Difference between revisions of "CMB spectrum & Likelihood Code"

Latest revision as of 10:05, 11 May 2021

2018 CMB spectra[edit]

General description[edit]

TT[edit]

The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles ℓ = 2-2508. Over the multipole range ℓ = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, including 86% of the sky (Planck-2020-A6^[1]). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.

For multipoles equal or greater than ℓ = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood Planck-2020-A5^[2], with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology. Associated 1σ errors include beam uncertainties. Commander is described in more detail in Planck-2020-A4^[3], and Plik is described in more detail in Planck-2020-A5^[2].

TE, EE, and EB, BB[edit]

The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range ℓ = 2-1996. In the multipole range 2 ≤ l ≤ 29, we plot the power spectra estimates from the SimAll likelihood (though only the EE spectrum is used in the baseline parameter analysis at l ≤ 29), see Planck-2020-A6^[1]). The spectra are obtained using a cross quasi maximum likelihood algorithm (QML) on the 100 and 143 GHz maps and validated against high fidelity end-to-end simulations.

In the range ℓ = 2-29, we also release the BB, and EB power spectra derived from the same maps. Error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates. Analogously to the TT case, the ℓ ≥ 30 spectrum is derived from the Plik likelihood Planck-2020-A3^[4] by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP ΛCDM run.

Best-fit model[edit]

We also provide best-fit LCDM CMB power spectra from the baseline Planck TT,TE,EE+lowE+lensing. The spectra must be divided by the best-fit Planck map-based calibration parameter squared, calPlanck**2, to be compared to the coadded CMB spectra. The best-fit calPlanck value can be found in the file "COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt".

Production process[edit]

The Plik high-multipole likelihood (described in detail in Planck-2020-A5^[2]) is a Gaussian approximation of the probability distributions of the TT, EE, and TE angular power spectra, with semi-analytic covariance matrices calculated assuming a fiducial cosmology. It includes multipoles in the range 30 to 2508 for TT and 30 to 1996 for TE and EE and is constructed from half-mission cross-spectra measured from the 100-, 143-, and 217-GHz HFI frequency maps. For more details see Planck-2020-A6^[1].

Inputs[edit]

The T T likelihood uses four half-mission cross-spectra with different multipole cuts to avoid multipole regions where noise dominates due to the limited resolution of the beams and to en-sure foreground contamination is correctly handled by our fore-ground model: 100 × 100 ( ℓ = 30–1197); 143 × 143 (ℓ = 30– 1996); 143 × 217 (ℓ = 30–2508); and 217 × 217 (ℓ = 30–2508). The TE and EE likelihoods also include the 100 × 143 and 100 × 217 cross-spectra to improve the signal-to-noise ratio, and have different multipole cuts: 100 × 100 (ℓ = 30–999); 100 × 143 (ℓ = 30–999); 100 × 217 (ℓ = 505–999); 143 × 143 (ℓ = 30– 1996); 143 × 217 (ℓ = 505–1996); and 217 × 217 (ℓ = 505– 1996). The 353, 545 and 857 GHz temperature and polarization maps are also used to build the dust templates, and contribute to the galactic and point source masks determination.

File names and meta-data[edit]

The CMB spectra and their uncertainties are distributed in ASCII text files named COM_PowerSpect_CMB_nn_R3.01.fits, where nn stands for the type of spectrum the file contains:

COM_PowerSpect_CMB-EE-full_R3.01.txt
COM_PowerSpect_CMB-TE-full_R3.01.txt
COM_PowerSpect_CMB-TT-full_R3.01.txt
COM_PowerSpect_CMB-low-ell-BB-full_R3.01.txt
COM_PowerSpect_CMB-low-ell-EB-full_R3.01.txt

The binned CMB spectra are also provided as ASCII files named COM_PowerSpect_CMB_nn-binned_R3.01.fits, where nn stands for the type of spectrum the file contains:

COM_PowerSpect_CMB-EE-binned_R3.02.txt
COM_PowerSpect_CMB-TE-binned_R3.02.txt
COM_PowerSpect_CMB-TT-binned_R3.01.txt

Update 19 August 2019: Version R3.01 of the TE and EE binned spectra (COM_PowerSpect_CMB-TE-binned_R3.01.txt and COM_PowerSpect_CMB-EE-binned_R3.01.txt) have been replaced with version R3.02 (COM_PowerSpect_CMB-TE-binned_R3.02.txt and COM_PowerSpect_CMB-EE-binned_R3.03.txt) because the contents of these two files were erroneously interchanged. COM_PowerSpect_CMB-TE-binned_R3.01.txt contained the spectra of EE and the file COM_PowerSpect_CMB-EE-binned_R3.01.txt contained the spectra of TE. This bug has been fixed and the udpated files are available in the PLA.

In addition we provide one file containing all the parameters of the Plik runs which yielded the spectra. This file is named

COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt

The theoretical spectrum of the best-fit model itself is provided in a separate file named

COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt

The data file columns give D_ℓ = ℓ(ℓ+1)C_ℓ / 2π in units of μK², and the lower and upper 68% uncertainties.

2018 Likelihood[edit]

The 2018 baseline likelihood release consists of a code package and a single data package. Five extended data packages are also available, enabling exploration of alternatives to the baseline results. The code compiles to a library, allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets. A data set permits the computation of a single likelihood among:

the high-ℓ temperature and polarization CMB (jointly or separately);
the low-ℓ temperature and polarization CMB (jointly or separately);
the CMB lensing reconstruction.

By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.

Only the baseline data package, COM_Likelihood_Data-baseline_R3.00.tar.gz, will be fully described on this page. It contains ten data sets, which are enough to compute all of the baseline Planck results that are discussed in Planck-2020-A5^[2], as well as some obvious variations (for example using only the Temperature CMB data). For the case of lensing, it also contains a CMB-marginalized version of the likelihood, allowing the computation of the CMB lensing likelihood independently of the CMB as explained in Planck-2020-A8^[5]. The baseline data package also contains a few ancillary files, describing the recommended priors for the high-ℓ likelihood, as well as some "cosmomc" ancillary files.

The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in Planck-2020-A5^[2] and Planck-2020-A8^[5].

Important update May 2021: A bug was reported in the code of the CMB marginalized version of the lensing likelihood. The bug caused a first order correction in the computation of the likelihood to be miscomputed and as a consequence biased cosmological results. The bug was only present in the distributed R3.00 and R3.01 of the likelihood code. It is not present in the other implementation of the likelihood (such as cosmoMC or cobaya version). The bug was not present in the versions of the code used to produce the Legacy lensing paper (Planck-2020-A8^[5]) or the released public chains. The issue is corrected with the package R3.10. The correction works with the previously distributed likelihood data files.

Library and tools

Description

The library consists of code written in C and Fortran 90. It can be called from both of those languages. Optionally, a python wrapper can be built as well. Scripts to simplify the linking of the library with other codes are part of the package, as well as some example codes that can be used to test the correct installation of the code and the integrity of the data packages. Optionally, a script is also available, allowing the user to modify the multipole range and in some cases the content of some of the likelihoods (including the high-ℓ polarized likelihoods) and reproduce the tests performed in the paper. A description of the tool, the API of the library, as well as different installation procedures, are detailed in the readme.md file in the code package.

File name

Update May 2021 : As of 2021_05_10 the code can be extracted from COM_Likelihood_Code-v3.0_R3.10.tar.gz.

Please read the file readme.md for installation instructions.

Changes compared to version R3.01 (2021_05_10)

Major : Correct a bug in the computation of the CMB marginalized lensing.
Configuration : new user modifiable file clik_extra_env gather the url, names and versions of the external packages that can be installed automatically by the likelihood code. This will hopefully simplify troubleshooting with new versions of the external packages in the future.
Configuration : update to latest version of waf. Print a warning when the compilation of C or fortran part will use a compiler defined by a user set CC or FC environment variable.
Python wrapper : correct a bug where error messages would not be properly displayed in python 3
Python wrapper : when both astropy and pyfits are available, prefer astropy

Changes compared to version R3.00 (2019_08_01)

Modify packaging and fixes two issues with intel fortran 2019 and gcc9 that were preventing compilation:

Improve parsing of intel fortran dryrun output to fix an issue with the building of the intel fortran link line which was broken for version 2019
Change an openmp scheduling option in src/plik/smica.c to go aroung an API incompatibility between intel 2019 openmp and gcc9 openmp which was preventing the code to correctly compile in this particular case.
The tar.gz no more unpack to a tar.bz2 and directly provide the code.

Please read the file readme.md for installation instructions.

Data sets - Baseline data

All of the released baseline data are distributed within a single file, COM_Likelihood_Data-baseline_R3.00.tar.gz .

This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.

Each data set is stored in its own directory. The directory structure follows similar rules for each data set, and stores data, template, and meta-data for each particular likelihood.

As in 2013, the CMB likelihood is cut into low-ℓ and high-ℓ parts. Moreover, for each of those, we distribute both a T-only data file and a joint T+P one. In the case of the high-ℓ part, we also distribute two specific versions of the likelihood, that allow for estimates of T and T+P marginalized over the nuisance parameters. Combining both the low-ℓ and high-ℓ files, one can compute the likelihood over the range ℓ=2-2508 in TT and ℓ=2-1996 in TE and EE. A full description of the low-ℓ and high-ℓ likelihood is available in Planck-2020-A5^[2].

For the case of lensing we only distribute the likelihood based on both the temperature and polarization data. A full description of the lensing likelihood is available in Planck-2020-A8^[5].

All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that this parameter is explored over the Gaussian prior 1.0000±0.0025.

Low-ℓ likelihoods

TT only - commander

This file allows for the computation of the CMB TT likelihood in the range ℓ=2-29. Using the optional tool in the code package, it can be modified to cover any multipole range up to ℓ<200.

Production process

The likelihood is based on the results of the Commander approach, which implements a Bayesian component-separation method in pixel space, sampling the posterior distribution of the parameters of a model that describes both the CMB and the foreground emissions in a combination of the Planck maps. The samples of this exploration are used to infer the foreground-marginalized low-ℓ likelihood for any TT CMB spectrum.

Inputs:

Planck 30- to 857-GHz frequency maps;
Commander 2018 confidence mask (Planck-2020-A4^[3]).

File name and usage

The commander likelihood is distributed in plc_3.0/low_l/commander/commander_dx12_v3_2_29.clik.

When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 29 (inclusive) and an extra nuisance parameter consisting of the overall Planck calibration. Note that the vector really starts at ℓ=0, although the first two entries are null.

EE only - simall

This file allows for the computation of the EE likelihood in the range ℓ=2-29. It should be used with the low-ℓ TT-only likelihood to form the baseline low-ℓ likelihood.

Production process

The likelihood is estimated by comparing a cross-quasi-maximum-likelihood algorithm (QML) on the 100- and 143-GHz maps to high fidelity end-to-end simulations of the HFI instrument, as described in Planck-2020-A5^[2]. The Galactic contamination (synchrotron and dust) in the input 100- and 143-GHz maps is mitigated by regressing the (LFI) 30-GHz and (HFI) 353-GHz maps. In order to avoid highly contaminated areas of the sky, the regions near the Galactic centre and plane are masked and we retain only about 50% of the sky. The mask is built by applying a threshold on the 353-GHz map and combined with the Commander confidence mask. The end-to-end simulations contain realistic Galactic contamination and our best knowledge of the HFI detector and analysis chain. The accuracy of the simulation is discussed in Planck-2020-A3^[4]. The end-to-end simulations only explore a single CMB realization, but at large scales a CMB swapping procedure can be implemented to explore different cosmological parameter sets (within ΛCDM) and different CMB realizations. The end-to-end realizations are processed in the same way as the data (foreground mitigation, masking, QML) and using the distance between the data and the simulations, an approximation of the log likelihood is produced for each multipole. The final likelihood thus ignores ℓ-to-ℓ correlations, as well as TT to EE ones. The likelihood files contains metadata allowing for the computation of the approximation for each multipole.

Inputs:

Planck 30-, 100-, 143- and 353-GHz frequency maps;
Commander 2018 confidence mask (Planck-2020-A4^[3]) and a specially designed Galactic mask based on the 353-GHz map
300 single CMB- and foreground-realization end-to-end simulations. 300000 large-scale CMB-only realization (300 map realizations for 1000 different random set of cosmological parameters).

File name and usage

The low-ℓ EE likelihood is distributed in plc_3.0/low_l/simall/simall_100x143_offlike5_EE_Aplanck_B.clik .

When used with the library, this expects a vector of parameters consisting of the EE CMB power spectrum from ℓ=0 to 29 (inclusive) and an extra nuisance parameter consisting of the overall Planck calibration. Note that the entries really start at ℓ=0, although the ℓ=0 and ℓ=1 values will be null.

BB only - simall

This file allows for the computation of the BB likelihood in the range ℓ=2-29. It is not part of the baseline likelihood. The BB spectrum at large scales is compatible with zero.

Production process

The likelihood is estimated by comparing a cross-quasi-maximum-likelihood algorithm (QML) on the 100- and 143-GHz maps to high fidelity end-to-end simulations of the HFI instrument, as described in Planck-2020-A5^[2]. The Galactic contamination (synchrotron and dust) in the input 100- and 143-GHz maps is mitigated by regressing the (LFI) 30-GHz and (HFI) 353-GHz maps. In order to avoid highly contaminated areas of the sky, the regions near the Galactic centre and plane are masked and we retain only about 50% of the sky. The mask is built by applying a threshold on the 353-GHz map and combined with the Commander confidence mask. The end-to-end simulations contain a realistic Galactic contamination and our best knowledge of the HFI detector and analysis chain. The accuracy of the simulation is discussed in Planck-2020-A3^[4]. The end-to-end simulations only explore a single CMB realization, but at large scales a CMB-swapping procedure can be implemented to explore different cosmological parameter sets (within ΛCDM) and different CMB realizations. The end-to-end realizations are processed in the same way as the data (foreground mitigation, masking, QML) and using the distance between the data and the simulations, an approximation of the log likelihood is produced for each multipole. The final likelihood thus ignores ℓ-to-ℓ correlations. The likelihood files contains metadata allowing for the computation of the approximation for each multipole.

