Difference between revisions of "Specially processed maps"
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− | {{DISPLAYTITLE:Additional maps}} | + | {{DISPLAYTITLE: 2015 Additional maps}} |
− | == | + | ==Introduction== |
− | This section describes products that | + | This section describes the products that required special processing. |
− | == Lensing map | + | == 2015 Lensing map == |
− | + | ||
− | + | We distribute the minimum-variance (MV) lensing potential estimate presented in {{PlanckPapers|planck2014-a17}} 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 {{PlanckPapers|planck2014-a11}}. | |
− | |||
− | + | The estimate is contained in a single gzipped tarball named ''{{PLASingleFile|fileType=map|name=COM_CompMap_Lensing_2048_R2.00.tgz|link=COM_CompMap_Lensing_2048_R2.00.tgz}}''. 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. | |
− | + | ||
− | + | ||
− | + | ||
− | |||
− | |||
− | === | + | {| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" |
+ | |+ ''' Contents of Lensing package ''' | ||
+ | |- bgcolor="ffdead" | ||
+ | ! 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 {{PlanckPapers|planck2014-a15}}. | ||
+ | |} | ||
− | + | == 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 {{PlanckPapers|planck2014-a28}}. We also provide the ILC weights per scale and per frequency that were used to produce these y-maps. IDL routines are also provide 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 provide and we call them FIRST and LAST y-maps. Additionally we construct a 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 that 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. | |
− | + | <span style="color:#ff0000"> Update 04 Aug 2017:</span> The file containing the masks named ''COM_CompMap_Compton-SZMap-masks_2048_R2.00.fits'' has been updated with the file ''COM_CompMap_Compton-SZMap-masks_2048_R2.01.fits''. The difference between the two is that in the R2.00 version a region around the Galactic pole had been masked, while only the Galactic plane should be masked. This has been fixed in version R2.01. The full updated data set is contained in a single gzipped tarball named ''COM_CompMap_YSZ_R2.01.fits.tgz''. The R2.00 version of the mask is not available in the PLA anymore, but can be requested via the PLA Helpdesk. | |
− | + | ||
− | with two | + | |
− | + | The contents of the full data set are described below. | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" | {| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" | ||
− | |+ ''' | + | |+ ''' Contents of COM_CompMap_YSZ_R2.01.fits.tgz ''' |
− | + | ||
− | + | ||
|- bgcolor="ffdead" | |- bgcolor="ffdead" | ||
− | ! | + | ! 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 ymaps. |
|- | |- | ||
− | | | + | | 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 ymaps. |
− | + | ||
− | + | ||
|- | |- | ||
− | | | + | | 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 ymap 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 ymap 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 ymap. |
|- | |- | ||
− | | | + | | nilc_homnoise_spect.fits || ASCII table FITS format || Contains the angular power spectrum of the homogeneous noise in the NILC full mission ymap. |
|- | |- | ||
− | | | + | | milca_homnoise_spect.fits || ASCII table FITS format || Contains the angular power spectrum of the homogeneous noise in the MILCA full mission ymap. |
− | |- | + | |- |
− | + | | 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 <i>B</i>-mode map == | ||
+ | |||
+ | We distribute the Planck map of the lensing-induced <i>B</i>-modes presented in {{PlanckPapers|planck2015-XLI}}. The Stokes parameter maps of the lensing <i>B</i>-modes are produced by combining the lensing potential map extracted from the SMICA CMB temperature map with <i>E</i>-mode data from the SMICA CMB polarization maps. The SMICA temperature and polarization products are described in {{PlanckPapers|planck2014-a11}}. The lensing-induced <i>B</i>-mode polarization maps are used in cross-correlation with the SMICA CMB polarization maps to obtain a lensing <i>B</i>-mode power spectrum measurement from approximately 70% of the sky. | ||
+ | |||
+ | 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 <i>B</i>-mode estimator defined in equation (6) of the paper. 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 <i>E</i>-mode polarization maps given in equation (5), 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 (12), as well as the "B70" 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 <i>B</i>-mode maps that are shown in figure 4 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 filter 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. | ||
+ | |||
+ | The lensing-induced Stokes parameter maps are provided without being masked for the user's convenience (in particular, it allows for various filtering to be tested). However, whenever they are utilized in view of obtaining scientific outcomes, they should be masked using the B70 mask, which is also provided. | ||
