEALPix ordering scheme ("NESTED"), the units (KCMB or MJy.sr-1) of each column, and of course the frequency channel ("FREQ"). Where polarization Q and U maps are provided, the "COSMO" polarization convention (used in HEALPix) is adopted, and it is specified in the "POLCCONV" keyword (see this section). The "COMMENT" fields give a one-line summary of the product, and some other information useful for traceability within the DPCs. The original filename is also given in the "FILENAME" keyword. The "BAD_DATA" keyword gives the value used by HEALPix to indicate pixels for which no signal is present (these will also have a hit-count value of 0). The main parameters are summarized in the table below.

Sky map file data structure
1. EXTNAME = 'FREQ-MAP' : Data columns
Column name Data type Units Description
I_STOKES Real*4 KCMB or MJy.sr-1 Stokes I map
Q_STOKES Real*4 KCMB or MJy.sr-1 Stokes Q map (optional)
U_STOKES Real*4 KCMB or MJy.sr-1 Stokes U map (optional)
HITS Int*4 none The hit-count map
II_COV Real*4 KCMB2 or (MJy.sr-1)2 II variance map
IQ_COV Real*4 KCMB2 or (MJy.sr-1)2 IQ variance map (optional)
IU_COV Real*4 KCMB2 or (MJy.sr-1)2 IQ variance map (optional)
QQ_COV Real*4 KCMB2 or (MJy.sr-1)2 QQ variance map (optional)
QU_COV Real*4 KCMB2 or (MJy.sr-1)2 QU variance map (optional)
UU_COV Real*4 KCMB2 or (MJy.sr-1)2 UU variance map (optional)
Keyword Data type Value Description
PIXTYPE String HEALPIX
COORDSYS String GALACTIC Coordinate system
ORDERING String NESTED Healpix ordering
POLCCONV String COSMO Polarization convention
NSIDE Int 1024 or 2048 HEALPix Nside
FIRSTPIX Int*4 0 First pixel number
LASTPIX Int*4 12 Nside2 – 1 Last pixel number
FREQ String nnn Frequency channel


The same structure applies to all "SkyMap" products, independent of whether they are full channel, survey of half-ring. The distinction between the types of maps is present in the FITS filename (and in the traceability comment fields).

Polarization convention used in the Planck project[edit]

The FITS keyword "POLCCONV" defines the polarization convention of the data within the file. The Planck collaboration used the COSMO convention for the polarization angle (as usually adopted in space-based and other CMB missions), whereas other subfields of astronomy usually adopt the IAU convention. The basic difference comes down to whether one thinks of the light rays being emitted from the origin (the usual mathematics/physics convention) or converging on the observer from the sky (the usual astronomy convention), and hence the "obvious" choice is different for a physicists and for an astronomer. Given that CMB results are of interest to a wide range of both physicists and astronomers, there is no single choice of convention that everyone would regard as self-evident. Hence one simply has to be aware of the convention being adopted. Because of this the Planck Collaboration has taken pains to point out which convention is being used in publications and in data releases. In the following we describe the difference between these two conventions, and the consequence if it is not taken into account correctly in the analysis.

Figure 1. Polarization conventions, showing the COSMO convention (left) and IAU convention (right). The vector [math]\hat{z}[/math] points in the outward direction in COSMO, and inwards in IAU. The bottom panel refers to the plane tangent to the sphere.

Changing the orientation convention is equivalent to a transformation ψ'=π-ψ of the polarization angle (Figure 1). The consequence of this transformation is the inversion of the Stokes parameter U. The components of the polarization tensor in the helicity basis [math]\epsilon^{\pm}=(\hat{x}\pm i\hat{y})/\sqrt{2}[/math] are

[math] (Q+iU)(\hat{n}) = \sum _{\ell m}a_{2,lm}{}_{2}Y_{\ell }^{m}(\hat{n}), \\(Q-iU)(\hat{n}) = \sum _{\ell m}a_{-2,lm}{}_{2}Y_{\ell }^{m}(\hat{n}), [/math]

where [math]{}_{2}Y_{\ell }^{m}(\hat{n})[/math] are the spin-weighted spherical harmonic functions. The E and B modes can be defined as

[math] E(\hat{n}) = \sum_{\ell m}a_{E,\ell m}Y_{\ell }^{m}(\hat{n}), \\B(\hat{n}) = \sum_{\ell m}a_{B,\ell m}Y_{\ell }^{m}(\hat{n}), [/math]

where the coefficients aE,ℓm and aB,ℓm are derived from linear combinations of the a2,ℓm, a-2,ℓm, defined implicitly in the first equation (Q± iU).

Test gradient.jpg
Figure 2. Error on Planck-LFI 70 GHz EE (top) and BB (bottom) power spectra, in the case of an incorrect choice being made for the polarization coordinate system convention (IAU instead of COSMO).

The effect of the sign inversion of U on the polarization spectra is a non-trivial mixing of E and B modes. An example of the typical error on EE and BB auto-spectra in the case of the wrong choice for the polarization basis is shown in Figure 2.

One should be careful to be aware of the polarization convention that is being adopted. If the IAU convention is used in computing the power spectra, then the sign of the U component of the Planck maps must be inverted before computing the E and B modes.

In astronomical applications it is common to define a pseudo-vector P to show the amplitude and orientation of polarization on a map. When plotting these line segments to show the orientation of the plane of polarization (or the orthogonal direction, often considered to be the projection of the magnetic field), the results are the same for both the COSMO and IAU conventions. This because the appearance of P is a property of the radiation and hence not affected by the sign of U.

Note on the convention used in the Planck Catalogue of Compact Sources (PCCS)[edit]

Planck non-cosmology papers sometimes follow the IAU convention for internal analysis, for ease of comparison with other studies (e.g., comparison of Planck-derived thermal dust emission polarization with the optical polarization of starlight). Nevertheless, Planck data products, such as component-separated maps, still use the COSMO convention. The one exception is for the compact source catalogue. Because catalogues of astronomical objects found by Planck need to be compared directly with other source catalogues, the polarized sources described in the Planck Catalogue of Compact Sources follow the IAU convention, and the polarization angles are defined on an interval of [-90°,90°]. To switch to the COSMO convention, the polarization angles listed in the catalogue should be shifted by 90° and multiplied by -1.

References[edit]


Other releases: 2020-NPIPE, 2015 and 2013[edit]

Expand

2020 - NPIPE

Expand

2015 Sky temperature and polarization maps

Expand

2013 Sky temperature maps

(Planck) High Frequency Instrument

(Planck) Low Frequency Instrument

(Hierarchical Equal Area isoLatitude Pixelation of a sphere, <ref name="Template:Gorski2005">HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere, K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, M. Bartelmann, ApJ, 622, 759-771, (2005).

Cosmic Microwave background

Flexible Image Transfer Specification

random telegraphic signal

Planck Legacy Archive

reduced IMO

To be defined / determined

Data Processing Center

Full-Width-at-Half-Maximum

Noise Equivalent Temperature

analog to digital converter

To be confirmed

sudden change of the baseline level inside a ring

Attitude History File

[ESA's] Mission Operation Center [Darmstadt, Germany]

Line Of Sight