Inputs:

Planck 30-, 100-, 143- and 353-GHz frequency maps;
Commander 2018 confidence mask (Planck-2020-A4^[3]) and a specially designed Galactic masks based on the 353-GHz map
300 single CMB- and foreground-realization end-to-end simulations. 300000 large-scale CMB-only realization (300 map realizations for 1000 different random set of cosmological parameters).

File name and usage

The low ell BB likelihood is distributed in plc_3.0/low_l/simall/simall_100x143_offlike5_BB_Aplanck_B.clik.

When used with the library, this expects a vector of parameters consisting of the BB CMB power spectrum from ℓ=0 to 29 (inclusive) and by an extra nuisance parameter consisting of the overall Planck calibration. Note that the entries really start at ℓ=0, although the ℓ=0 and ℓ=1 values will be null.

EEBB - simall

This file allows for the computation of the EEBB likelihood in the range ℓ=2-29. It is not part of the baseline likelihood. Since correlations between spectra and multipole are ignored in simall, using this file is equivalent (up to a possible normalization) to summing the log likelihood provided by the EE- and BB-only simall files.

Production process

The likelihood is estimated by comparing a cross-quasi-maximum-likelihood algorithm (QML) on the 100- and 143-GHz maps to high fidelity end-to-end simulation of the HFI instrument, as described in Planck-2020-A5^[2]. The Galactic contamination (synchrotron and dust) in the input 100- and 143-GHz maps is mitigated by regressing the (LFI) 30-GHz and (HFI) 353-GHz maps. In order to avoid highly contaminated areas of the sky, the regions near the Galactic centre and plane are masked and we retain only about 50% of the sky. The mask is built by applying a threshold on the 353-GHz map and combined with the Commander confidence mask. The end-to-end simulations contain a realistic Galactic contamination and our best knowledge of the HFI detector and analysis chain. The accuracy of the simulation is discussed in Planck-2020-A3^[4]. The end-to-end simulations only explore a single CMB realization, but at large scales a CMB swapping procedure can be implemented to explore different cosmological parameter sets (within ΛCDM) and different CMB realizations. The end-to-end realizations are processed in the same way as the data (foreground mitigation, masking, QML) and using the distance between the data and the simulations, an approximation of the log likelihood is produced for each multipole. The final likelihood thus ignore ℓ-to-ℓ correlations. The likelihood files contains metadata allowing for computation of the approximation for each multipole.

Inputs:

Planck 30-, 100-, 143- and 353-GHz frequency maps;
Commander 2018 confidence mask (Planck-2020-A4^[3]) and a specially designed Galactic mask based on the 353-GHz map
300 single CMB- and foreground-realization end-to-end simulations. 300000 large scale CMB-only realization (300 map realizations for 1000 different random set of cosmological parameters.)

File name and usage

The low ell EEBB likelihood is distributed in plc_3.0/low_l/simall/simall_100x143_offlike5_EEBB_Aplanck_B.clik.

When used with the library, this expects a vector of parameters consisting of the EE CMB power spectrum from ℓ=0 to 29 (inclusive), followed by BB CMB power spectrum from ℓ=0 to 29 (inclusive) and by an extra nuisance parameter consisting of the overall Planck calibration. Note that the entries really start at ℓ=0, although the ℓ=0 and ℓ=1 values will be null.

High-ℓ likelihoods

TT only - Plik

This file allows for the computation of the CMB TT likelihood in the range ℓ=30-2508. Using the optional tools in the code package it can be modified to cover any multipole range within 29<ℓ<2509, and to remove the contribution of any range of multipole from any of the cross-spectra considered in the approximation.

Production process

The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission TT cross-spectra. Only the 100×100, 143×143, 143×217, and 217×217 spectra are actually used. Masks and multipole ranges for each spectrum are different and described in Planck-2020-A5^[2]. Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps. The file also contains templates for the residual foreground contamination of each spectrum. The templates are needed to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates. The covariance matrix is computed for a fiducial cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters. The beam matrix computed for the specific masks and data cuts are applied to the 2015 TT ΛCDM best-fit spectra to predict leakage templates. Subpixel effect are predicted for the specific masks and data cuts.

Inputs:

Planck 100-, 143-, and 217-GHz half-mission T maps;
CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;
Planck 545-GHz maps for the dust residual-contamination template;
CIB, tSZ, kSZ, and CIB×SZ templates;
Beam-matrix (effective beams and leakage) and subpixel-effect templates computed for the specific masks and sky fractions retained for the likelihood.

File name and usage

The high-ℓ, Plik TT likelihood is distributed in plc_3.0/hi_l/plik/plik_rd12_HM_v22_TT.clik.

When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 2508 (inclusive), followed by a vector of 20 nuisance parameters. Those are, in order:

A_cib_217, the CIB contamination at ℓ=3000 in the 217-GHz Planck map;
cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;
xi_sz_cib, the SZ×CIB cross-correlation;
A_sz, the tSZ contamination at 143 GHz;
ps_A_100_100, the point-source contribution in 100×100;
ps_A_143_143, the point-source contribution in 143×143;
ps_A_143_217, the point-source contribution in 143×217;
ps_A_217_217, the point-source contribution in 217×217;
ksz_norm, the kSZ contamination;
gal545_A_100, the dust residual contamination at ℓ=200 in 100×100;
gal545_A_143, the dust residual contamination at ℓ=200 in 143×143;
gal545_A_143_217, the dust residual contamination at ℓ=200 in 143×217;
gal545_A_217, the dust residual contamination at ℓ=200 in 217×217;
A_sbpx_100_100_TT, a rescaling amplitude for the subpixel effects at ℓ=200 in 100×100 (default is 1);
A_sbpx_143_143_TT, a rescaling amplitude for the subpixel effects at ℓ=200 in 143×143 (default is 1);
A_sbpx_143_217_TT, a rescaling amplitude for the subpixel effects at ℓ=200 in 143×217 (default is 1);
A_sbpx_217_217_TT, a rescaling amplitude for the subpixel effects at ℓ=200 in 217×217 (default is 1);
calib_100T, the relative calibration between the 100 and 143 spectra;
calib_217T, the relative calibration between the 217 and 143 spectra;
A_planck, the Planck absolute calibration.

Recommended priors can be found in the file plc_3.0/hi_l/plik/plik_recommended_priors.txt For cosmomc users, a set of initialization files is available in plc_3.0/cosmomc

TT+TE+EE - Plik

This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range ℓ=30-2508 for TT and ℓ=30-1996 for TE and EE. Using the optional tools in the code package it can be modified to cover any multipole range within 29<ℓ<2509, and to remove the contribution of any range of multipole from any of the cross-spectra (in TT, TE EE and any cross-frequencies) considered in the approximation.

Production process

The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission T and E cross-spectra. In temperature, only the 100×100, 143×143, 143×217, and 217×217 spectra are actually used, while in TE and EE all of them are used. Masks and multipole ranges for each spectrum are different and described in Planck-2020-A5^[2]. Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point-source part, and on the CO maps. The file also contains templates for the residual foreground contamination of each spectrum. The templates are needed to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates. The covariance matrix is computed for a fiducial cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters. The beam matrix computed for the specific masks and data cuts are applied to the 2015 TT ΛCDM best-fit spectra to predict leakage templates. Subpixel effect are predicted for the specific masks and data cuts. The 300 end-to-end HFI simulations from the FFP10 suite are used to estimate correlated-noise residuals in the EE auto-spectra at 100, 143, and 217 GHz.

Inputs:

Planck 100-, 143-, and 217-GHz half-mission T+P maps;
CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;
Planck 545-GHz and 353-GHz maps for the dust residual-contamination template;
CIB, tSZ, kSZ, and CIB×SZ templates;
Beam-matrix (effective beams and leakage) and subpixel-effect templates computed for the specific masks and sky fractions retained for the likelihood;
300 end-to-end HFI simulations and resulting smoothed correlated-noise templates.

File name and usage

The high-ℓ, plik TTTEEE likelihood is distributed in plc_3.0/hi_l/plik/plik_rd12_HM_v22b_TTTEEE.clik.

This file should not be used with any other TT-only high-ℓ file.

When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 2508 (inclusive), followed the EE and TE spectra (same range) and by a vector of 47 nuisance parameters.

Those are, in order:

A_cib_217, the CIB contamination at ℓ=3000 in the 217-GHz Planck map;
cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;
xi_sz_cib, the SZ×CIB cross-correlation;
A_sz, the tSZ contamination at 143 GHz;
ps_A_100_100, the point-source contribution in 100×100;
ps_A_143_143, the point-source contribution in 143×143;
ps_A_143_217, the point-source contribution in 143×217;
ps_A_217_217, the point-source contribution in 217×217;
ksz_norm, the kSZ contamination;
gal545_A_100, the dust residual contamination at ℓ=200 in 100×100TT;
gal545_A_143, the dust residual contamination at ℓ=200 in 143×143TT;
gal545_A_143_217, the dust residual contamination at ℓ=200 in 143×217TT;
gal545_A_217, the dust residual contamination at ℓ=200 in 217×217TT;
galf_EE_A_100, the dust residual contamination at ℓ=500 in 100×100EE;
galf_EE_A_100_143, the dust residual contamination at ℓ=500 in 100×143EE;
galf_EE_A_100_217, the dust residual contamination at ℓ=500 in 100×217EE;
galf_EE_A_143, the dust residual contamination at ℓ=500 in 143×143EE;
galf_EE_A_143_217, the dust residual contamination at ℓ=500 in 143×217EE;
galf_EE_A_217, the dust residual contamination at ℓ=500 in 217×217EE;
galf_EE_index, the dust EE template slope, which should be set to -2.4;
galf_TE_A_100, the dust residual contamination at ℓ=500 in 100×100TE;
galf_TE_A_100_143, the dust residual contamination at ℓ=500 in 100×143TE;
galf_TE_A_100_217, the dust residual contamination at ℓ=500 in 100×217TE;
galf_TE_A_143, the dust residual contamination at ℓ=500 in 143x143TE;
galf_TE_A_143_217, the dust residual contamination at ℓ=500 in 143×217TE;
galf_TE_A_217, the dust residual contamination at ℓ=500 in 217×217TE;
galf_TE_index, the dust EE template slope, which should be set to -2.4;
A_cnoise_e2e_100_100_EE normalization for the end-to-end empirical correlated-noise template at 100 GHz (should be set to 1, set to 0 to null effect of the template);
A_cnoise_e2e_143_143_EE normalization for the end-to-end empirical correlated-noise template at 143 GHz (should be set to 1, set to 0 to null effect of the template);
A_cnoise_e2e_217_217_EE normalization for the end-to-end empirical correlated-noise template at 217 GHz (should be set to 1, set to 0 to null effect of the template);
A_sbpx_100_100_TT normalization for the subpixel-effect correction at 100$\times$100 TT (should be set to 1);
A_sbpx_143_143_TT normalization for the subpixel-effect correction at 143$\times$143 TT (should be set to 1);
A_sbpx_143_217_TT normalization for the subpixel-effect correction at 143$\times$217 TT (should be set to 1);
A_sbpx_217_217_TT normalization for the subpixel-effect correction at 217$\times$217 TT (should be set to 1);
A_sbpx_100_100_EE normalization for the subpixel-effect correction at 100$\times$100 EE (should be set to 1);
A_sbpx_100_143_EE normalization for the subpixel-effect correction at 100$\times$143 EE (should be set to 1);
A_sbpx_100_217_EE normalization for the subpixel-effect correction at 100$\times$217 EE (should be set to 1);
A_sbpx_143_143_EE normalization for the subpixel-effect correction at 143$\times$143 EE (should be set to 1);
A_sbpx_143_217_EE normalization for the subpixel-effect correction at 143$\times$217 EE (should be set to 1);
A_sbpx_217_217_EE normalization for the subpixel-effect correction at 217$\times$217 EE (should be set to 1);
calib_100T, the relative calibration between 100 and 143 TT spectra;
calib_217T, the relative calibration between 217 and 143 TT spectra;
calib_100P, the calibration of the 100 EE;
calib_143P, the calibration of the 143 EE;
calib_217P, the calibration of the 217 EE;
A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;
A_planck, the Planck absolute calibration.

Recommended priors can be found in the file plc_3.0/hi_l/plik/plik_recommended_priors.txt For cosmomc users, a set of initialization files is available in plc_3.0/cosmomc

TT only - Plik lite

This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range ℓ=30-2508. It should not be used with the regular high-ℓ TT or TTTEEE files.

Production process

The Plik likelihood files described above have been explored using a Bayesian algorithm described in Planck-2020-A5^[2]. The joint posterior of the CMB TT spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-ℓ likelihood approximation for the CMB spectrum only. The nuisance parameters have been marginalized over the priors described above.

Inputs:

Plik plik_rd12_HM_v22b_TTTEEE likelihood;
dust residual, CIB, tSZ, kSZ, and CIB×SZ, leakage and subpixel templates.

File name and usage

The high-ℓ, Plik TT, nuisance-marginalized likelihood is distributed in plc_3.0/hi_l/plik_lite/plik_lite_v22_TT.clik .

When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.

TT EE TE - Plik lite

This file allows for the computation of the nuisance-marginalized CMB joint TT, TE, EE likelihood in the range ℓ=30-2508 for temperature and ℓ=30-1996 for TE and EE. It should not be used with the regular high-ℓ TT or TTTEEE files.

Production process

The Plik likelihood files described above have been explored using a Bayesian algorithm described in Planck-2020-A5^[2]. The joint posterior of the CMB TT, TE, and EE spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.

