Lensing

2018 Lensing products

2018 Lensing maps

We distribute several variations of lensing potential estimates presented in Planck-2020-A8 as part of the 2018 data release, together with matching simulation packages.

There are 4 lensing data packages:

• COM_Lensing_4096_R3.00

Baseline lensing potential estimates from SMICA DX12 CMB maps. Provided are temperature-only (TT), polarization-only (PP) and minimum-variance (MV) estimates.

• COM_Lensing_Sz_4096_R3.00

Variations obtained without galaxy cluster masking.

• COM_Lensing_Inhf_2048_R3.00

Variations obtained using inhomogeneous noise filtering.

• COM_Lensing-Szdeproj_4096_R3.00

Variation obtained from thermal Sunyaev-Zeldovich deprojected SMICA CMB map (TT only).

Each map represents an estimate of the CMB lensing potential on approximately 70% of the sky. The lensing estimates from COM_Lensing_4096_R3.00 also forms the basis for the Planck 2018 lensing likelihood.

These data packages have the following common file structure:

Contents of lensing data package COM_Lensing_4096_R3.00

Filename	Format	Description
mask.fits.gz	HEALPix FITS format map, with [math]N_{\rm side}=2048[/math]	Lens reconstruction analysis mask.
TT/dat_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math] (from temperature only, after mean-field subtraction).
TT/mf_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Estimated lensing convergence mean-field [math] \langle \hat{\kappa}_{LM} \rangle_{\rm{MC}} [/math] subtracted from the raw temperature-only data estimate.
PP/dat_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=2048[/math]	Estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math] (from polarization only, after mean-field subtraction).
PP/mf_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Estimated lensing convergence mean-field [math] \langle \hat{\kappa}_{LM} \rangle_{\rm{MC}} [/math] subtracted from the raw polarization-only data estimate.
MV/dat_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math] (minimum-variance estimate from temperature and polarization, after mean-field subtraction).
MV/mf_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Estimated lensing convergence mean-field [math] \langle \hat{\kappa}_{LM} \rangle_{\rm{MC}} [/math] subtracted from the raw minimum variance data estimate.
TT/nlkk.dat	ASCII text file, with columns = ([math]L[/math], [math]N_L [/math], [math]C_L+N_L[/math])	Temperature-only reconstruction 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-2020-A8.
PP/nlkk.dat	ASCII text file, with columns = ([math]L[/math], [math]N_L [/math], [math]C_L+N_L[/math])	Polarization-only reconstruction 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-2020-A8..
MV/nlkk.dat	ASCII text file, with columns = ([math]L[/math], [math]N_L [/math], [math]C_L+N_L[/math])	Minimum-variance reconstruction 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-2020-A8.

with slight variations:

- in COM_Lensing_Inhf_2048_R3.00, all HEALPix FITS format alm files have [math]L_{\rm max}=2048[/math].

- COM_Lensing-Szdeproj_4096_R3.00 only provides the temperature-only reconstruction.

The matching 4 lensing simulation packages are

• COM_Lensing-SimMap_4096_R3.00
• COM_Lensing-SimMap_Sz_4096_R3.00
• COM_Lensing-SimMap_Inhf_2048_R3.00
• COM_Lensing-SimMap-Szdeproj_4096_R3.00

with the following content:

Contents of lensing simulation package COM_Lensing-SimMap_4096_R3.00

Filenames	Format	Description
/inputs/mask.fits.gz	compressed HEALPix FITS format map, with [math]N_{\rm side}=2048[/math]	Lens reconstruction analysis mask.
/inputs/FFP10_wdipole_lenspotentialCls.dat	ASCII text file, with columns = ([math]L[/math], [math]C_L^{TT} [/math], [math]C_L^{EE} [/math],[math]C_L^{BB} [/math],[math]C_L^{TE} [/math],[math]C_L^{\phi\phi} [/math],[math]C_L^{T\phi} [/math],[math]C_L^{E\phi} [/math])	Input unlensed CMB spectra of the fiducial cosmology used in Planck-2020-A8.
TT/sim_klm_{???}.fits	300 HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math] (from temperature only, no mean-field subtraction) of all 300 FFP10 simulations used in Planck-2020-A8.
PP/sim_klm_{???}.fits	300 HEALPix FITS format alm, with [math]L_{\rm max}=2048[/math]	Estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math] (from polarization only, no mean-field subtraction) of all 300 FFP10 simulations used in Planck-2020-A8.
MV/sim_klm_{???}.fits	300 HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math] (minimum-variance estimate from temperature and polarization, no mean-field subtraction) of all 300 FFP10 simulations used in Planck-2020-A8.
TT/dat_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math] (from temperature only, no mean-field subtraction).
PP/dat_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=2048[/math]	Estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math] (from polarization only, no mean-field subtraction).
MV/dat_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Estimated lensing convergence [math] \hat{\kappa}_{LM} = \frac{1}{2} L(L+1)\hat{\phi}_{LM} [/math] (minimum-variance estimate from temperature and polarization, no mean-field subtraction).
TT/nlkk.dat	ASCII text file, with columns = ([math]L[/math], [math]\textrm{RD-}N_L^{0} [/math], [math]\textrm{MC-}N_L^{0}[/math], [math]N_L^{1}[/math], [math]{PS}_L[/math], [math]\langle \hat C^{\kappa\kappa}_L - C_L^{\kappa\kappa, \rm fid}\rangle_{\rm MC}[/math], [math]1/\mathcal R^\kappa_L[/math])	Temperature-only reconstruction lensing spectrum biases and quadratic estimator normalization (inverse response), as defined in Planck-2020-A8.
PP/nlkk.dat	ASCII text file, with columns = ([math]L[/math], [math]\textrm{RD-}N_L^{0} [/math], [math]\textrm{MC-}N_L^{0}[/math], [math]N_L^{1}[/math], [math]{PS}_L[/math], [math]\langle \hat C^{\kappa\kappa}_L - C_L^{\kappa\kappa, \rm fid}\rangle_{\rm MC}[/math], [math]1/\mathcal R^\kappa_L[/math])	Polarization-only reconstruction lensing spectrum biases and quadratic estimator normalization (inverse response), as defined in Planck-2020-A8.
MV/nlkk.dat	ASCII text file, with columns = ([math]L[/math], [math]\textrm{RD-}N_L^{0} [/math], [math]\textrm{MC-}N_L^{0}[/math], [math]N_L^{1}[/math], [math]{PS}_L[/math], [math]\langle \hat C^{\kappa\kappa}_L - C_L^{\kappa\kappa, \rm fid}\rangle_{\rm MC}[/math], [math]1/\mathcal R^\kappa_L[/math])	Minimum variance reconstruction lensing spectrum biases and quadratic estimator normalization (inverse response), as defined in Planck-2020-A8.

with the same slight variations:

- in COM_Lensing-SimMap_Inhf_2048_R3.00, all HEALPix FITS format alm files have [math]L_{\rm max}=2048[/math].

- COM_Lensing-SimMap-Szdeproj_4096_R3.00 only provides the temperature-only reconstructions.

We further provide the input lensing convergence realizations of all 300 FFP10 simulations in

• COM_Lensing-SimMap-inputs_4096_R3.00

with contents

Contents of lensing simulation package COM_Lensing-SimMap-inputs_4096_R3.00

Filenames	Format	Description
/inputs/clkk.dat	ASCII text file, with columns = ([math]L[/math], [math]C_L^{\kappa\kappa}[/math])	Input lensing convergence CMB spectrum of the fiducial cosmology used in Planck-2020-A8.
sky_klm_{???}.fits	300 HEALPix FITS format alm, with [math]L_{\rm max}=4096[/math]	Input lensing convergence [math] {\kappa}_{LM} = \frac{1}{2} L(L+1){\phi}_{LM} [/math] realizations of all 300 FFP10 simulations used in Planck-2020-A8.

2018 Lensing-induced B-mode maps

We distribute maps of the lensing-induced B-modes presented in Planck-2020-A8, together with a matching simulation suite. The Stokes parameter maps of the lensing B-modes are produced by combining tracers of lensing potential with E-mode data from the SMICA CMB polarization maps. These lensing-induced B-mode polarization maps are provided on approximately 60% of the sky. Planck-2020-A8 details the construction of these maps.

These maps come in two variations. In the first we use the [math]TT + TE + EE[/math] quadratic estimator built from the DX12 SMICA CMB maps (we discard [math]TB[/math] and [math]EB[/math] in order to use lensing tracers that are statistically independent of the [math]B[/math]-mode map). In the second we further add CIB information at 545 GHz (GNILC) to the lensing tracer.

