Difference between revisions of "Specially processed maps"

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{{DISPLAYTITLE: 2015 Additional maps}}
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{{DISPLAYTITLE: Additional maps}}
 
==Introduction==
 
==Introduction==
  
 
This section describes the map-based products that required special processing.
 
This section describes the map-based products that required special processing.
  
−
== 2015 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}}.
 
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 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.
  
  
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|}
 
|}
  
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== 2015 Compton parameter map ==
+
== 2015 Compton <i>y</i> parameter map ==
  
 
We distribute here the Planck full mission Compton parameter maps (<i>y</i>-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 <i>y</i>-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 <i>y</i>-maps. Additionally we construct noise estimates of full mission Planck <i>y</i>-maps from the half difference of the FIRST and LAST <i>y</i>-maps. These estimates are used to construct standard deviation maps of the noise in the full mission Planck <i>y</i>-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.
 
We distribute here the Planck full mission Compton parameter maps (<i>y</i>-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 <i>y</i>-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 <i>y</i>-maps. Additionally we construct noise estimates of full mission Planck <i>y</i>-maps from the half difference of the FIRST and LAST <i>y</i>-maps. These estimates are used to construct standard deviation maps of the noise in the full mission Planck <i>y</i>-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.
Line 59: Line 59:
 
|}
 
|}
  
−
== 2015 Lensing-induced B-mode map ==
+
== 2015 lensing-induced <i>B</i>-mode map ==
  
−
We distribute the lensing-induced <i>B</i>-mode map presented in PIP116{{PlanckPapers|planck2015-pip116}}. The lensing <i>B</i>-mode Stokes parameter maps are produced by combining the lensing potential reconstruction 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, as described in PIP116{{PlanckPapers|planck2015-pip116}}.  
+
We distribute the lensing-induced <i>B</i>-mode map presented in {{PlanckPapers|planck2015-XLI}}. The lensing <i>B</i>-mode Stokes parameter maps are produced by combining the lensing potential reconstruction 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, as described in {{PlanckPapers|planck2015-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.  
 
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.  
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=== Raw products ===  
 
=== 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 PIP116. They are defined as
+
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 {{PlanckPapers|planck2015-XLI}}. They are defined as
  
 
<math> \begin{eqnarray}
 
<math> \begin{eqnarray}
−
\bar Q^{\rm{lens}}({\bf n}) &=& \widetilde Q^{E}({\bf n}) \cdot \nabla \widetilde \phi({\bf n}) \\
+
\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}),
 
\bar U^{\rm{lens}}({\bf n}) &=& \widetilde U^{E}({\bf n}) \cdot \nabla \widetilde \phi({\bf n}),
 
\end{eqnarray} </math>
 
\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) of PIP116, and <math> \widetilde \phi</math> is the filtered lensing potential estimate.   
+
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) of {{PlanckPapers|planck2015-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 PIP116, as well as the L70 mask <math> M({\bf n}) </math> that retains 69% of the sky before  
+
We also provide the normalization transfer function <math> \mathcal{B}_\ell </math> defined in equation (11) of {{PlanckPapers|planck2015-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>.
 
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 of PIP116 are generated from  
+
As an example of the utilization of these products, the lensing <i>B</i>-mode maps that are shown in figure 4 of {{PlanckPapers|planck2015-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>,
 
<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 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 ''smoothing'' HEALPix routine, and using the product <math> G_\ell\mathcal{B}_\ell^{-1} </math> as an input filtering function.
+
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 ===  
 
=== Specific products ===  
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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.
 
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 <i>B</i>-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>:
+
The lensing <i>B</i>-mode power spectrum estimate <math> \hat{C}_\ell^{BB^{\rm{lens}}} </math> discussed in {{PlanckPapers|planck2015-XLI}} 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>,
 
<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 arcminGaussian beam that convolves the SMICA CMB maps.  
+
where <math> G_\ell </math> is the 5 arcmin Gaussian beam that convolves the SMICA CMB maps.  
  
  
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! Filename ||  Format ||  Description
 
! 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_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 U Stokes parameter map <math> \bar U^{\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 L70 mask.
 
| mask.fits || HEALPix FITS format map in Galactic coordinates with <math> N_{\rm  side} = 2048 </math> || The L70 mask.
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| 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_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 9 of {{PlanckPapers|planck2015-pip116}} (for plotting purpose only).
+
| 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 9 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 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.
 
|}
 
|}
  

Latest revision as of 06:56, 26 April 2016

Introduction[edit]

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

2015 lensing map[edit]

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 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[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.


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[3].

2015 Compton y parameter map[edit]

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 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[edit]

We distribute the lensing-induced B-mode map presented in Planck-2015-XLI[5]. 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[2]. 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[5].

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[edit]

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[5]. 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[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 (11) of Planck-2015-XLI[5], 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[5] 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[edit]

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[5] 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_R2.00.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 Planck-2015-XLI[5] (for plotting purposes only).

2015 Integrated Sachs-Wolfe effect map[edit]

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 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.

References[edit]

  1. ↑ Planck 2015 results. XV. Gravitational Lensing, Planck Collaboration, 2016, A&A, 594, A15.
  2. ↑ 2.02.1 Planck 2015 results. XI. Diffuse component separation: CMB maps, Planck Collaboration, 2016, A&A, 594, A9.
  3. ↑ Planck 2015 results. XIII. Cosmological parameters, Planck Collaboration, 2016, A&A, 594, A13.
  4. ↑ Planck 2015 results. XXII. A map of the thermal Sunyaev-Zeldovich effect, Planck Collaboration, 2016, A&A, 594, A22.
  5. ↑ 5.05.15.25.35.45.55.65.7 Planck intermediate results. XLI. A map of lensing-induced B-modes, Planck Collaboration Int. XLI A&A, 596, A102, (2016).
  6. ↑ Planck 2015 results. XXI. The integrated Sachs-Wolfe effect, Planck Collaboration, 2016, A&A, 594, A21.

Cosmic Microwave background

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

Flexible Image Transfer Specification

Planck Legacy Archive

Full-Width-at-Half-Maximum

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