Inputs:

Plik plik_rd12_HM_v22b_TTTEEE likelihood;

dust residual, CIB, tSZ, kSZ, and CIB×SZ leakage, subpixel and correlated noise templates.

File name and usage

The high-ℓ, Plik TTTEEE, nuisance-marginalized likelihood is distributed in plc_3.0/hi_l/plik_lite/plik_lite_v22_TTTEEE.clik.

When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 2508 (inclusive), followed by the EE, and TE spectra (same range) and by the Planck absolute calibration nuisance parameter.

Lensing likelihoods

CMB dependent likelihood

This file allows for the computation of the baseline lensing likelihood, using the SMICA temperature and polarization map-based lensing reconstruction. Only the lensing multipole range ℓ=8-400 is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes the computation of a model-dependent correction to the normalization and the "N1 bias". To speed up those computations, both are performed using a linear approximation.

Production process The SMICA T maps are filtered and correlated to reconstruct an optimal lensing-reconstruction map. Biases are corrected using Monte Carlo simulations for the dominant "mean field" and "N0" contributions, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned. The covariance matrix of this binned spectrum is evaluated using numerical simulations. The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.

Inputs:

SMICA temperature and polarization CMB map;

Galactic mask;

best-fit Planck CMB model.

File name and usage

The lensing likelihood is distributed in plc_3.0/hi_l/lensing/smicadx12_Dec5_ftl_mv2_ndclpp_p_teb_consext8.clik_lensing.

When used with the library, this expects a vector of parameters consisting of the φφ lensing spectrum for ℓ=0 to 2500 (inclusive), followed by the followed by the TT CMB power spectrum for ℓ=0 to 2500 (inclusive), the EE and TE power spectra (same range) and by the Planck absolute calibration nuisance parameter.

The TT, EE, and TE spectra are needed to compute the normalization and N1 corrections.

CMB marginalized lensing likelihood

This file allows for the computation of the baseline lensing likelihood, marginalized over the CMB power spectrum. The covariance is enlarged compared to the previous case to account for the change in N0 and N1 dues to possible variations of the CMB power spectrum. As in the previous case, only the lensing multipoles in the range range ℓ=8-400 are used.

Production process

The covariance of the CMB dependent likelihood is enlarged, and the theory spectrum is shifted to account for the marginalization over the CMB spectrum, using a Gaussian approximation. The "plik_lite" likelihood is used to provide the CMB spectra and covariances.

Inputs:

SMICA T and E CMB maps;

Galactic mask;

best-fit Planck CMB model.

plik_lite likelihood

File name and usage

The CMB marginalized lensing likelihood is distributed in plc_3.0/hi_l/lensing/smicadx12_Dec5_ftl_mv2_ndclpp_p_teb_consext8_CMBmarged.clik_lensing.

When used with the library, this expects a vector of parameters consisting of the φφ lensing spectrum for ℓ=0 to 2500 (inclusive), followed by the Planck absolute calibration nuisance parameter.

Data sets - Extended data

Five other data files are available. Those extend the baseline delivery by adding:

The LFI based low-ℓ likelihood for TEB, COM_Likelihood_Data-extra-bflike-ext_R3.00.tar.gz;

TE, EE, unbinned and spectrum-model PE correction high-&#8467 Plik likelihoods, COM_Likelihood_Data-extra-plik-ext_R3.00.tar.gz;

TE and EE high-&#8467 foreground- and nuisance-marginalized Plik_lite likelihoods COM_Likelihood_Data-extra-plik-lite-ext_R3.00.tar.gz;

TT, TE, EE, TTTEEE, TTTE, TEEE and TTEE alternative high-&#8467 Camspec likelihoods COM_Likelihood_Data-extra-camspec-ext_R3.00.tar.gz;

extended &#8467 range lensing likelihood, COM_Likelihood_Data-extra-lensing-ext_R3.00.tar.gz .

Note that although these products are discussed in the Planck papers, they are not used for the baseline results.

Each file contains a readme.md description of the content and the use of the different likelihood files.

Previous Releases: (2015) and (2013) CMB spectrum and Likelihood[edit]

2015 CMB spectrum and Likelihood

2015 CMB spectra
General description
TT The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles ℓ = 2-2508. Over the multipole range ℓ = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky (Planck-2015-A10^[6]). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.
For multipoles equal or greater than ℓ = 30, instead, the spectrum is derived from the "Plik" likelihood Planck-2015-A11^[7] by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP ΛCDM run. Associated 1σ errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.

Planck 2015 TT power spectrum. The x-axis is logarithmic up to ℓ = 30 and linear at higher ℓ. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]). Residuals with respect to this model are shown in the lower panel. The error bars show ±1σ uncertainties.

TE, EE, and TB, EB, BB
The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range ℓ = 2-1996. The data points relative to the multipole range ℓ = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz Q and U Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see Planck-2015-A11^[7]). In the range ℓ = 2-29, we also release the BB, TB, and EB power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates. Analogously to the TT case, the ℓ ≥ 30 spectrum is derived from the Plik likelihood Planck-2015-A11^[7] by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP ΛCDM run.

Planck 2015 EE power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A13^[8]). Residuals with respect to this model are shown in the lower panel. The error bars show ±1σ uncertainties.

Planck 2015 TE power spectrum. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A13^[8]). Residuals with respect to this model are shown in the lower panel. The error bars show ±1σ uncertainties.

Production process The ℓ < 30 part of the Planck TT power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters (Planck-2015-A10^[6]). The power spectrum at any multipole ℓ is given as the maximum probability point for the posterior C_ℓ distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see Planck-2015-A10^[6]. The polarization spectra (EE, TE, BB, TB, EB) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of Planck-2015-A11^[7] for details about the foreground cleaning procedure. The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again Planck-2015-A11^[7]). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors.
The ℓ ≥ 30 part of the TT, TE, and EE power spectra have been derived by the Plik likelihood, a code that implements a pseudo-C_ℓ based technique, extensively described in section 2.2 and the appendix of Planck-2013-XV^[9], and more recently in Planck-2015-A11^[7]. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of Planck-2015-A13^[8] and in Planck-2015-A11^[7]. The final power spectrum is an optimal combination of the 100, 143, 143×217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for TT we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for TE and EE we use the best fit from Planck+TT+lowP, cf. table 3 of Planck-2015-A13^[8]). A thorough description of the models of unresolved foregrounds is given in Planck-2015-A11^[7]. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The ℓ ≥ 30 CMB TT spectrum and associated covariance matrix are available in two formats.

Unbinned: TT, 2479 bandpowers (ℓ = 30-2508); TE or EE, 1697 bandpowers (ℓ = 30-1996).

Binned, in bins of Δℓ = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.
We bin the C_ℓ power spectrum with a weight proportional to ℓ(ℓ+1), so that the C_{ℓ_b} binned bandpower centred on ℓ_b is Equivalently, using the matrix formalism, we can construct the binning matrix B as where B is an n_b×n_ℓ matrix, with n_b=83 being the number of bins and n_ℓ=2479 the number of unbinned multipoles. Thus Here, is the vector containing all the binned (unbinned) C_ℓ bandpowers, [math]\mathrm{cov}[/math] is the covariance matrix, and ℓ_b is the weighted average multipole in each bin. Note that following this definition, ℓ_b can be a non-integer. The binned D_{ℓ_b} power spectrum is then calculated as
Inputs

Low-ℓ spectrum (ℓ<30):
Planck 30 and 44 GHz frequency maps;

Planck 70 to 857 GHz detector and detector-set maps;

9-year WMAP temperature sky maps between 23 and 94 GHz;

408-MHz survey of Haslam et al. (1982);

Commander χ²-based LM93 confidence mask (Planck-2015-A10^[6]).
High-ℓ spectrum (30≤ℓ≤2508):
100, 143, 143×217 and 217 GHz spectra and their covariance matrix (setion 3.3 of Planck-2015-A13^[8]);

best-fit foreground templates and inter-frequency calibration factors (table 3 of Planck-2015-A13^[8]);

beam transfer function uncertainties (Planck-2015-A07^[10]).
File names and meta-data
The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named COM_PowerSpect_CMB_R2.nn.fits.

R2.00 contains (unbinned) TT spectra for low ℓ and TT, TE and EE spectra at high ℓ, both binned and unbinned (7 extensions).

R2.01 corrects a small error in the effective ℓ of the bin of the binned data, which was truncated to an integer. Since these are weighted averages of the ℓ's used in a particular bin, they should be a reals.

R2.02 contains low ℓ *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).
Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).

1. TT low-ℓ, unbinned (TTLOLUNB)

with the low-ℓ part of the spectrum, not binned, and for ℓ=2-29. The table columns are:
ELL (integer), multipole number;

D_ELL (float), D_ℓ as described above;

ERRUP (float), the upward uncertainty;

ERRDOWN (float), the downward uncertainty.
2. TE low-ℓ, unbinned (TTLOLUNB)

with the low-ℓ part of the spectrum, not binned, and for ℓ=2-29. The table columns are:
ELL (integer), multipole number;

D_ELL (float), D_ℓ as described above;

ERRUP (float), the upward uncertainty;

ERRDOWN (float), the downward uncertainty.
3. EE low-ℓ, unbinned (TTLOLUNB)

with the low-ℓ part of the spectrum, not binned, and for ℓ=2-29. The table columns are:
ELL (integer), multipole number;

D_ELL (float), D_ℓ as described above;

ERRUP (float), the upward uncertainty;

ERRDOWN (float), the downward uncertainty.
4. TB low-ℓ, unbinned (TTLOLUNB)

with the low-ℓ part of the spectrum, not binned, and for ℓ=2-29. The table columns are:
ELL (integer), multipole number;

D_ELL (float), D_ℓ as described above;

ERRUP (float), the upward uncertainty;

ERRDOWN (float), the downward uncertainty.
5. EB low-ℓ, unbinned (TTLOLUNB)

with the low-ℓ part of the spectrum, not binned, and for ℓ=2-29. The table columns are:
ELL (integer), multipole number;

D_ELL (float), D_ℓ as described above;

ERRUP (float), the upward uncertainty;

ERRDOWN (float), the downward uncertainty.
6. BB low-ℓ, unbinned (TTLOLUNB)

with the low-ℓ part of the spectrum, not binned, and for ℓ=2-29. The table columns are:
ELL (integer), multipole number;

D_ELL (float), D_ℓ as described above;

ERRUP (float), the upward uncertainty;

ERRDOWN (float), the downward uncertainty.
7. TT high-ℓ, binned (TTHILBIN)

with the high-ℓ part of the spectrum, binned into 83 bins covering 〈ℓ〉= 47-2499 in bins of width ℓ=30 (with the exception of the last bin that is smaller). The table columns are:
ELL (float), mean multipole number of bin;

L_MIN (integer), lowest multipole of bin;

L_MAX (integer), highest multipole of bin;

D_ELL (float), D_ℓ as described above;

ERR (float), the uncertainty.
8. TT high-ℓ unbinned (TTHILUNB)

with the high-ℓ part of the spectrum, unbinned, in 2979 bins covering 〈ℓ〉= 30-2508. The table columns are:
ELL (integer), multipole;

D_ELL (float), D_ℓ as described above;

ERR (float), the uncertainty.
9. TE high-ℓ, binned (TEHILBIN)

with the high-ℓ part of the spectrum, binned into 83 bins covering 〈ℓ〉= 47-1988 in bins of width ℓ=30 (with the exception of the last bin that is smaller). The table columns are:
ELL (float), mean multipole number of bin;

L_MIN (integer), lowest multipole of bin;

L_MAX (integer), highest multipole of bin;

D_ELL (float), D_ℓ as described above;

ERR (float), the uncertainty.
10. TE high-ℓ, unbinned (TEHILUNB)

with the high-ℓ part of the spectrum, unbinned, in 2979 bins covering 〈ℓ〉= 30-1996. The table columns are:
ELL (integer), multipole;

D_ELL (float), D_ℓ as described above;

ERR (float), the uncertainty.
11. EE high-ℓ, binned (EEHILBIN)

with the high-ℓ part of the spectrum, binned into 83 bins covering 〈ℓ〉= 47-1988 in bins of width ℓ=30 (with the exception of the last bin that is smaller). The table columns are:
ELL (float), mean multipole number of bin;

L_MIN (integer), lowest multipole of bin;

L_MAX (integer), highest multipole of bin;

D_ELL (float), D_ℓ as described above;

ERR (float), the uncertainty.
12. EE high-ℓ, unbinned (EEHILUNB)

with the high-ℓ part of the spectrum, unbinned, in 2979 bins covering 〈ℓ〉= 30-1996. The table columns are:
ELL (integer), multipole;

D_ELL (float), D_ℓ as described above;

