Specially processed maps

Introduction

This section describes the map-based products that required special processing.

2015 Lensing map

We distribute the minimum-variance (MV) lensing potential estimate presented in Planck-2015-A15 as part of the 2014 data release. This map represents an estimate of the CMB lensing potential on approximately 70% of the sky, and also forms the basis for the Planck 2014 lensing likelihood. It is produced using filtered temperature and polarization data from the SMICA DX11 CMB map; its construction is discussed in detail in Planck-2015-A09.

The estimate is contained in a single gzipped tarball named COM_CompMap_Lensing_2048_R2.00.tgz. Its contents are described below.

Contents of Lensing package

Filename	Format	Description
dat_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=2048[/math]	Contains the estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math].
mask.fits.gz	HEALPix FITS format map, with [math]N_{\rm side}=2048[/math]	Contains the lens reconstruction analysis mask.
nlkk.dat	ASCII text file, with columns = ([math]L[/math], [math]N_L [/math], [math]C_L+N_L[/math])	The approximate noise [math]N_L[/math] (and signal+noise, [math]C_L+N_L[/math]) power spectrum of [math] \hat{\kappa}_{LM} [/math], for the fiducial cosmology used in Planck-2015-A13.

2015 Compton parameter map

We distribute here the Planck full mission Compton parameter maps (y-maps hereafter) obtained using the NILC and MILCA component-separation algorithms as described in Planck-2015-A22. We also provide the ILC weights per scale and per frequency that were used to produce these y-maps. IDL routines are also provided to allow the user to apply those weights. Compton parameters produced by keeping either the first or the second half of stable pointing periods are also provided; we call these the FIRST and LAST y-maps. Additionally we construct noise estimates of full mission Planck y-maps from the half difference of the FIRST and LAST y-maps. These estimates are used to construct standard deviation maps of the noise in the full mission Planck y-maps, which are also provided. To complement this we also provide the power spectra of the noise estimate maps after correcting for inhomogeneities using the standard deviation maps. We also deliver foreground masks including point-source and Galactic masks.

The full data set is contained in a single gzipped tarball named COM_CompMap_YSZ_R2.00.fits.tgz. Its contents are described below. Temporarily the tarball file can be found in the Supplement Data area of the PLA (go to pla.esac.esa.int/pla, go to Subsection Supplementary Data and type "YSZ" in the search form)

Contents of COM_CompMap_YSZ_R2.00.fits.tgz}

Filename	Format	Description
nilc_ymaps.fits	HEALPix FITS format map in Galactic coordinates with [math]N_{\rm side}=2048 [/math]	Contains the NILC full mission, FIRST and LAST y-maps.
milca_ymaps.fits	HEALPix FITS format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math]	Contains the MILCA full mission, FIRST and LAST y-maps.
nilc_weights_BAND.fits	HEALPix FITS format map in Galactic coordinates with [math] N_{\rm side} = 128 [/math]	Contains the NILC ILC weights for the full mission y-map for band BAND 0 to 9. For each band we provide a weight map per frequency.
milca_FREQ_Csz.fits	HEALPix FITS format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math]	Contains the MILCA ILC weights for the full mission y-map for frequency FREQ (100, 143, 217, 353, 545, 857). For each frequency we provide a weight map per filter band.
nilc_stddev.fits	HEALPix FITS format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math]	Contains the stddev map for the NILC full mission y-map.
milca_stddev.fits	HEALPix FITS format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math]	Contains the stddev maps for the MILCA full mission y-map.
nilc_homnoise_spect.fits	ASCII table FITS format	Contains the angular power spectrum of the homogeneous noise in the NILC full mission y-map.
milca_homnoise_spect.fits	ASCII table FITS format	Contains the angular power spectrum of the homogeneous noise in the MILCA full mission y-map.
masks.fits	HEALPix FITS format map, with [math] N_{\rm side} = 2048 [/math]	Contains foreground masks.
nilc_bands.fits	ASCII table FITS format	Contains NILC wavelet bands in multipole space

2015 Lensing-induced B-mode map

We distribute the lensing-induced B-mode map presented in PIP116. The lensing B-mode Stokes parameter maps are produced by combining the lensing potential reconstruction from the SMICA CMB temperature map with E-mode data from the SMICA CMB polarization maps. The SMICA temperature and polarization products are described in Planck-2015-A09. The lensing-induced B-mode polarization maps are used in cross-correlation with the SMICA CMB polarization maps to obtain a lensing B-mode power spectrum measurement on approximately 70% of the sky, as described in PIP116.

We provide both raw products, which can be utilized to generate products adapted to one's specific needs in term of mask, filtering, etc., and "ready-to-use" products for cross-correlation study purposes.

Raw products

We deliver the non-normalized lensing-induced Stokes parameter maps, labelled [math] \bar{Q}^{\rm{lens}} [/math] and [math] \bar{U}^{\rm{lens}} [/math], which form the basis of the final lensing B-mode estimator defined in Eq. (6) of PIP116. They are defined as

[math] \begin{eqnarray} \bar Q^{\rm{lens}}({\bf n}) &=& \widetilde Q^{E}({\bf n}) \cdot \nabla \widetilde \phi({\bf n}) \\ \bar U^{\rm{lens}}({\bf n}) &=& \widetilde U^{E}({\bf n}) \cdot \nabla \widetilde \phi({\bf n}), \end{eqnarray} [/math]

where [math] \widetilde Q^{E} [/math] and [math] \widetilde U^{E} [/math] are the filtered pure E-mode polarization maps given in Eq. (5) of PIP116, and [math] \widetilde \phi[/math], the filtered lensing potential estimate.