These maps are filtered template of the lensing B-mode (both the lensing tracer and [math]E[/math]-mode used to build the B template are Wiener-filtered). The simulation suite may be used to assess the filter, as was done in Planck-2020-A8 to produce the B-mode power spectrum (Fig. 14).

The B-mode template package is

• COM_Lensing-Bmode_2048_R3.00

with contents

Contents of B-mode template data package COM_Lensing-Bmode_2048_R3.00

Filenames	Format	Description
/inputs/mask.fits.gz	compressed HEALPix FITS format map, with [math]N_{\rm side}=2048[/math]	[math]B[/math]-mode analysis mask used in Planck-2020-A8.
/inputs/clbb.dat	ASCII text file, with columns = ([math]\ell[/math], [math]C_\ell^{BB}[/math])	Input lensing [math]B[/math]-mode power spectrum for the fiducial cosmology used in Planck-2020-A8.
dat_blm_TTTEETEE.fits	HEALPix FITS format alm, with [math]\ell_{\rm max}=2048[/math]	Lensing [math]B[/math]-mode template built from the [math]\hat \phi^{TT + TE + EE}[/math] lensing tracer and [math]E[/math]-mode map.
dat_blm_545_TTTEETEE.fits	HEALPix FITS format alm, with [math]\ell_{\rm max}=2048[/math]	Lensing [math]B[/math]-mode template built from the [math]\hat \phi^{TT + TE + EE} + \rm{CIB}[/math] lensing tracer and [math]E[/math]-mode map.

The B-mode template simulation package is

• COM_Lensing-SimMap-Bmode_2048_R3.00

with contents

Contents of B-mode template simulation package COM_Lensing-SimMap-Bmode_2048_R3.00

Filenames	Format	Description
/inputs/mask.fits.gz	compressed HEALPix FITS format map, with [math]N_{\rm side}=2048[/math]	[math]B[/math]-mode analysis mask used in Planck-2020-A8.
/inputs/clbb.dat	ASCII text file, with columns = ([math]\ell[/math], [math]C_\ell^{BB}[/math])	Input lensing [math]B[/math]-mode power spectrum for the fiducial cosmology used in Planck-2020-A8.
/TTTEETE/blm_{???}.fits	300 HEALPix FITS format alm, with [math]\ell_{\rm max}=2048[/math]	Lensing [math]B[/math]-mode template built from the [math]\hat \phi^{TT + TE + EE}[/math] lensing tracer and [math]E[/math]-mode map of all 300 FFP10 simulations used in Planck-2020-A8.
/545_TTTEETE/blm_{???}.fits	300 HEALPix FITS format alm, with [math]\ell_{\rm max}=2048[/math]	Lensing [math]B[/math]-mode template built from the [math]\hat \phi^{TT + TE + EE} + \rm{CIB}[/math] lensing tracer and [math]E[/math]-mode map of all 300 FFP10 simulations used in Planck-2020-A8.
/TTTEETE/dat_blm.fits	HEALPix FITS format alm, with [math]\ell_{\rm max}=2048[/math]	Lensing [math]B[/math]-mode template built from the [math]\hat \phi^{TT + TE + EE}[/math] lensing tracer and [math]E[/math]-mode map.
/545_TTTEETE/dat_blm.fits	HEALPix FITS format alm, with [math]\ell_{\rm max}=2048[/math]	Lensing [math]B[/math]-mode template built from the [math]\hat \phi^{TT + TE + EE} + \rm{CIB}[/math] lensing tracer and [math]E[/math]-mode map.

2018 Lensing combined tracers maps

We distribute estimates of the CMB lensing convergence maps built combining the Planck 2018 quadratic estimators and CIB data at 545 GHz (GNILC), together with a matching simulation suite. The construction of these maps is decribed in details in Planck-2020-A8. The maps are built on about 60% of the sky.

The tracer are Wiener-filtered estimates of the convergence [math]\hat \kappa_{LM} = \frac 12 L (L + 1) \hat \phi_{LM}[/math].

These maps come in two variations. In the first we use the minimum-variance (MV) quadratic estimator together with the CIB. In the second we use the [math]TT + TE + EE[/math] quadratic estimator together with the CIB, and is statistically independent from the CMB B-polarization.