+ | |||
+ | === Specific products === | ||
+ | |||
+ | We provide the lensing <i>B</i>-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 band-pass filter that retain the multipole 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 <i>B</i>-mode power spectrum estimate <math> \hat{C}_\ell^{BB^{\rm{lens}}} </math> is obtained by forming the cross-correlation power spectrum of <math> B_{\ell m}^{\rm{lens}} </math> and the <i>B</i>-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 [http://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_Lensing-Bmode_R2.01.tgz COM_Lensing-Bmode_R2.01.tgz]. Its contents are described below. | ||
+ | |||
+ | |||
+ | |||
+ | {| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" | ||
+ | |+ ''' Contents of Lensing B-mode package ''' | ||
|- bgcolor="ffdead" | |- bgcolor="ffdead" | ||
− | ! | + | ! 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 <i>Q</i> 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 <i>U</i> 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 B70 mask (apodized version). |
|- | |- | ||
− | | | + | | mask_noapo.fits || HEALPix FITS format map in Galactic coordinates with <math> N_{\rm side} = 2048 </math> || The B70 mask without apodization. |
+ | |- | ||
+ | | transfer_function_b_l.dat || ASCII text file, with columns = (<math>\ell</math>, <math> \mathcal{B}_\ell </math>) || The transfer function of the lensing B-mode estimator. | ||
+ | |- | ||
+ | | lensing_bmode_b_lm.fits || HEALPix FITS format alm, with <math> \ell_{\rm max} = 2000 </math> || Contains the lensing <i>B</i>-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 <i>B</i>-mode bandpower estimate on approximativily 70% of the sky and over the multipole range from 10 to 2000 shown in figure 10 of {{PlanckPapers|planck2015-XLI}} (for plotting purposes only). | ||
+ | |} | ||
+ | |||
+ | == 2015 Integrated Sachs-Wolfe effect map == | ||
+ | |||
+ | We distribute estimates of the integrated Sachs-Wolfe (ISW) maps presented in {{PlanckPapers|planck2014-a26}} 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 [http://cdsads.u-strasbg.fr/abs/2008ISTSP...2..747B| Barreiro et al. 2008] and [http://cdsads.u-strasbg.fr/doi/10.1093/mnras/stw415| Bonavera et al. 2016]. | ||
+ | |||
+ | These ISW maps, together with their corresponding uncertainties maps and masks, are given in a single file named ''{{PLASingleFile|fileType=map|name=COM_CompMap_ISW_0064_R2.00.fits|link=COM_CompMap_ISW_0064_R2.00.fits}}''. Its contents are described below. | ||
+ | |||
+ | |||
+ | {| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" | ||
+ | |+ ''' Contents of the ISW maps file: COM_CompMap_ISW_0064_R2.00.fits ''' | ||
+ | |- bgcolor="ffdead" | ||
+ | ! 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. | ||
|} | |} | ||
==References== | ==References== | ||
− | < | + | <References /> |
− | + | ||
− | + | ||
[[Category:Mission products|010]] | [[Category:Mission products|010]] |
Latest revision as of 08:29, 7 August 2017
Introduction
This section describes the products that required special processing.
2015 Lensing map
We distribute the minimum-variance (MV) lensing potential estimate presented in Planck-2015-A15^{[1]} as part of the 2014 data release. This map represents an estimate of the CMBCosmic Microwave background 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 CMBCosmic Microwave background map; its construction is discussed in detail in Planck-2015-A09^{[2]}.
The estimate is contained in a single gzipped tarball named COM_CompMap_Lensing_2048_R2.00.tgz. 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.
Filename | Format | Description |
---|---|---|
dat_klm.fits | HEALPIX FITSFlexible Image Transfer Specification 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 FITSFlexible Image Transfer Specification 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^{[3]}. |
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^{[4]}. We also provide the ILC weights per scale and per frequency that were used to produce these y-maps. IDL routines are also provide 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 provide and we call them FIRST and LAST y-maps. Additionally we construct a 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 that 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.
Update 04 Aug 2017: The file containing the masks named COM_CompMap_Compton-SZMap-masks_2048_R2.00.fits has been updated with the file COM_CompMap_Compton-SZMap-masks_2048_R2.01.fits. The difference between the two is that in the R2.00 version a region around the Galactic pole had been masked, while only the Galactic plane should be masked. This has been fixed in version R2.01. The full updated data set is contained in a single gzipped tarball named COM_CompMap_YSZ_R2.01.fits.tgz. The R2.00 version of the mask is not available in the PLAPlanck Legacy Archive anymore, but can be requested via the PLAPlanck Legacy Archive Helpdesk.
The contents of the full data set are described below.