ERR (float), the uncertainty.
The spectra give D_ℓ = ℓ(ℓ+1)C_ℓ / 2π in units of μK². The covariance matrices of the spectra will be released at a later time.
The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.
Likelihood
The 2015 baseline likelihood release consists of a code package and a single data package. Four extended data packages are also available enabling exploration of alternatives to the baseline results. The code compiles to a library allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets. A data set permits the computation of a single likelihood among:

the high-ℓ temperature and polarization CMB (jointly or separately);

the low-ℓ temperature and polarization CMB (jointly or separately);

the CMB lensing reconstruction.
By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.
Only the baseline data package, COM_Likelihood_Data-baseline_R2.00.tar.gz, will be fully described on this page. It contains six data sets, which are enough to compute all of the baseline Planck results that are discussed in Planck-2015-A12^[11]. In particular it allows for the computation of the CMB and lensing likelihood from either the Temperature data only, or the Temperature + Polarization combination.
The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in Planck-2015-A11^[7] and Planck-2015-A15^[12]. Their full description is contained in the documentation included in each of the extended data packages.
Library and tools
Description The library consists of code written in C and Fortran 90. It can be called from both of those languages. Optionally, a python wrapper can be built as well. Scripts to simplify the linking of the library with other codes are part of the package, as well as some example codes that can be used to test the correct installation of the code and the integrity of the data packages. Optionally, a script is also available, allowing the user to modify the multipole range of the TT likelihoods and reproduce the hybridization test performed in the paper. A description of the tool, the API of the library, as well as different installation procedure are detailed in the readme.md file in the code package.
File name The code can be extracted from COM_Likelihood_Code-v2.0_R2.00.tar.bz2.
Please read the file readme.md for installation instructions.
Data sets - Baseline data All of the released baseline data are distributed within a single file, COM_Likelihood_Data-baseline_R2.00.tar.gz.
This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.
Each data set is stored in its own directory. The directory structure follows similar rules for each data set, and stores data, template, and meta-data for each particular likelihood.
As in 2013, the CMB likelihood is cut into low-ℓ and high-ℓ parts. Moreover, for each of those, we distribute both a T-only datafile and a joint T+P one. In the case of the high-ℓ part, we also distribute two specific versions of the likelihood, that allow for estimate of T and T+P marginalized over the nuisance parameters. Combining both the low-ℓ and high-ℓ files, one can compute the likelihood over the range ℓ=2-2508 in TT and ℓ=2-1996 in TE and EE. A full description of the low-ℓ and high-ℓ likelihood is available in Planck-2015-A11^[7].
Similarly, for the case of lensing, we also distribute the likelihood using both the reconstruction based on the T map only, or on T+P maps. A full description of the lensing likelihood is available in Planck-2015-A15^[12].
All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that his parameter is explored in the Gaussian prior 1.0000±0.0025.
Low-ℓ likelihoods
TT only - commander This file allows for the computation of the CMB TT likelihood in the range ℓ=2-29. Using the optional tool in the code package, it can be modified to cover any multipole range up to ℓ<200.
Production process The likelihood is based on the results of the Commander approach, which implements a Bayesian component separation method in pixel space, sampling the posterior distribution of the parameters of a model that describes both the CMB and the foreground emissions in a combination of the Planck maps, the WMAP map, and the 408-MHz survey. The samples of this exploration are used to infer the foreground marginalized low-ℓ likelihood for any TT CMB spectrum.
Inputs:

Planck 30- and 44-GHz frequency maps;

Planck 70- to 857-GHz detector and detector-set maps;

9-year WMAP temperature sky maps between 23 and 94 GHz;

408-MHz survey of Haslam et al. (1982);

Commander χ²-based LM93 confidence mask (Planck-2015-A10^[6]).
File name and usage The commander likelihood is distributed in plc_2.0/low_l/commander/commander_rc2_v1.1_l2_29_B.clik
When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 29 (inclusive) and an extra nuisance parameter consisting of the overall Planck calibration. Note that the vector really starts at ℓ=0, although the first two entries are null.
TEB This file allows for the computation of the CMB joint TT,EE, BB and TE likelihood in the range ℓ=2-29. It should not be used with the low-ℓ TT-only likelihood.
Production process The file allows for the computation of the pixel based likelihood of T, E, and B maps. The T map is the best-fit map obtained from the commander algorithm, as described above, while the E and B maps are obtained from the 70GHz LFI full mission data, but excluding the second and fourth surveys. Foreground contamination is dealt with by marginalizing over templates based on the 30-GHz LFI and 353-GHz HFI maps. The covariance matrix comes from the Planck detector sensitivity modulated on the sky by the scanning strategy. The covariance matrix is further enlarged to account for the foreground template removal. To speed up the computation by about an order of magnitude, the problem is projected into C_ℓ space using the Sherman-Morrison-Woodbury identity. Only the projected quantities are stored in the data package.
Inputs:

Planck 30- and 44-GHz frequency maps;

Planck 70- to 857-GHz detector and detector-set maps;

9-year WMAP temperature sky maps between 23 and 94 GHz;

408-MHz survey of Haslam et al. (1982);

Commander χ²-based LM93 confidence mask Planck-2015-A10^[6].

File name and usage The low ell TEB likelihood is distributed in plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik.
When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 29 (inclusive), followed by the EE (ℓ=0 to 29), BB (ℓ=0 to 29) and TE (ℓ=0 to 29) spectra, and by an extra nuisance parameter consisting of the overall Planck calibration. Note that the entries really start at ℓ=0, although the ℓ=0 and ℓ=1 values will be null.
High-ℓ likelihoods
TT only - Plik This file allows for the computation of the CMB TT likelihood in the range ℓ=30-2508. Using the optional tool in the code package it can be modified to cover any multipole range within 29<ℓ<2509.
Production process The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission TT cross-spectra. Only the 100×100, 143×143, 143×217, and 217×217 spectra are actually used. Masks and multipole ranges for each spectrum are different and described in Planck-2015-A11^[7]. Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps. The file also contains templates for the residual foreground contamination of each spectrum. The templates are needed to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates. The covariance matrix is computed for a fiducial cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.
Inputs:

Planck 100-, 143-, and 217-GHz half-mission T maps;

CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;

Planck 545-GHz maps for the dust residual contamination template;

CIB, tSZ, kSZ, and CIB×SZ templates.
File name and usage The high-ℓ, Plik TT likelihood is distributed in plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik.
When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 2508 (inclusive), followed by a vector of 16 nuisance parameters. Those are, in order:

A_cib_217, the CIB contamination at ℓ=3000 in the 217-GHz Planck map;

cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;

xi_sz_cib, the SZ×CIB cross-correlation;

A_sz, the tSZ contamination at 143GHz;

ps_A_100_100, the point source contribution in 100×100;

ps_A_143_143, the point source contribution in 143×143;

ps_A_143_217, the point source contribution in 143×217;

ps_A_217_217, the point source contribution in 217×217;

ksz_norm, the kSZ contamination;

gal545_A_100, the dust residual contamination at ℓ=200 in 100×100;

gal545_A_143, the dust residual contamination at ℓ=200 in 143×143;

gal545_A_143_217, the dust residual contamination at ℓ=200 in 143×217;

gal545_A_217, the dust residual contamination at ℓ=200 in 217×217;

calib_100T, the relative calibration between the 100 and 143 spectra;

calib_217T, the relative calibration between the 217 and 143 spectra;

A_planck, the Planck absolute calibration.
We recommend using the following Gaussian priors:

ksz_norm + 1.6 × A_sz = 9.5±3.0;

cib_index = -1.3;

gal545_A_100 = 7±2;

gal545_A_143 = 9±2;

gal545_A_143_217 = 21.0±8.5;

gal545_A_217 = 80±20;

calib_100T = 0.999±0.001;

calib_217T = 0.995±0.002;

A_planck = 1.0000±0.0025.
TT+TE+EE - Plik This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range ℓ=30-2508 for TT and ℓ=30-1996 for TE and EE.
Production process The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission T and E cross-spectra. In temperature, only the 100×100, 143×143, 143×217, and 217×217 spectra are actually used, while in TE and EE all of them are used. Masks and multipole ranges for each spectrum are different and described in Planck-2015-A11^[7]. Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps. The file also contains templates for the residual foreground contamination of each spectrum. The templates are needed to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates. The covariance matrix is computed for a fiducial cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.
Inputs:

Planck 100-, 143-, and 217-GHz half-mission T+P maps;

CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;

Planck 545-GHz and 353-GHz maps for the dust residual contamination template;

CIB, tSZ, kSZ, and CIB×SZ templates;

best-fit CMB+foreground model for the beam-leakage template.
File name and usage The high-ℓ, plik TTTEEE likelihood is distributed in plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik.
This file should not be used with any other TT-only high-ℓ file.
When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 2508 (inclusive), followed the EE and TE spectra (same range) and by a vector of 94 nuisance parameters. Those are, in g:

A_cib_217, the CIB contamination at ℓ=3000 in the 217-GHz Planck map;

cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;

xi_sz_cib, the SZ×CIB cross-correlation;

A_sz, the tSZ contamination at 143GHz;

ps_A_100_100, the point source contribution in 100×100;

ps_A_143_143, the point source contribution in 143×143;

ps_A_143_217, the point source contribution in 143×217;

ps_A_217_217, the point source contribution in 217×217;

ksz_norm, the kSZ contamination;

gal545_A_100, the dust residual contamination at ℓ=200 in 100×100TT;

gal545_A_143, the dust residual contamination at ℓ=200 in 143×143TT;

gal545_A_143_217, the dust residual contamination at ℓ=200 in 143×217TT;

gal545_A_217, the dust residual contamination at ℓ=200 in 217×217TT;

galf_EE_A_100, the dust residual contamination at ℓ=500 in 100×100EE;

galf_EE_A_100_143, the dust residual contamination at ℓ=500 in 100×143EE;

galf_EE_A_100_217, the dust residual contamination at ℓ=500 in 100×217EE;

galf_EE_A_143, the dust residual contamination at ℓ=500 in 143×143EE;

galf_EE_A_143_217, the dust residual contamination at ℓ=500 in 143×217EE;

galf_EE_A_217, the dust residual contamination at ℓ=500 in 217×217EE;

galf_EE_index, the dust EE template slope, which should be set to -2.4;

galf_TE_A_100, the dust residual contamination at ℓ=500 in 100×100TE;

galf_TE_A_100_143, the dust residual contamination at ℓ=500 in 100×143TE;

galf_TE_A_100_217, the dust residual contamination at ℓ=500 in 100×217TE;

galf_TE_A_143, the dust residual contamination at ℓ=500 in 143x143TE;

galf_TE_A_143_217, the dust residual contamination at ℓ=500 in 143×217TE;

galf_TE_A_217, the dust residual contamination at ℓ=500 in 217×217TE;

galf_TE_index, the dust EE template slope, which should be set to -2.4;

bleak_epsilon_0_0T_0E, beam-leakage parameter, espilon_0, 100×100 TE;

bleak_epsilon_1_0T_0E, beam-leakage parameter, espilon_1, 100×100 TE;

bleak_epsilon_2_0T_0E, beam-leakage parameter, espilon_2, 100×100 TE;

bleak_epsilon_3_0T_0E, beam-leakage parameter, espilon_3, 100×100 TE;

bleak_epsilon_4_0T_0E, beam-leakage parameter, espilon_4, 100×100 TE;

bleak_epsilon_0_0T_1E, beam-leakage parameter, espilon_0, 100×143 TE;

bleak_epsilon_1_0T_1E, beam-leakage parameter, espilon_1, 100×143 TE;

bleak_epsilon_2_0T_1E, beam-leakage parameter, espilon_2, 100×143 TE;

bleak_epsilon_3_0T_1E, beam-leakage parameter, espilon_3, 100×143 TE;

bleak_epsilon_4_0T_1E, beam-leakage parameter, espilon_4, 100×143 TE;

bleak_epsilon_0_0T_2E, beam-leakage parameter, espilon_0, 100×217 TE;

bleak_epsilon_1_0T_2E, beam-leakage parameter, espilon_1, 100×217 TE;

bleak_epsilon_2_0T_2E, beam-leakage parameter, espilon_2, 100×217 TE;

bleak_epsilon_3_0T_2E, beam-leakage parameter, espilon_3, 100×217 TE;

bleak_epsilon_4_0T_2E, beam-leakage parameter, espilon_4, 100×217 TE;

bleak_epsilon_0_1T_1E, beam-leakage parameter, espilon_0, 143×143 TE;

bleak_epsilon_1_1T_1E, beam-leakage parameter, espilon_1, 143×143 TE;

bleak_epsilon_2_1T_1E, beam-leakage parameter, espilon_2, 143×143 TE;

bleak_epsilon_3_1T_1E, beam-leakage parameter, espilon_3, 143×143 TE;

bleak_epsilon_4_1T_1E, beam-leakage parameter, espilon_4, 143×143 TE;

bleak_epsilon_0_1T_2E, beam-leakage parameter, espilon_0, 143×217 TE;

bleak_epsilon_1_1T_2E, beam-leakage parameter, espilon_1, 143×217 TE;

bleak_epsilon_2_1T_2E, beam-leakage parameter, espilon_2, 143×217 TE;

bleak_epsilon_3_1T_2E, beam-leakage parameter, espilon_3, 143×217 TE;

bleak_epsilon_4_1T_2E, beam-leakage parameter, espilon_4, 143×217 TE;

bleak_epsilon_0_2T_2E, beam-leakage parameter, espilon_0, 217×217 TE;

bleak_epsilon_1_2T_2E, beam-leakage parameter, espilon_1, 217×217 TE;

bleak_epsilon_2_2T_2E, beam-leakage parameter, espilon_2, 217×217 TE;

bleak_epsilon_3_2T_2E, beam-leakage parameter, espilon_3, 217×217 TE;

bleak_epsilon_4_2T_2E, beam-leakage parameter, espilon_4, 217×217 TE;

bleak_epsilon_0_0E_0E, beam-leakage parameter, espilon_0, 100×100 EE;

bleak_epsilon_1_0E_0E, beam-leakage parameter, espilon_1, 100×100 EE;

bleak_epsilon_2_0E_0E, beam-leakage parameter, espilon_2, 100×100 EE;

bleak_epsilon_3_0E_0E, beam-leakage parameter, espilon_3, 100×100 EE;

bleak_epsilon_4_0E_0E, beam-leakage parameter, espilon_4, 100×100 EE;

bleak_epsilon_0_0E_1E, beam-leakage parameter, espilon_0, 100×143 EE;

bleak_epsilon_1_0E_1E, beam-leakage parameter, espilon_1, 100×143 EE;

bleak_epsilon_2_0E_1E, beam-leakage parameter, espilon_2, 100×143 EE;

bleak_epsilon_3_0E_1E, beam-leakage parameter, espilon_3, 100×143 EE;