The lensing combined tracer data package is

• COM_Lensing-CIBcomb_2000_R3.00

with contents

Contents of lensing combined tracer data package COM_Lensing-CIBcomb_2000_R3.00

Filenames	Format	Description
/inputs/mask.fits.gz	compressed HEALPix FITS format map, with [math]N_{\rm side}=2048[/math]	Tracer combination analysis mask used in Planck-2020-A8.
dat_klm_545_MV.fits	HEALPix FITS format alm, with [math]L_{\rm max}=2000[/math]	Lensing tracer built from the minimum-variance quadratic estimator and the CIB (GNILC 545 GHz map).
dat_klm_545_TTTEETEE.fits	HEALPix FITS format alm, with [math]L_{\rm max}=2000[/math]	Lensing tracer built from the [math]TT + TE + EE[/math] quadratic estimator and the CIB (GNILC 545 GHz map).

The lensing combined tracer simulation package is

• COM_Lensing-SimMap-CIBcomb_2000_R3.00

with contents

Contents of lensing combined tracer simulation package COM_Lensing-SimMap-CIBcomb_2000_R3.00

Filenames	Format	Description
/inputs/mask.fits.gz	compressed HEALPix FITS format map, with [math]N_{\rm side}=2048[/math]	Tracer combination analysis mask used in Planck-2020-A8.
545_MV/sim_klm_{???}.fits	300 HEALPix FITS format alm, with [math]L_{\rm max}=2000[/math]	Lensing tracer built from the minimum-variance quadratic estimator and the CIB (GNILC 545 GHz map) of all 300 FFP10 simulations used in Planck-2020-A8.
545_TTTEETEE/sim_klm_{???}.fits	300 HEALPix FITS format alm, with [math]L_{\rm max}=2000[/math]	Lensing tracer built from the [math]TT + TE + EE[/math] quadratic estimator and the CIB (GNILC 545 GHz map) of all 300 FFP10 simulations used in Planck-2020-A8.
545_MV/dat_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=2000[/math]	Lensing tracer built from the minimum-variance quadratic estimator and the CIB (GNILC 545 GHz map).
545_TTTEETEE/dat_klm.fits	HEALPix FITS format alm, with [math]L_{\rm max}=2000[/math]	Lensing tracer built from the [math]TT + TE + EE[/math] quadratic estimator and the CIB (GNILC 545 GHz map).

Also part of this package are high-resolution figures of the lensing deflection (similar to Fig. 3 and Fig. 13 of Planck-2020-A8). The figures show the Wiener-filtered, gradient [math](E)[/math] mode of the displacement [math]\hat \alpha_{LM} = \sqrt{L (L + 1)} \hat \phi_{LM}[/math].

Mollveide projection of the minimum variance quadratic estimator lensing map:

• Lensing_2018_MV_alphaA0_YlGnBu_300dpi_47in_moll.png

Orthographic projection of the minimum variance quadratic estimatorlensing map:

• Lensing_2018_compMV_alphaA0_YlGnBu_300dpi_47in_moll.png

Orthographic projection of the minimum variance quadratic estimator combined with the CIB (GNILC 545 GHz map) lensing tracer map:

• Lensing_2018_compMV545_alphaA0_YlGnBu_300dpi_47in_orth.png

2018 Lensing band powers and likelihoods

The lensing reconstruction spectrum band powers, covariance matrix and likelihood linear corrections are provided as a zip of a series of ASCII files

• planck_lensing_2018.zip

The files are in CosmoMC format, a piece of software available here. A new Python code called Cobaya which follows the same methodology will be soon available and should produce the same results.

We provide CosmoMC files for 8 different likelihoods

• smicadx12_Dec5_ftl_mv2_ndclpttptt_p_teb_consext8
• smicadx12_Dec5_ftl_mv2_ndclpttptt_p_teb_consext8_CMBmarged
• smicadx12_Dec5_ftl_mv2_ndclpttptt_p_teb_agr2
• smicadx12_Dec5_ftl_mv2_ndclpttptt_p_teb_agr2_CMBmarged
• smicadx12_Dec5_ftl_mv2_ndclpp_p_teb_consext8
• smicadx12_Dec5_ftl_mv2_ndclpp_p_teb_consext8_CMBmarged
• smicadx12_Dec5_ftl_mv2_ndclpp_p_teb_agr2
• smicadx12_Dec5_ftl_mv2_ndclpp_p_teb_agr2_CMBmarged

following these variations:

• Reconstructions from temperature-only ('pttptt_p_teb') or minimum-variance ('pp_p_teb') combination of temperature and polarization
• Conservative ('consext8') [math]( 8 \leq L \leq 400 )[/math] or aggressive ('agr2') [math]( 8 \leq L \leq 2048 )[/math] lensing multipole range.
• Likelihood with ('CMBmarged', used for lensing-only constraints) and without CMB power spectra errors marginalization.

