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.