bleak_epsilon_4_0E_1E, beam-leakage parameter, espilon_4, 100×143 EE;

bleak_epsilon_0_0E_2E, beam-leakage parameter, espilon_0, 100×217 EE;

bleak_epsilon_1_0E_2E, beam-leakage parameter, espilon_1, 100×217 EE;

bleak_epsilon_2_0E_2E, beam-leakage parameter, espilon_2, 100×217 EE;

bleak_epsilon_3_0E_2E, beam-leakage parameter, espilon_3, 100×217 EE;

bleak_epsilon_4_0E_2E, beam-leakage parameter, espilon_4, 100×217 EE;

bleak_epsilon_0_1E_1E, beam-leakage parameter, espilon_0, 143×143 EE;

bleak_epsilon_1_1E_1E, beam-leakage parameter, espilon_1, 143×143 EE;

bleak_epsilon_2_1E_1E, beam-leakage parameter, espilon_2, 143×143 EE;

bleak_epsilon_3_1E_1E, beam-leakage parameter, espilon_3, 143×143 EE;

bleak_epsilon_4_1E_1E, beam-leakage parameter, espilon_4, 143×143 EE;

bleak_epsilon_0_1E_2E, beam-leakage parameter, espilon_0, 143×217 EE;

bleak_epsilon_1_1E_2E, beam-leakage parameter, espilon_1, 143×217 EE;

bleak_epsilon_2_1E_2E, beam-leakage parameter, espilon_2, 143×217 EE;

bleak_epsilon_3_1E_2E, beam-leakage parameter, espilon_3, 143×217 EE;

bleak_epsilon_4_1E_2E, beam-leakage parameter, espilon_4, 143×217 EE;

bleak_epsilon_0_2E_2E, beam-leakage parameter, espilon_0, 217×217 EE;

bleak_epsilon_1_2E_2E, beam-leakage parameter, espilon_1, 217×217 EE;

bleak_epsilon_2_2E_2E, beam-leakage parameter, espilon_2, 217×217 EE;

bleak_epsilon_3_2E_2E, beam-leakage parameter, espilon_3, 217×217 EE;

bleak_epsilon_4_2E_2E, beam-leakage parameter, espilon_4, 217×217 EE;

calib_100T, the relative calibration between 100 and 143 TT spectra;

calib_217T, the relative calibration between 217 and 143 TT spectra;

calib_100P, the calibration of the 100 EE spectra, which should be set to 1;

calib_143P, the calibration of the 143 EE spectra, which should be set to 1;

calib_217P, the calibration of the 217 EE spectra, which should be set to 1;

A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;

A_planck, the Planck absolute calibration.
We recommend using the following Gaussian priors:

ksz_norm + 1.6 × A_sz = 9.5±3.0;

cib_index = -1.3;

gal545_A_100 = 7±2;

gal545_A_143 = 9±2;

gal545_A_143_217 = 21.0±8.5;

gal545_A_217 = 80±20;

galf_EE_A_100 = 0.060±0.012;

galf_EE_A_100_143 = 0.050±0.015;

galf_EE_A_100_217 = 0.110±0.033;

galf_EE_A_143 = 0.10±0.02;

galf_EE_A_143_217 = 0.240±0.048;

galf_EE_A_217 = 0.72±0.14;

galf_EE_index = -2.4;

galf_TE_A_100 = 0.140±0.042;

galf_TE_A_100_143 = 0.120±0.036;

galf_TE_A_100_217 = 0.30±0.09;

galf_TE_A_143 = 0.240±0.072;

galf_TE_A_143_217 = 0.60±0.018;

galf_TE_A_217 = 1.80±0.54;

galf_TE_index = -2.4;

bleak_epsilon_0_0T_0E = 0;

bleak_epsilon_1_0T_0E = 0;

bleak_epsilon_2_0T_0E = 0;

bleak_epsilon_3_0T_0E = 0;

bleak_epsilon_4_0T_0E = 0;

bleak_epsilon_0_0T_1E = 0;

bleak_epsilon_1_0T_1E = 0;

bleak_epsilon_2_0T_1E = 0;

bleak_epsilon_3_0T_1E = 0;

bleak_epsilon_4_0T_1E = 0;

bleak_epsilon_0_0T_2E = 0;

bleak_epsilon_1_0T_2E = 0;

bleak_epsilon_2_0T_2E = 0;

bleak_epsilon_3_0T_2E = 0;

bleak_epsilon_4_0T_2E = 0;

bleak_epsilon_0_1T_1E = 0;

bleak_epsilon_1_1T_1E = 0;

bleak_epsilon_2_1T_1E = 0;

bleak_epsilon_3_1T_1E = 0;

bleak_epsilon_4_1T_1E = 0;

bleak_epsilon_0_1T_2E = 0;

bleak_epsilon_1_1T_2E = 0;

bleak_epsilon_2_1T_2E = 0;

bleak_epsilon_3_1T_2E = 0;

bleak_epsilon_4_1T_2E = 0;

bleak_epsilon_0_2T_2E = 0;

bleak_epsilon_1_2T_2E = 0;

bleak_epsilon_2_2T_2E = 0;

bleak_epsilon_3_2T_2E = 0;

bleak_epsilon_4_2T_2E = 0;

bleak_epsilon_0_0E_0E = 0;

bleak_epsilon_1_0E_0E = 0;

bleak_epsilon_2_0E_0E = 0;

bleak_epsilon_3_0E_0E = 0;

bleak_epsilon_4_0E_0E = 0;

bleak_epsilon_0_0E_1E = 0;

bleak_epsilon_1_0E_1E = 0;

bleak_epsilon_2_0E_1E = 0;

bleak_epsilon_3_0E_1E = 0;

bleak_epsilon_4_0E_1E = 0;

bleak_epsilon_0_0E_2E = 0;

bleak_epsilon_1_0E_2E = 0;

bleak_epsilon_2_0E_2E = 0;

bleak_epsilon_3_0E_2E = 0;

bleak_epsilon_4_0E_2E = 0;

bleak_epsilon_0_1E_1E = 0;

bleak_epsilon_1_1E_1E = 0;

bleak_epsilon_2_1E_1E = 0;

bleak_epsilon_3_1E_1E = 0;

bleak_epsilon_4_1E_1E = 0;

bleak_epsilon_0_1E_2E = 0;

bleak_epsilon_1_1E_2E = 0;

bleak_epsilon_2_1E_2E = 0;

bleak_epsilon_3_1E_2E = 0;

bleak_epsilon_4_1E_2E = 0;

bleak_epsilon_0_2E_2E = 0;

bleak_epsilon_1_2E_2E = 0;

bleak_epsilon_2_2E_2E = 0;

bleak_epsilon_3_2E_2E = 0;

bleak_epsilon_4_2E_2E = 0;

calib_100T = 0.999±0.001;

calib_217T = 0.995±0.002;

calib_100P = 1;

calib_143P = 1;

calib_217P = 1;

A_pol = 1;

A_planck = 1.0000±0.0025.
TT only - Plik lite This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range ℓ=30-2508. It should not be used with the regular high-ℓ TT or TTTEEE files.

Production process The Plik likelihood files described above have been explored using a Bayesian algorithm described in Planck-2015-A11^[7]. The joint posterior of the CMB TT spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-ℓ likelihood approximation for the CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.
Inputs:

Plik plik_dx11dr2_HM_v18_TT likelihood;

dust residual, CIB, tSZ, kSZ, and CIB×SZ templates.
File name and usage The high-ℓ, Plik TT, nuisance-marginalized likelihood is distributed in plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik.
When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.
TT EE TE - Plik lite This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range ℓ=30-2508 for temperature and ℓ=30-1996 for TE and EE. It should not be used with the regular high-ℓ TT or TTTEEE files.

Production process The Plik likelihood file described above have been explored using a Bayesian algorithm described in Planck-2015-A11^[7]. The joint posterior of the CMB TT, TE, and EE spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.

Inputs:

Plik plik_dx11dr2_HM_v18_TTTEEE likelihood;

dust residual, CIB, tSZ, kSZ, and CIB×SZ templates.
File name and usage The high-ℓ, Plik TTTEEE, nuisance-marginalized likelihood is distributed in plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik.
When used with the library, this expects a vector of parameters consisting of the TT CMB power spectrum from ℓ=0 to 2508 (inclusive), followed by the EE, and TE spectra (same range) and by the Planck absolute calibration nuisance parameter.
Lensing likelihoods
T only This file allows for the computation of the baseline lensing likelihood, using only the SMICA T map-based lensing reconstruction. Only the lensing multipole range ℓ=40-400 is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes the computation of a model-dependent correction to the normalization and the "N1 bias." To speed up those computations, both are performed using a linear approximation.
Production process The SMICA T maps are filtered and correlated to reconstruct an optimal lensing reconstruction map. Biases are corrected using Monte Carlo simulations for the dominant "mean field" and "N0" contribution, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned. The covariance matrix of this binned spectrum is evaluated using numerical simulations. The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.
Inputs:

SMICA T CMB map;

60% Galactic mask;

best-fit Planck CMB model.
File name and usage The T-only lensing likelihood is distributed in plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing.
When used with the library, this expects a vector of parameters consisting of the φφ lensing spectrum for ℓ=0 to 2048 (inclusive), followed by the TT CMB power spectrum for ℓ=0 to 2048 (inclusive) and by the Planck absolute calibration nuisance parameter.
The TT spectrum is needed to compute the normalization and N1 corrections.
T+P This file allows for the computation of the baseline lensing likelihood, using both the T and P SMICA map-based lensing reconstruction. Only the lensing multipole rangeℓ=40-400 is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes the computation of model dependent correction to the normalization and the N1 bias. To speed up those computations, both are performed using a linear approximation.
Production process The SMICA T and P maps are filtered and correlated to reconstruct an optimal lensing reconstruction map. Biases are corrected using Monte Carlo simulations for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured outside a large mask, and binned. The covariance matrix of this binned spectrum is evaluated using numerical simulations. The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.
Inputs:

SMICA T and E CMB maps;

60% Galactic mask;

best-fit Planck CMB model.
File name and usage The T+P-only lensing likelihood is distributed in plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing.
When used with the library, this expects a vector of parameters consisting of the φφ lensing spectrum for ℓ=0 to 2048 (inclusive), followed by the TT CMB power spectrum for ℓ=0 to 2048 (inclusive), the EE and TE power spectra (same range) and by the Planck absolute calibration nuisance parameter.
The TT, EE, and TE spectra are needed to compute the normalization and N1 corrections.
Data sets - Extended data
Four other data files are available. Those extend the baseline delivery by adding:

TE, EE and other joint high-&#8467 Plik likelihoods, COM_Likelihood_Data-extra-plik-HM-ext_R2.00.tar.gz;

TT and TTTEEE unbinned high-&#8467 Plik likelihood, COM_Likelihood_Data-extra-plik-unbinned_R2.00.tar.gz;

TT, TE, EE, and TTTEEE Plik likelihood using the detset cross-spectra instead of the half-mission one, and including empirical correlated noise correction for the TT spectra, COM_Likelihood_Data-extra-plik-DS_R2.00.tar.gz;

extended &#8467 range lensing likelihood, COM_Likelihood_Data-extra-lensing-ext_R2.00.tar.gz.
Note that although these products are discussed in the Planck papers, they are not used for the baseline results.
Each file contains a readme.md description of the content and the use of the different likelihood files.

Likelihood Masks
General description
We provide the masks for Temperature and Polarisation used to exclude the regions of strongest foreground emission in the CMB maps when computing the empirical spectra that we use to form the high-&#8467 likelihood. The masks are provided for each frequency between 100 and 217 GHz, masking the appropriate part of the Galactic Plane and, for temperature only, the relevant population of point sources. Note that to compute the empirical power spectrum of the maps, one should also take into account missing pixels in a particular map. This is not included in the masks we distribute.
Production Process Complete production process for those masks is described in Planck-2015-A11^[7].
The temperature masks are the combination of a Galactic mask, a point source mask and (for 100Ghz and 217GHz) a CO mask. Extended objects, planets, etc are included in the point source mask. The polarization masks are simply the Galactic masks.
The Galactic masks are obtained by thresholding a CMB corrected and [math]10^o[/math] smoothed 353GHz map. The threshold is tuned so as to retain a given fraction of the sky, between 50% and 80%. Each mask is apodized by a [math]4^o.71[/math] FWHM gaussian window function using the distance map. Special care is taken to smooth this distance map, in order to avoid strong caustics. The apodization down-weights an effective 10% of the sky. Following Planck-2015-A11^[7], the Galactic masks are named by the effective unmasked sky area G70, G60, G50 and G41.
The point source masks are different for each frequency. They are based on the 2015 Planck catalog and cut out all the sources detected at S/N = 5 or higher in each channel. Each source is masked with a circular aperture of size 3xFWHM of that channel (i.e. 3x9.′66 at 100GHz, 3x7.′22 at 143GHz, and 3x4.′90 at 217GHz). Note that we include in the point source masks all sources above our threshold, including possible galactic ones. The mask is further apodized with a gaussian window function with FWHM=30'.
The CO masks is used only at 100GHz and 217GHz, since there is no (strong) CO line in the 147 GHz channel. They are based on the Type 3 CO map from the Planck2013 delivery. The CO map is smoothed to 120' and a threshold is applied to mask all regions above [math]1 K_{RJ} km s^{−1}[/math]. The mask is further apodized to 30'.
Mask combinations are performed by multiplying a galactic, a point source, and possibly a CO mask together.
The Temperature masks are named in Planck-2015-A11^[7] using the capital letter T and the effective sky fraction that is left unmasked. They are produced using the following

100Ghz: T66 = G70+Point source mask 100Ghz+CO mask

143Ghz: T57 = G60+Point source mask 143Ghz

217Ghz: T47 = G50+Point source mask 217Ghz+CO mask
The Polarization masks are named in Planck-2015-A11^[7] using the capital letter P and the effective sky fraction that is left unmasked. They are produced using the following

100Ghz: P70 = G70

143Ghz: P50 = G50

217Ghz: P41 = G41
Inputs

Galactic masks: The SMICA CMB temperature map, the 353GHz temperature map.