Filename | Format | Description |
---|---|---|
nilc_ymaps.fits | HEALPIX FITSFlexible Image Transfer Specification format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math] | Contains the NILC full mission, FIRST and LAST ymaps. |
milca_ymaps.fits | HEALPIX FITSFlexible Image Transfer Specification format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math] | Contains the MILCA full mission, FIRST and LAST ymaps. |
nilc_weights_BAND.fits | HEALPIX FITSFlexible Image Transfer Specification format map in Galactic coordinates with [math] N_{\rm side} = 128 [/math] | Contains the NILC ILC weights for the full mission ymap for band BAND 0 to 9. For each band we provide a weight map per frequency. |
milca_FREQ_Csz.fits | HEALPIX FITSFlexible Image Transfer Specification format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math] | Contains the MILCA ILC weights for the full mission ymap for frequency FREQ (100,143,217,353,545,857). For each frequency we provide a weight map per filter band. |
nilc_stddev.fits | HEALPIX FITSFlexible Image Transfer Specification 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 FITSFlexible Image Transfer Specification format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math] | Contains the stddev maps for the MILCA full mission ymap. |
nilc_homnoise_spect.fits | ASCII table FITSFlexible Image Transfer Specification format | Contains the angular power spectrum of the homogeneous noise in the NILC full mission ymap. |
milca_homnoise_spect.fits | ASCII table FITSFlexible Image Transfer Specification format | Contains the angular power spectrum of the homogeneous noise in the MILCA full mission ymap. |
masks.fits | HEALPIX FITSFlexible Image Transfer Specification format map, with [math] N_{\rm side} = 2048 [/math] | Contains foreground masks. |
nilc_bands.fits | ASCII table FITSFlexible Image Transfer Specification format | Contains NILC wavelet bands in multipole space |
2015 Lensing-induced B-mode map
We distribute the Planck map of the lensing-induced B-modes presented in Planck-2015-XLI^{[5]}. The Stokes parameter maps of the lensing B-modes are produced by combining the lensing potential map extracted from the SMICA CMBCosmic Microwave background temperature map with E-mode data from the SMICA CMBCosmic Microwave background polarization maps. The SMICA temperature and polarization products are described in Planck-2015-A09^{[2]}. The lensing-induced B-mode polarization maps are used in cross-correlation with the SMICA CMBCosmic Microwave background polarization maps to obtain a lensing B-mode power spectrum measurement from approximately 70% of the sky.
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 the paper. 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), 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 (12), as well as the "B70" 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 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 filter of 60 arcmin FWHMFull-Width-at-Half-Maximum (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([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). "smoothing" routine, and using the product [math] G_\ell\mathcal{B}_\ell^{-1} [/math] as an input filtering function.
The lensing-induced Stokes parameter maps are provided without being masked for the user's convenience (in particular, it allows for various filtering to be tested). However, whenever they are utilized in view of obtaining scientific outcomes, they should be masked using the B70 mask, which is also provided.
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 band-pass filter that retain the multipole 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([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). "anafast" tool.
The lensing B-mode power spectrum estimate [math] \hat{C}_\ell^{BB^{\rm{lens}}} [/math] 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 CMBCosmic Microwave background maps.
The products are contained in a single gzipped tarball named COM_Lensing-Bmode_R2.01.tgz. Its contents are described below.
Filename | Format | Description |
---|---|---|
bar_q_lens_map.fits | HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). FITSFlexible Image Transfer Specification 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([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). FITSFlexible Image Transfer Specification 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([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). FITSFlexible Image Transfer Specification format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math] | The B70 mask (apodized version). |
mask_noapo.fits | HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). FITSFlexible Image Transfer Specification format map in Galactic coordinates with [math] N_{\rm side} = 2048 [/math] | The B70 mask without apodization. |
transfer_function_b_l.dat | ASCII text file, with columns = ([math]\ell[/math], [math] \mathcal{B}_\ell [/math]) | The transfer function of the lensing B-mode estimator. |
lensing_bmode_b_lm.fits | HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). FITSFlexible Image Transfer Specification 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 10 of Planck-2015-XLI^{[5]} (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^{[6]} as part of the 2015 data release. These map represents an estimate of the ISW anisotropies using different data sets:
- SEVEM DX11 CMBCosmic Microwave background 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 CMBCosmic Microwave background 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 single file named COM_CompMap_ISW_0064_R2.00.fits. Its contents are described below.
Extension | Format | Description | Used data sets |
---|---|---|---|
0 | HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). FITSFlexible Image Transfer Specification 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 CMBCosmic Microwave background + NVSS + SDSS + WISE + Planck lensing. |
1 | HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). FITSFlexible Image Transfer Specification 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([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). FITSFlexible Image Transfer Specification 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 CMBCosmic Microwave background + NVSS + Planck lensing. |
References
- ↑ Planck 2015 results. XV. Gravitational Lensing, Planck Collaboration, 2016, A&A, 594, A15.
- ↑ ^{2.0} ^{2.1} Planck 2015 results. XI. Diffuse component separation: CMB maps, Planck Collaboration, 2016, A&A, 594, A9.
- ↑ Planck 2015 results. XIII. Cosmological parameters, Planck Collaboration, 2016, A&A, 594, A13.
- ↑ Planck 2015 results. XXII. A map of the thermal Sunyaev-Zeldovich effect, Planck Collaboration, 2016, A&A, 594, A22.
- ↑ ^{5.0} ^{5.1} Planck intermediate results. XLI. A map of lensing-induced B-modes, Planck Collaboration Int. XLI A&A, 596, A102, (2016).
- ↑ Planck 2015 results. XXI. The integrated Sachs-Wolfe effect, Planck Collaboration, 2016, A&A, 594, A21.