We also provide the normalization transfer function [math] \mathcal{B}_\ell [/math] defined in Eq. (11) of PIP116, as well as the 'L70' mask [math] M({\bf n}) [/math] that retains 69% of the sky before apodization, and its apodized version [math] \tilde{M}({\bf n}) [/math], which has an effective sky fraction [math] f_{\rm{sky}}^{\rm{eff}} = 65\% [/math].

As an example of the utilization of these products, the lensing B-mode Stokes parameter maps that are shown in the figure 4 of PIP116 are generated from

[math] Q^{\rm{lens}} \pm i U^{\rm{lens}} = \sum_{\ell m} \left( G_\ell \mathcal{B}_\ell^{-1} \int d{\bf n} {\, }_{\pm 2}Y_{\ell m}^*({\bf n}) \left(\bar{Q}^{\rm{lens}} \pm i \bar{U}^{\rm{lens}} \right) \right) {\, }_{\pm 2}Y_{\ell m}({\bf n}) [/math],

where [math]G_\ell[/math] is a Gaussian function of 60' FWHM (introduced for highlighting large angulare scales, it can be replaced by any other filters or removed). This can be practically done by ingesting [math]\bar{Q}^{\rm{lens}} [/math] and [math] \bar{U}^{\rm{lens}} [/math] in the smoothing HEALPIX routine, and using the product [math] G_\ell\mathcal{B}_\ell^{-1} [/math] as an input filtering function.

Specific products

We provide the lensing B-mode spherical harmonic coefficient estimate [math] B_{\ell m}^{\rm{lens}} [/math] on approximately 70% of the sky.

It can also be constructed using the raw products described above from

[math] B_{\ell m}^{\rm{lens}} = f_{10 \rightarrow 2000} \, \mathcal{B}_\ell^{-1} \, \, {\, }_{\pm 2}\mathcal{Y} \left[ \tilde{M}({\bf n}) \left( \bar{Q}^{\rm{lens}}({\bf n}) \pm i \bar{U}^{\rm{lens}}({\bf n}) \right) \right] [/math],

where [math] f_{10 \rightarrow 2000} [/math] is a function for producing band-powers over the range [math] 10 \le \ell \le 2000 [/math], and [math] {\, }_{\pm2}\mathcal{Y} [/math] is a short-hand notation for transforming a map into spin-weighted spherical harmonic coefficients [math] {\, }_{+2}a_{\ell m}[/math], [math]{\, }_{-2}a_{\ell m} [/math] and forming [math]1/(2i)\left({\, }_{+2}a_{\ell m} - {\, }_{-2}a_{\ell m}\right)[/math]. This can be done using e.g. the HEALPix "anafact" tool.

The lensing B-mode power spectrum estimate [math] \hat{C}_\ell^{BB^{\rm{lens}}} [/math] discussed in PIP116 is obtained by forming the cross-correlation power spectrum of [math] B_{\ell m}^{\rm{lens}} [/math] and the B-mode data from the SMICA polarization maps [math] B_{\ell m} [/math]:

[math] \hat{C}_\ell^{BB^{\rm{lens}}} = \frac{\left(f_{\rm{sky}}^{\rm{eff}}\right)^{-1}}{2 \ell +1} G_\ell^{-2} \sum_m B_{\ell m}^* B_{\ell m}^{\rm{lens}}[/math],

where [math] G_\ell [/math] is the 5' Gaussian beam that convolves the SMICA CMB maps.

The products are contained in a single gzipped tarball named COM_Lensing-Bmode_R2.00.tgz. Its contents are described below.

Contents of Lensing B-mode package

Filename	Format	Description
bar_q_lens_map.fits	HEALPix FITS format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math]	Contains the non-normalized lensing-induced Q Stokes parameter map [math] \bar Q^{\rm{lens}}({\bf n}) [/math].
bar_u_lens_map.fits	HEALPix FITS format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math]	Contains the non-normalized lensing-induced U Stokes parameter map [math] \bar U^{\rm{lens}}({\bf n}) [/math].
mask.fits	HEALPix FITS format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math]	The L70 mask.
mask_noapo.fits	HEALPix FITS format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math]	The L70 mask without apodization.
transfer_function_b_l.dat	ASCII text file, with columns = ([math]\ell[/math], [math] \mathcal{B}_\ell [/math])	The transfer function.
lensing_bmode_b_lm.fits	HEALPix FITS format alm, with [math] \ell_{\rm max} = 2000 [/math]	Contains the lensing B-mode harmonic coefficients [math] B_{\ell m}^{\rm{lens}} [/math].
lensing_bmode_bandpowers.dat	ASCII text file, with columns = ([math]\ell_{\rm min}[/math], [math]\ell_{\rm b} [/math], [math]\ell_{\rm max} [/math], [math] \hat{C}_{\ell_{\rm b}}^{BB^{\rm{lens}}} [/math], [math] \Delta \hat{C}_{\ell_{\rm b}}^{BB^{\rm{lens}}} [/math] )	The lensing B-mode bandpower estimate on approximativily 70% of the sky and over the multipole range from 10 to 2000 shown in figure 9 of (for plotting purpose only).