Point source masks: The Planck 2015 catalog, the FWHM of each of the frequencies.

CO mask: the Type 3 CO map from the Planck 2013 delivery.
File names and meta-data The masks are distributed in a single tar file COM_Likelihood_Masks_R2.00.tar.gz. The files extract to 6 files

temperature_100.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 100Ghz, i.e. T66

temperature_143.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 143Ghz, i.e. T57

temperature_217.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 217Ghz, i.e. T47

polarization_100.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 100Ghz, i.e. P70

polarization_143.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 143Ghz, i.e. P50

polarization_217.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 217Ghz, i.e. P41

2013 CMB spectrum and Likelihood

General description

CMB spectra
The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles [math] \ell [/math] = 2-2479. Over the multipole range [math] \ell [/math] = 2–49, the power spectrum is derived from a component-separation algorithm, Commander, applied to maps in the frequency range 30–353 GHz over 91% of the sky Planck-2013-XII^[13]. The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction. For multipoles greater than [math]\ell=50[/math], instead, the spectrum is derived from the CAMspec likelihood Planck-2013-XV^[9] by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds. Associated 1-sigma errors include beam and foreground uncertainties. Both Commander and CAMspec are described in more details in the sections below.

CMB spectrum. Logarithmic x-scale up to [math]\ell=50[/math], linear at higher [math]\ell[/math]; all points with error bars. The red line is the Planck best-fit primordial power spectrum (cf Planck+WP+highL in Table 5 of Planck-2013-XVI^[14]).

Likelihood
The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model.
Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the Power spectrum & Likelihood Paper Planck-2013-XV^[9] (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) Planck-2013-XVII^[15].
The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute

one low-[math]\ell[/math] temperature only likelihood (commander),

one low-[math]\ell[/math] temperature and polarisation likelihood (lowlike), and

one higl-[math]\ell[/math] likelihood CAMspec.
The Commander likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-[math]\ell[/math] temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See Planck-2013-XV^[9] section 8.1 for more details.
The lowlike likelihood covers the multipoles 2 to 32 for temperature and polarization data. Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see Planck-2013-XV^[9] section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.
The CAMspec likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See Planck-2013-XV^[9] section 2.1 for more details.
The act/spt likelihood covers the multipoles 1500 to 10000 for temperature. It is described in^[16]^[17]^[18]. It uses the code and data that can be retrieved from the Lambda archive for ACT and SPT. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in^[16], the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 ± 0.2 and a_gs = 0.4 ± 0.2. Those priors are not included in the log likelihood computed by the code.
The lensing likelihood covers the multipoles 40 to 400 using the result of the lensing reconstruction. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. This means that the code will need both the TT and $\phi\phi$ power spectrum up to [math]\ell[/math] = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between [math]\ell[/math] = 40 to 400. See Planck-2013-XVII^[15] section 6.1 for more details.
Production process
CMB spectra
The [math]\ell[/math] < 50 part of the Planck power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters Planck-2013-XII^[13]. The power spectrum at any multipole [math]\ell[/math] is given as the maximum probability point for the posterior [math]C_\ell[/math] distribution, marginalized over the other multipoles, and the error bars are 68% confidence level Planck-2013-XV^[9].
The [math]\ell[/math] > 50 part of the CMB temperature power spectrum has been derived by the CamSpec likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of Planck-2013-XV^[9]. Frequency spectra are computed as noise weighted averages of the cross-spectra between single detector and sets of detector maps. Mask and multipole range choices for each frequency spectrum are summarized in Table 4 of Planck-2013-XV^[9]. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (cf Planck+WP+highL in Table 5 of Planck-2013-XVI^[14]). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of Planck-2013-XV^[9] and Sec. 4 of Planck-2013-XVI^[14]. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with unresolved foreground and beam uncertainties. Both spectrum and associated covariance matrix are given as uniformly weighted band averages in 74 bins.
Likelihood
The code is based on some basic routines from the libpmc library in the cosmoPMC code. It also uses some code from the WMAP9 likelihood for the lowlike likelihood and^[16]^[17]^[18] for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper Planck-2013-XV^[9] (section 2 and 8) and in the lensing paper Planck-2013-XVII^[15] (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.
Each dataset comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10[math]^{-6}[/math] or less are expected depending of the architecture.
Inputs

CMB spectra

Low-l spectrum ([math]\ell \lt 50[/math])

frequency maps from 30–353 GHz

common mask Planck-2013-XII^[13]

compact sources catalog
High-l spectrum ([math]50 \lt \ell \lt 2500[/math])

100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 2 in Planck-2013-XV^[9])

best-fit foreground templates and inter-frequency calibration factors (Table 5 of Planck-2013-XVI^[14])

Beam transfer function uncertainties Planck-2013-VII^[19]
Likelihood

commander

all Planck channels maps

compact source catalogs

common masks

beam transfer functions for all channels
lowlike

WMAP9 likelihood data

Low-[math]\ell[/math] Commander map
CAMspec

100, 143 and 217 GHz detector and detsets maps

857GHz channel map

compact source catalog

common masks (0,1 & 3)

beam transfer function and error eigenmodes and covariance for 100, 143 and 217 GHz detectors & detsets

theoretical templates for the tSZ and kSZ contributions

color corrections for the CIB emission for the 143 and 217GHz detectors and detsets

fiducial CMB model (bootstrapped from WMAP7 best fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz
lensing

the lensing map

beam error eigenmodes and covariance for the 143 and 217GHz channel maps

fiducial CMB model (from Planck cosmological parameter best fit)
act/spt

data and code from here

the tSZ andkSZ template are changed to match those of CAMspec
File names and Meta data

CMB spectra
The CMB spectrum and its covariance matrix are distributed in a single FITS file named

COM_PowerSpect_CMB_R1.10.fits
which contains 3 extensions

LOW-ELL (BINTABLE)

with the low ell part of the spectrum, not binned, and for l=2-49. The table columns are
ELL (integer): multipole number

D_ELL (float): $D_l$ as described below

ERRUP (float): the upward uncertainty

ERRDOWN (float): the downward uncertainty
HIGH-ELL (BINTABLE)

with the high-ell part of the spectrum, binned into 74 bins covering in bins of width [math]l=31[/math] (with the exception of the last 4 bins that are wider). The table columns are as follows:
ELL (integer): mean multipole number of bin

L_MIN (integer): lowest multipole of bin

L_MAX (integer): highest multipole of bin

D_ELL (float): $D_l$ as described below

ERR (float): the uncertainty
COV-MAT (IMAGE)

with the covariance matrix of the high-ell part of the spectrum in a 74x74 pixel image, i.e., covering the same bins as the HIGH-ELL table.
The spectra give $D_\ell = \ell(\ell+1)C_\ell / 2\pi$ in units of $\mu\, K^2$, and the covariance matrix is in units of $\mu\, K^4$. The spectra are shown in the figure below, in blue and red for the low- and high-[math]\ell[/math] parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.

CMB spectrum. Linear x-scale; error bars only at high [math]\ell[/math].

Likelihood
Likelihood source code
The source code is in the file

COM_Code_Likelihood-v1.0_R1.10.tar.gz (C, f90 and python likelihood library and tools)
Likelihood data packages
The data packages are

COM_Data_Likelihood-commander_R1.10.tar.gz (low-ell TT likelihood)

COM_Data_Likelihood-lowlike_R1.10.tar.gz (low-ell TE,EE,BB likelihood)

COM_Data_Likelihood-CAMspec_R1.10.tar.gz (high-ell TT likelihood)

COM_Data_Likelihood-actspt_R1.10.tar.gz (high-ell TT likelihood)

COM_Data_Likelihood-lensing_R1.10.tar.gz (lensing likelihood)
Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.
The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing. The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb"). Those files are not user modifiable and do not contain interesting meta data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.
Likelihood masks
The masks used in the Likelihood paper Planck-2013-XV^[9] are found in COM_Mask_Likelihood_2048_R1.10.fits
which contains ten masks which are written into a single BINTABLE extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map). The structure is as follows, where the column names are the names of the masks:

Likelihodd masks file data structure
1. EXTNAME = 'MSK-LIKE' : Data columns
Column Name Data Type Units Description
CL31 Real*4 none mask
CL39 Real*4 none mask
CL49 Real*4 none mask
G22 Real*4 none mask
G35 Real*4 none mask
G45 Real*4 none mask
G56 Real*4 none mask
G65 Real*4 none mask
PS96 Real*4 none mask
PSA82 Real*4 none mask
Keyword Data Type Value Description
PIXTYPE string HEALPIX
COORDSYS string GALACTIC Coordinate system
ORDERING string NESTED Healpix ordering
NSIDE Int 2048 Healpix Nside
FIRSTPIX Int*4 0 First pixel number
LASTPIX Int*4 50331647 Last pixel number, for LFI and HFI, respectively

References[edit]
↑ ^1.0^1.1^1.2 Planck 2018 results. VI. Cosmological parameters, Planck Collaboration, 2020, A&A, 641, A6.

↑ ^2.00^2.01^2.02^2.03^2.04^2.05^2.06^2.07^2.08^2.09^2.10^2.11^2.12 Planck 2018 results. V. CMB Power Spectra and Likelihoods, Planck Collaboration, 2020, A&A, 641, A5.

↑ ^3.0^3.1^3.2^3.3^3.4 Planck 2018 results. IV. Diffuse component separation, Planck Collaboration, 2020, A&A, 641, A4.

↑ ^4.0^4.1^4.2^4.3 Planck 2018 results. III. High Frequency Instrument data processing and frequency maps, Planck Collaboration, 2020, A&A, 641, A3.

↑ ^5.0^5.1^5.2^5.3 Planck 2018 results. VIII. Lensing, Planck Collaboration, 2020, A&A, 641, A8.

↑ ^6.0^6.1^6.2^6.3^6.4^6.5 Planck 2015 results. X. Diffuse component separation: Foreground maps, Planck Collaboration, 2016, A&A, 594, A10.

↑ ^7.00^7.01^7.02^7.03^7.04^7.05^7.06^7.07^7.08^7.09^7.10^7.11^7.12^7.13^7.14^7.15^7.16^7.17 Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of cosmological parameters, Planck Collaboration, 2016, A&A, 594, A11.

↑ ^8.0^8.1^8.2^8.3^8.4^8.5 Planck 2015 results. XIII. Cosmological parameters, Planck Collaboration, 2016, A&A, 594, A13.

↑ ^9.00^9.01^9.02^9.03^9.04^9.05^9.06^9.07^9.08^9.09^9.10^9.11^9.12 Planck 2013 results. XV. CMB power spectra and likelihood, Planck Collaboration, 2014, A&A, 571, A15.

↑ Planck 2015 results. VII. High Frequency Instrument data processing: Time-ordered information and beam processing, Planck Collaboration, 2016, A&A, 594, A7.

↑ Planck 2015 results. XII. Full Focal Plane Simulations, Planck Collaboration, 2016, A&A, 594, A12.

↑ ^12.0^12.1 Planck 2015 results. XV. Gravitational Lensing, Planck Collaboration, 2016, A&A, 594, A15.

↑ ^13.0^13.1^13.2 Planck 2013 results. XI. Component separation, Planck Collaboration, 2014, A&A, 571, A11.

↑ ^14.0^14.1^14.2^14.3 Planck 2013 results. XVI. Cosmological parameters, Planck Collaboration, 2014, A&A, 571, A16.

↑ ^15.0^15.1^15.2 Planck 2013 results. XVII. Gravitational lensing by large-scale structure, Planck Collaboration, 2014, A&A, 571, A17.

↑ ^16.0^16.1^16.2 The Atacama Cosmology Telescope: likelihood for small-scale CMB data, J. Dunkley, E. Calabrese, J. Sievers, G. E. Addison, N. Battaglia, E. S. Battistelli, J. R. Bond, S. Das, M. J. Devlin, R. Dunner, J. W. Fowler, M. Gralla, A. Hajian, M. Halpern, M. Hasselfield, A. D. Hincks, R. Hlozek, J. P. Hughes, K. D. Irwin, A. Kosowsky, T. Louis, T. A. Marriage, D. Marsden, F. Menanteau, K. Moodley, M. Niemack, M. R. Nolta, L. A. Page, B. Partridge, N. Sehgal, D. N. Spergel, S. T. Staggs, E. R. Switzer, H. Trac, E. Wollack, ArXiv e-prints, (2013).

↑ ^17.0^17.1 A Measurement of the Damping Tail of the Cosmic Microwave Background Power Spectrum with the South Pole Telescope, R. Keisler, C. L. Reichardt, K. A. Aird, B. A. Benson, L. E. Bleem, J. E. Carlstrom, C. L. Chang, H. M. Cho, T. M. Crawford, A. T. Crites, T. de Haan, M. A. Dobbs, J. Dudley, E. M. George, N. W. Halverson, G. P. Holder, W. L. Holzapfel, S. Hoover, Z. Hou, J. D. Hrubes, M. Jo, L. Knox, A. T. Lee, E. M. Leitch, M. Lueker, D. Luong-Van, J. J. McMahon, J. Mehl, S. S. Meyer, M. Millea, J. J. Mohr, T. E. Montroy, T. Natoli, S. Padin, T. Plagge, C. Pryke, J. E. Ruhl, K. K. Schaffer, L. Shaw, E. Shirokoff, H. G. Spieler, Z. Staniszewski, A. A. Stark, K. Story, A. van Engelen, K. Vanderlinde, J. D. Vieira, R. Williamson, O. Zahn, ApJ, 743, 28, (2011).