The band powers and likelihood construction, together with detailed consistency and robustness tests are provided in Planck-2020-A8. The aggressive range is considered less reliable than the conservative range.

Lensing-only MCMC chains used for this release are available here. Follow this link for joint constraints and parameter tables.

Previous Releases: Lensing products (2015) and (2013)

Lensing products 2015 data release

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.tar. Its contents are described below. The convergence map "dat_klm.fits" that can be found in the tarball, has been categorized as COM_Lensing-Convergence-dat-klm_2048_R2.00.fits in the Lensing Products section of the archive.

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 lensing-induced B-mode map

We distribute the lensing-induced B-mode map presented in Planck-2015-XLI. 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 from approximately 70% of the sky, as described in Planck-2015-XLI.

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 equation (6) of Planck-2015-XLI. 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 equation (5) of Planck-2015-XLI, and [math] \widetilde \phi[/math] is the filtered lensing potential estimate.

We also provide the normalization transfer function [math] \mathcal{B}_\ell [/math] defined in equation (11) of Planck-2015-XLI, 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 maps that are shown in figure 4 of Planck-2015-XLI 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 of 60 arcmin FWHM (introduced for highlighting large angular scales, although it can be removed or replaced by any other filter). This can be practically done by ingesting [math]\bar{Q}^{\rm{lens}} [/math] and [math] \bar{U}^{\rm{lens}} [/math] in the HEALPix "smoothing" 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] over 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 "anafast" tool.

The lensing B-mode power spectrum estimate [math] \hat{C}_\ell^{BB^{\rm{lens}}} [/math] discussed in Planck-2015-XLI 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 arcmin Gaussian beam that convolves the SMICA CMB maps.

The products are contained in a single gzipped tarball named COM_Lensing-Bmode_R2.01.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 Planck-2015-XLI (for plotting purposes only).

2015 Integrated Sachs-Wolfe effect map

We distribute estimates of the integrated Sachs-Wolfe (ISW) maps presented in Planck-2015-A21 as part of the 2015 data release. These map represents an estimate of the ISW anisotropies using different data sets:

• SEVEM DX11 CMB map, together with all the large-scale structure tracers considered in the ISW paper, namely: NVSS, SDSS, WISE, and the Planck lensing map
• Using only the large-scale structure tracers mentioned above
• SEVEM DX11 CMB map, together with NVSS and the Planck lensing maps (since these two tracers capture most of the information, as compared to SDSS and WISE)

For all the three cases, the reconstruction is provided on approximately 85% of the sky, and they are produced using the LCB filter described in the Planck ISW paper (Section 5), described in detail in Barreiro et al. 2008 and Bonavera et al. 2016.

These ISW maps, together with their corresponding uncertainties maps and masks, are given in a file named COM_CompMap_ISW_0064_R2.00.fits. Its contents are described below.

Contents of the ISW maps file: COM_CompMap_ISW_0064_R2.00.fits

Extension	Format	Description	Used data sets
0	HEALPix FITS format map with three components, [math]N_{\rm side}=64[/math], Ordering='Nest'	Contains three components: i) ISW map [Kelvin], ii) Error map [Kelvin], iii) Mask map	SEVEM DX11 CMB + NVSS + SDSS + WISE + Planck lensing.
1	HEALPix FITS format map with three components, [math]N_{\rm side}=64[/math], Ordering='Nest'	Contains three components: i) ISW map [Kelvin], ii) Error map [Kelvin], iii) Mask map	NVSS + SDSS + WISE + Planck lensing.
2	HEALPix FITS format map with three components, [math]N_{\rm side}=64[/math], Ordering='Nest'	Contains three components: i) ISW map [Kelvin], ii) Error map [Kelvin], iii) Mask map	SEVEM DX11 CMB + NVSS + Planck lensing.