↑ ^18.0^18.1 A Measurement of Secondary Cosmic Microwave Background Anisotropies with Two Years of South Pole Telescope Observations, C. L. Reichardt, L. Shaw, O. Zahn, K. A. Aird, B. A. Benson, L. E. Bleem, J. E. Carlstrom, C. L. Chang, H. M. Cho, T. M. Crawford, A. T. Crites, T. de Haan, M. A. Dobbs, J. Dudley, E. M. George, N. W. Halverson, G. P. Holder, W.L. Holzapfel, S. Hoover, Z. Hou, J. D. Hrubes, M. Joy, R. Keisler, L. Knox, A. T. Lee, E. M. Leitch, M. Lueker, D. Luong-Van, J. J. McMahon, J. Mehl, S. S. Meyer, M. Millea, J. J. Mohr, T. E. Montroy, T. Natoli, S. Padin, T. Plagge, C. Pryke, J. E. Ruhl, K. K. Schaffer, E. Shirokoff, H. G. Spieler, Z. Staniszewski, A. A. Stark, K. Story, A. van Engelen, K. Vanderlinde, J. D. Vieira, R. Williamson, ApJ, 755, 70, (2012).

↑ Planck 2013 results. VII. HFI time response and beams, Planck Collaboration, 2014, A&A, 571, A7.

[planck2016-l06-1] 1.0^1.1^1.2 Planck 2018 results. VI. Cosmological parameters, Planck Collaboration, 2020, A&A, 641, A6.

[planck2016-l05-2] 2.00^2.01^2.02^2.03^2.04^2.05^2.06^2.07^2.08^2.09^2.10^2.11^2.12 Planck 2018 results. V. CMB Power Spectra and Likelihoods, Planck Collaboration, 2020, A&A, 641, A5.

[planck2016-l04-3] 3.0^3.1^3.2^3.3^3.4 Planck 2018 results. IV. Diffuse component separation, Planck Collaboration, 2020, A&A, 641, A4.

[planck2016-l03-4] 4.0^4.1^4.2^4.3 Planck 2018 results. III. High Frequency Instrument data processing and frequency maps, Planck Collaboration, 2020, A&A, 641, A3.

[planck2016-l08-5] 5.0^5.1^5.2^5.3 Planck 2018 results. VIII. Lensing, Planck Collaboration, 2020, A&A, 641, A8.

[planck2014-a12-6] 6.0^6.1^6.2^6.3^6.4^6.5 Planck 2015 results. X. Diffuse component separation: Foreground maps, Planck Collaboration, 2016, A&A, 594, A10.

[planck2014-a13-7] 7.00^7.01^7.02^7.03^7.04^7.05^7.06^7.07^7.08^7.09^7.10^7.11^7.12^7.13^7.14^7.15^7.16^7.17 Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of cosmological parameters, Planck Collaboration, 2016, A&A, 594, A11.

[planck2014-a15-8] 8.0^8.1^8.2^8.3^8.4^8.5 Planck 2015 results. XIII. Cosmological parameters, Planck Collaboration, 2016, A&A, 594, A13.

[planck2013-p08-9] 9.00^9.01^9.02^9.03^9.04^9.05^9.06^9.07^9.08^9.09^9.10^9.11^9.12 Planck 2013 results. XV. CMB power spectra and likelihood, Planck Collaboration, 2014, A&A, 571, A15.

[planck2014-a08-10] Planck 2015 results. VII. High Frequency Instrument data processing: Time-ordered information and beam processing, Planck Collaboration, 2016, A&A, 594, A7.

[planck2014-a14-11] Planck 2015 results. XII. Full Focal Plane Simulations, Planck Collaboration, 2016, A&A, 594, A12.

[planck2014-a17-12] 12.0^12.1 Planck 2015 results. XV. Gravitational Lensing, Planck Collaboration, 2016, A&A, 594, A15.

[planck2013-p06-13] 13.0^13.1^13.2 Planck 2013 results. XI. Component separation, Planck Collaboration, 2014, A&A, 571, A11.

[planck2013-p11-14] 14.0^14.1^14.2^14.3 Planck 2013 results. XVI. Cosmological parameters, Planck Collaboration, 2014, A&A, 571, A16.

[planck2013-p12-15] 15.0^15.1^15.2 Planck 2013 results. XVII. Gravitational lensing by large-scale structure, Planck Collaboration, 2014, A&A, 571, A17.

[.5B.5B:Template:Dun2013.5D.5D-16] 16.0^16.1^16.2 The Atacama Cosmology Telescope: likelihood for small-scale CMB data, J. Dunkley, E. Calabrese, J. Sievers, G. E. Addison, N. Battaglia, E. S. Battistelli, J. R. Bond, S. Das, M. J. Devlin, R. Dunner, J. W. Fowler, M. Gralla, A. Hajian, M. Halpern, M. Hasselfield, A. D. Hincks, R. Hlozek, J. P. Hughes, K. D. Irwin, A. Kosowsky, T. Louis, T. A. Marriage, D. Marsden, F. Menanteau, K. Moodley, M. Niemack, M. R. Nolta, L. A. Page, B. Partridge, N. Sehgal, D. N. Spergel, S. T. Staggs, E. R. Switzer, H. Trac, E. Wollack, ArXiv e-prints, (2013).

[.5B.5B:Template:Keis2011.5D.5D-17] 17.0^17.1 A Measurement of the Damping Tail of the Cosmic Microwave Background Power Spectrum with the South Pole Telescope, R. Keisler, C. L. Reichardt, K. A. Aird, B. A. Benson, L. E. Bleem, J. E. Carlstrom, C. L. Chang, H. M. Cho, T. M. Crawford, A. T. Crites, T. de Haan, M. A. Dobbs, J. Dudley, E. M. George, N. W. Halverson, G. P. Holder, W. L. Holzapfel, S. Hoover, Z. Hou, J. D. Hrubes, M. Jo, L. Knox, A. T. Lee, E. M. Leitch, M. Lueker, D. Luong-Van, J. J. McMahon, J. Mehl, S. S. Meyer, M. Millea, J. J. Mohr, T. E. Montroy, T. Natoli, S. Padin, T. Plagge, C. Pryke, J. E. Ruhl, K. K. Schaffer, L. Shaw, E. Shirokoff, H. G. Spieler, Z. Staniszewski, A. A. Stark, K. Story, A. van Engelen, K. Vanderlinde, J. D. Vieira, R. Williamson, O. Zahn, ApJ, 743, 28, (2011).

[.5B.5B:Template:Reic2012.5D.5D-18] 18.0^18.1 A Measurement of Secondary Cosmic Microwave Background Anisotropies with Two Years of South Pole Telescope Observations, C. L. Reichardt, L. Shaw, O. Zahn, K. A. Aird, B. A. Benson, L. E. Bleem, J. E. Carlstrom, C. L. Chang, H. M. Cho, T. M. Crawford, A. T. Crites, T. de Haan, M. A. Dobbs, J. Dudley, E. M. George, N. W. Halverson, G. P. Holder, W.L. Holzapfel, S. Hoover, Z. Hou, J. D. Hrubes, M. Joy, R. Keisler, L. Knox, A. T. Lee, E. M. Leitch, M. Lueker, D. Luong-Van, J. J. McMahon, J. Mehl, S. S. Meyer, M. Millea, J. J. Mohr, T. E. Montroy, T. Natoli, S. Padin, T. Plagge, C. Pryke, J. E. Ruhl, K. K. Schaffer, E. Shirokoff, H. G. Spieler, Z. Staniszewski, A. A. Stark, K. Story, A. van Engelen, K. Vanderlinde, J. D. Vieira, R. Williamson, ApJ, 755, 70, (2012).

[planck2013-p03c-19] Planck 2013 results. VII. HFI time response and beams, Planck Collaboration, 2014, A&A, 571, A7.

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Difference between revisions of "CMB spectrum & Likelihood Code"

Latest revision as of 10:05, 11 May 2021

Contents

2018 CMB spectra[edit]

General description[edit]

TT[edit]

TE, EE, and EB, BB[edit]

Best-fit model[edit]

Production process[edit]

Inputs[edit]

File names and meta-data[edit]

2018 Likelihood[edit]

Previous Releases: (2015) and (2013) CMB spectrum and Likelihood[edit]

References[edit]