2015 Low-frequency foregrounds maps (Planck only & Planck+WMAP) 1) CMB/free-free/Dust Nulled ILC at 28.4 GHz (Planck only)

Linear combination of Planck 28.4, 44.1, 143 and 353 GHz maps (all at 1 degree resolution), with weights listed in column w_2 of Table 1 in Planck-2015-A25. These weights exactly null the CMB, almost exactly null free-free emission, and null thermal dust emission to high accuracy except along the inner Galactic plane,where the brightness is uncertain by around 20% due to variation in the dust spectrum. The normalisation leaves a beta = -3 power law at the same amplitude as in the Planck 28.4 GHz map. (As presented in Fig. 3a of Planck 2015 Results XXV.)

2) CMB/free-free/Dust Nulled ILC at 28.4 GHz (Planck + WMAP) Linear combination of WMAP K, Ka, and Q band, and Planck 28.4, 44.1, 143 and 353 GHz maps (all at 1 degree resolution), with weights listed in column w_3 of Table 1 in Planck-2015-A25. These weights exactly null the CMB, almost exactly null free-free emission, and null thermal dust emission to high accuracy except along the inner Galactic plane, where the brightness is uncertain by around 20% due to variation in the dust spectrum. The normalisation leaves a beta = -3 power law at the same amplitude as in the Planck 28.4 GHz map. (As presented in Fig. 3b of Planck-2015-A25.)

Lensing products 2013 data release

Lensing map

Here we present the minimum-variance (MV) lens reconstruction which forms the basis for the main results of Planck-2013-XVII. 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.

We distribute:

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].

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.

RLPP 

This column contains the response function [math]R_L^{\phi\phi}[/math].

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 Planck-2013-XVII. Note that the noise power spectrum estimate here is not sufficiently accurate for a power spectrum analysis.

Also, the table below gives the lensing curl-mode power spectrum data used to produce Figure A2 of Planck-2013-XVII:

'MV' curl reconstruction bandpowers from Fig A2 of Planck-2013-XVII

[math]L[/math]min	[math]L[/math]max	[math]{\hat{C}_L}^{\psi\psi} (L(L+1))^2/(2\pi)[/math]	[math] std({\hat{C}_L}^{\psi\psi}) (L(L+1))^2 /(2\pi)[/math]
2	7	-13.6379	15.3409
8	20	6.0184	4.8881
21	39	-1.0675	3.0940
40	65	0.6135	1.8474
66	100	1.5030	1.2696
101	144	1.3760	0.9950
145	198	-1.2289	0.8286
199	263	1.1910	0.7001
264	338	-0.6567	0.6197
339	425	-0.8201	0.5235
426	525	-0.7581	0.4850
526	637	-0.3201	0.5134
638	762	-0.1589	0.4073
763	901	-0.6451	0.4044
902	1054	0.4910	0.3718
1055	1221	-0.2186	0.3702
1222	1404	-0.3295	0.4146
1405	1602	-0.3647	0.4703
1603	1816	-0.1060	0.5904
1817	2020	-0.7887	0.8507

Production process

The construction PHIBAR, RLPP and NLPP are described in detail in Sec. 2.1 of Planck-2013-XVII. 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.

Inputs

This product is built from the 143 and 217 GHz Planck frequency maps, with 857GHz projected out as a dust template. 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 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, including the ERCSC, SZ and PCCS . The reconstruction was performed using the fiducial beam window functions B(l) from the HFI RIMO . Details of the procedure used to produce a lensing estimate from these inputs are given in Planck-2013-XVII.

File names and format

A single file named

• COM_CompMap_Lensing_2048_R1.10.fits

with two BINTABLE extensions containing the items described below.

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].

• 

  Galactic north

• 

  Galactic south

FITS file structure

1. EXTNAME = LENS-MAP
Column Name	Data Type	Units	Description
PHIBAR	Real*4	none	Map of the lensing potential estimate, convolved with RLPP
MASK	Int	none	Region over which the lensing potential is reconstructed
Keyword	Data Type	Value	Description
PIXTYPE	string	HEALPIX
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	NESTED	Healpix ordering
NSIDE	Int*4	2048	Healpix Nside
FIRSTPIX	Int*4	0
LASTPIX	Int*4	50331647
2. EXTNAME = TransFun
Column Name	Data Type	Units	Description
RLPP	Real*4	none	Response function
NLPP	Real*4	none	Sky-averaged noise power spectrum estimate
Keyword	Data Type	Value	Description
L_MIN	Int*4	0	First multipole
L_MAX	Int*4	2048	Last multipole