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@@ Line 1: / Line 1: @@
-{{DISPLAYTITLE:2015 CMB spectra and likelihood code}}
+{{DISPLAYTITLE:CMB spectra and likelihood code}}
-==2015 CMB spectra==
+== 2018 CMB spectra==
 ===General description===
 ====TT====
-The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles <math> \ell </math> = 2-2508. Over the multipole range <math> \ell </math> = 2–29, the power spectrum is derived from the ''Commander'': component separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408 MHz Haslam et al. (1982) survey, including 93% of the sky {{PlanckPapers|planck2014-a12}} . The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.
+The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2018 temperature data between 30 and 857 GHz, including 86% of the sky ({{PlanckPapers|planck2016-l06}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.
-For multipoles equal or greater than <math>\ell=30</math>, instead, the spectrum is derived from the ''Plik'' likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP <math>\Lambda</math>CDM run. Associated 1-sigma errors include beam  uncertainties. Both ''Commander'' and ''Plik'' are described in more details in the sections below.
+For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" cross-half-mission likelihood {{PlanckPapers|planck2016-l05}}, with foreground and other nuisance parameters fixed to a best fit assuming the base-ΛCDM cosmology.  Associated 1&sigma; errors include beam uncertainties. Commander is described in more detail in {{PlanckPapers|planck2016-l04}}, and  Plik is described in more detail in {{PlanckPapers|planck2016-l05}}.
-[[File: A15_TT.png|thumb|center|700px|'''The Planck 2015 TT power spectrum. Logarithmic x-scale up to <math>\ell = 30 </math> , linear at higher <math>\ell</math>. The red line is the Planck best-fit primordial power spectrum (cf Planck TT+lowP in Table 3 of Planck-2015-A15[3]).  Residuals with respect to this model are shown in the lower panel. The error bars show <math>\pm 1\sigma</math> uncertainties.''']]
+[[File:Screen Shot 2018-07-16 at 05.51.48.png|thumb|600px|center]]
-====TE and EE====
+====TE, EE, and EB, BB ====
-The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range <math> \ell </math> = 2-1996. The data points relative to the multipole range <math> \ell </math> = 2-29 are quadratic maximum likelihood estimates from foreground cleaned Planck 70 GHz Q and U Stokes parameters maps using 46% of the sky (the same maps that are used in the lowP likelihood, see {{PlanckPapers|planck2014-a13}}). In the range <math> \ell </math> = 2-29, we also release the BB, TB and EB power spectra derived from the same maps (for the cross-spectra involving temperature, the ''Commander'' map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.
+The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. In the multipole range 2 ≤ l ≤ 29, we plot the power spectra estimates from the SimAll likelihood (though only the EE spectrum is used in the baseline parameter analysis at l ≤ 29), see {{PlanckPapers|planck2016-l06}}). The spectra are obtained using a cross quasi maximum likelihood algorithm (QML) on the 100 and 143 GHz maps and validated against high fidelity end-to-end simulations.
-Analogously to the TT case, the <math> \ell\ge 30 </math> spectrum is derived from the ''Plik'' likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP <math>\Lambda</math>CDM run.
+[[File:Screen Shot 2018-07-16 at 05.52.35.png|thumb|600px|center]]
+[[File:Screen Shot 2018-07-16 at 05.52.24.png|thumb|600px|center]]
+In the range &#8467; = 2-29, we also release the <i>BB</i>, and <i>EB</i> power spectra derived from the same maps. Error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.
+Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2016-l03}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run.
+==== Best-fit model ====
+We also provide best-fit LCDM CMB power spectra from the baseline Planck TT,TE,EE+lowE+lensing. The spectra must be divided by the best-fit Planck map-based calibration parameter squared, calPlanck**2, to be compared to the coadded CMB spectra. The best-fit calPlanck value can be found in the file "COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt".
+===Production process===
+The Plik high-multipole likelihood (described in detail in {{PlanckPapers|planck2016-l05}}) is a Gaussian approximation of the probability distributions of the <i>TT</i>, <i>EE</i>, and <i>TE</i> angular power spectra, with semi-analytic covariance matrices calculated assuming a fiducial cosmology. It includes multipoles in the range 30 to 2508 for TT and 30 to 1996 for <i>TE</i> and <i>EE</i> and is constructed from half-mission cross-spectra measured from the 100-, 143-, and 217-GHz HFI frequency maps. For more details see {{PlanckPapers|planck2016-l06}}.
+===Inputs===
+The T T likelihood uses four half-mission cross-spectra with different multipole cuts to avoid multipole regions where noise dominates due to the limited resolution of the beams and to en-sure foreground contamination is correctly handled by our fore-ground model: 100 × 100 (  &#8467; = 30–1197); 143 × 143 (&#8467;  = 30– 1996); 143 × 217 (&#8467; = 30–2508); and 217 × 217 (&#8467; = 30–2508). The TE and EE likelihoods also include the 100 × 143 and 100 × 217 cross-spectra to improve the signal-to-noise ratio, and have different multipole cuts: 100 × 100 (&#8467; = 30–999); 100 × 143 (&#8467; = 30–999); 100 × 217 (&#8467; = 505–999); 143 × 143 (&#8467; = 30– 1996); 143 × 217 (&#8467; = 505–1996); and 217 × 217 (&#8467; = 505– 1996). The 353, 545 and 857 GHz temperature and polarization maps are also used to build the dust templates, and contribute to the galactic and point source masks determination.
+=== File names and meta-data ===
+The CMB spectra and their uncertainties are distributed in ASCII text files named ''COM_PowerSpect_CMB_nn_R3.01.fits'', where nn stands for the type of spectrum the file contains:
+* COM_PowerSpect_CMB-EE-full_R3.01.txt
+* COM_PowerSpect_CMB-TE-full_R3.01.txt
+* COM_PowerSpect_CMB-TT-full_R3.01.txt
+* COM_PowerSpect_CMB-low-ell-BB-full_R3.01.txt
+* COM_PowerSpect_CMB-low-ell-EB-full_R3.01.txt
+The binned CMB spectra are also provided as ASCII files named ''COM_PowerSpect_CMB_nn-binned_R3.01.fits'', where nn stands for the type of spectrum the file contains:
+* COM_PowerSpect_CMB-EE-binned_R3.02.txt
+* COM_PowerSpect_CMB-TE-binned_R3.02.txt
+* COM_PowerSpect_CMB-TT-binned_R3.01.txt
+<span style="color:#ff0000"> Update 19 August 2019:</span> Version R3.01 of the TE and EE binned spectra (COM_PowerSpect_CMB-TE-binned_R3.01.txt and COM_PowerSpect_CMB-EE-binned_R3.01.txt) have been replaced with version R3.02 (COM_PowerSpect_CMB-TE-binned_R3.02.txt and COM_PowerSpect_CMB-EE-binned_R3.03.txt) because the contents of these two files were erroneously interchanged. COM_PowerSpect_CMB-TE-binned_R3.01.txt contained the spectra of EE and the file COM_PowerSpect_CMB-EE-binned_R3.01.txt contained the spectra of TE. This bug has been fixed and the udpated files are available in the PLA.
+In addition we provide one file containing all the parameters of the Plik runs which yielded the spectra. This file is named
+* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum_R3.01.txt
+The theoretical spectrum of the best-fit model itself is provided in a separate file named
+* COM_PowerSpect_CMB-base-plikHM_TTTEEE-lowl-lowE-lensing-minimum-theory_R3.01.txt
+The data file columns give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>, and the lower and upper 68% uncertainties.
+== 2018 Likelihood==
+The 2018 baseline likelihood release consists of a code package and a single data package. Five extended data packages are also available, enabling exploration of alternatives to the baseline results.
+The code compiles to a library, allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets.  A data set permits the computation of a single likelihood among:
+* the high-&#8467; temperature and polarization CMB (jointly or separately);
+* the low-&#8467; temperature and polarization CMB (jointly or separately);
+* the CMB lensing reconstruction.
+By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.
+Only the baseline data package, ''[https://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_Likelihood_Data-baseline_R3.00.tar.gz COM_Likelihood_Data-baseline_R3.00.tar.gz]'', will be fully described on this page. It contains ten data sets, which are enough to compute all of the baseline Planck results that are discussed in {{PlanckPapers|planck2016-l05}}, as well as some obvious variations (for example using only the Temperature CMB data). For the case of lensing, it also contains a CMB-marginalized version of the likelihood, allowing the computation of the CMB lensing likelihood independently of the CMB as explained in {{PlanckPapers|planck2016-l08}}. The baseline data package also contains a few ancillary files, describing the recommended priors for the high-&#8467; likelihood, as well as some "cosmomc" ancillary files.
+The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in {{PlanckPapers|planck2016-l05}} and {{PlanckPapers|planck2016-l08}}.
+<span style="color:#ff0000"> Important update May 2021:</span>  A bug was reported in the code of the CMB marginalized version of the lensing likelihood. The bug caused a first order correction in the computation of the likelihood to be miscomputed and as a consequence biased cosmological results. The bug was only present in the distributed R3.00 and R3.01 of the likelihood code. It is not present in the other implementation of the likelihood (such as cosmoMC or cobaya version). The bug was not present in the versions of the code used to produce the Legacy lensing paper ({{PlanckPapers|planck2016-l08}}) or the released public chains. The issue is corrected with the package R3.10. The correction works with the previously distributed likelihood data files.
+'''Library and tools'''
+'''Description'''
+The library consists of code written in C and Fortran 90. It can be called from both of
+those languages. Optionally, a python wrapper can be built as well. Scripts to
+simplify the linking of the library with other codes are part of the package, as
+well as some example codes that can be used to test the correct installation of
+the code and the integrity of the data packages. Optionally, a script is also available, allowing
+the user to modify the multipole range and in some cases the content of some of the likelihoods (including the high-&#8467; polarized likelihoods) and reproduce the tests performed in the paper.
+A description of the tool, the API of the library, as well as different
+installation procedures, are detailed in the ''readme.md'' file in the code package.
+'''File name'''
+<span style="color:#ff0000"> Update May 2021 :</span> As of 2021_05_10 the code can be extracted from
+''[https://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_Likelihood_Code-v3.0_R3.10.tar.gz COM_Likelihood_Code-v3.0_R3.10.tar.gz]''.
+Please read the file ''readme.md'' for installation instructions.
+''Changes compared to version R3.01 (2021_05_10)''
+* Major : Correct a bug in the computation of the CMB marginalized lensing.
+* Configuration : new user modifiable file ''clik_extra_env'' gather the url, names and versions of the external packages that can be installed automatically by the likelihood code. This will hopefully simplify troubleshooting with new versions of the external packages in the future.
+* Configuration : update to latest version of waf. Print a warning when the compilation of C or fortran part will use a compiler defined by a user set CC or FC environment variable.
+* Python wrapper : correct a bug where error messages would not be properly displayed in python 3
+* Python wrapper : when both astropy and pyfits are available, prefer astropy
+''Changes compared to version R3.00 (2019_08_01)''
+Modify packaging and fixes two issues with intel fortran 2019 and gcc9 that were preventing compilation:
+* Improve parsing of intel fortran dryrun output to fix an issue with the building of the intel fortran link line which was broken for version 2019
+* Change an openmp scheduling option in src/plik/smica.c to go aroung an API incompatibility between intel 2019 openmp and gcc9 openmp which was preventing the code to correctly compile in this particular case.
+* The tar.gz no more unpack to a tar.bz2 and directly provide the code.
+Please read the file ''readme.md'' for installation instructions.
+'''Data sets - Baseline data'''
+All of the released baseline data are distributed within a single file,
+''[https://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_Likelihood_Data-baseline_R3.00.tar.gz COM_Likelihood_Data-baseline_R3.00.tar.gz]'' .
+This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.
+Each data set is stored in its own directory. The directory structure follows similar rules for each data set, and stores data, template, and meta-data for each particular likelihood.
+As in 2013, the CMB likelihood is cut into low-&#8467; and high-&#8467; parts. Moreover,
+for each of those, we distribute both a T-only data file and a joint T+P one. In the case
+of the high-&#8467; part, we also distribute two specific versions of the likelihood,
+that allow for estimates of T and T+P marginalized over the nuisance parameters.
+Combining both the low-&#8467; and high-&#8467; files, one can compute the likelihood over the
+range &#8467;=2-2508 in TT and &#8467;=2-1996 in TE and EE. A full description of the low-&#8467;
+and high-&#8467; likelihood is available in {{PlanckPapers|planck2016-l05}}.
+For the case of lensing we only distribute the likelihood based on both the temperature and polarization data.
+A full description of the lensing likelihood is available in {{PlanckPapers|planck2016-l08}}.
+All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that this parameter is explored over the Gaussian prior 1.0000&plusmn;0.0025.
+''' Low-&#8467; likelihoods '''
+'''TT only - commander'''
+This file allows for the computation of the CMB TT likelihood in the range &#8467;=2-29.
+Using the optional tool in the code package, it can be modified to cover any multipole range
+up to &#8467;&lt;200.
+''' Production process'''
+The likelihood is based on the results of the Commander approach, which implements a
+Bayesian component-separation method in pixel space, sampling the posterior distribution
+of the parameters of a model that describes both the CMB and the foreground emissions
+in a combination of the Planck maps. The samples
+of this exploration are used to infer the foreground-marginalized low-&#8467; likelihood
+for any <i>TT</i> CMB spectrum.
+''' Inputs: '''
+* Planck 30- to 857-GHz  frequency maps;
+* Commander 2018 confidence mask ({{PlanckPapers|planck2016-l04}}).
+'''File name and usage'''
+The commander likelihood is distributed in
+''plc_3.0/low_l/commander/commander_dx12_v3_2_29.clik''.
+When used with the library, this expects a vector of parameters consisting of the
+<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter
+consisting of the overall Planck calibration.  Note that the vector really starts at &#8467;=0, although
+the first two entries are null.
+'''EE only - simall '''
+This file allows for the computation of the EE likelihood
+in the range &#8467;=2-29. It should be used with the low-&#8467; TT-only likelihood to form the baseline low-&#8467; likelihood.
+''' Production process'''
+The likelihood is estimated by comparing a cross-quasi-maximum-likelihood algorithm (QML) on the 100- and 143-GHz maps to high fidelity end-to-end simulations of the HFI instrument, as described in {{PlanckPapers|planck2016-l05}}.
+The Galactic contamination (synchrotron and dust) in the input 100- and 143-GHz maps is mitigated by regressing the (LFI) 30-GHz and (HFI) 353-GHz maps. In order to avoid highly contaminated areas of the sky, the regions near the Galactic centre and plane are masked and we retain only about 50% of the sky. The mask is built by applying a threshold on the 353-GHz map and combined with the Commander confidence mask.
+The end-to-end simulations contain realistic Galactic contamination and our best knowledge of the HFI detector and analysis chain. The accuracy of the simulation is discussed in {{PlanckPapers|planck2016-l03}}.
+The end-to-end simulations only explore a single CMB realization, but at large scales a CMB swapping procedure can be implemented to explore different cosmological parameter sets (within &Lambda;CDM) and different CMB realizations. The end-to-end realizations are processed in the same way as the data (foreground mitigation, masking, QML) and using the distance between the data and the simulations, an approximation of the log likelihood is produced for each multipole. The final likelihood thus ignores &#8467;-to-&#8467; correlations, as well as <i>TT</i> to <i>EE</i> ones.
+The likelihood files contains metadata allowing for the computation of the approximation for each multipole.
+''' Inputs: '''
+* Planck 30-, 100-, 143- and 353-GHz frequency maps;
+* Commander 2018 confidence mask ({{PlanckPapers|planck2016-l04}}) and a specially designed Galactic mask based on the 353-GHz map
+* 300 single CMB- and foreground-realization end-to-end simulations. 300000 large-scale CMB-only realization (300 map realizations for 1000 different random set of cosmological parameters).
+'''File name and usage'''
+The low-&#8467; EE likelihood is distributed in
+''plc_3.0/low_l/simall/simall_100x143_offlike5_EE_Aplanck_B.clik'' .
+When used with the library, this expects a vector of parameters consisting of the
+<i>EE</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter
+consisting of the overall Planck calibration.  Note that the entries really start at &#8467;=0, although the
+&#8467;=0 and &#8467;=1 values will be null.
+'''BB only - simall '''
+This file allows for the computation of the BB likelihood
+in the range &#8467;=2-29. It is not part of the baseline likelihood. The <i>BB</i> spectrum at large scales is compatible with zero.
+''' Production process'''
+The likelihood is estimated by comparing a cross-quasi-maximum-likelihood algorithm (QML) on the 100- and 143-GHz maps to high fidelity end-to-end simulations of the HFI instrument, as described in {{PlanckPapers|planck2016-l05}}.
+The Galactic contamination (synchrotron and dust) in the input 100- and 143-GHz maps is mitigated by regressing the (LFI) 30-GHz and (HFI) 353-GHz maps. In order to avoid highly contaminated areas of the sky, the regions near the Galactic centre and plane are masked and we retain only about 50% of the sky. The mask is built by applying a threshold on the 353-GHz map and combined with the Commander confidence mask.
+The end-to-end simulations contain a realistic Galactic contamination and our best knowledge of the HFI detector and analysis chain. The accuracy of the simulation is discussed in {{PlanckPapers|planck2016-l03}}.
+The end-to-end simulations only explore a single CMB realization, but at large scales a CMB-swapping procedure can be implemented to explore different cosmological parameter sets (within &Lambda;CDM) and different CMB realizations. The end-to-end realizations are processed in the same way as the data (foreground mitigation, masking, QML) and using the distance between the data and the simulations, an approximation of the log likelihood is produced for each multipole. The final likelihood thus ignores &#8467;-to-&#8467; correlations.
+The likelihood files contains metadata allowing for the computation of the approximation for each multipole.
+''' Inputs: '''
+* Planck 30-, 100-, 143- and 353-GHz frequency maps;
+* Commander 2018 confidence mask ({{PlanckPapers|planck2016-l04}}) and a specially designed Galactic masks based on the 353-GHz map
+* 300 single CMB- and foreground-realization end-to-end simulations. 300000 large-scale CMB-only realization (300 map realizations for 1000 different random set of cosmological parameters).
+'''File name and usage'''
+The low ell BB likelihood is distributed in
+''plc_3.0/low_l/simall/simall_100x143_offlike5_BB_Aplanck_B.clik''.
+When used with the library, this expects a vector of parameters consisting of the
+<i>BB</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and by an extra nuisance parameter
+consisting of the overall Planck calibration.  Note that the entries really start at &#8467;=0, although the
+&#8467;=0 and &#8467;=1 values will be null.
+'''EEBB - simall '''
+This file allows for the computation of the EEBB likelihood
+in the range &#8467;=2-29. It is not part of the baseline likelihood. Since correlations between spectra and multipole are ignored in simall, using this file is equivalent (up to a possible normalization) to summing the log likelihood provided by the EE- and BB-only simall files.
+''' Production process'''
+The likelihood is estimated by comparing a cross-quasi-maximum-likelihood algorithm (QML) on the 100- and 143-GHz maps to high fidelity end-to-end simulation of the HFI instrument, as described in {{PlanckPapers|planck2016-l05}}.
+The Galactic contamination (synchrotron and dust) in the input 100- and 143-GHz maps is mitigated by regressing the (LFI) 30-GHz and (HFI) 353-GHz maps. In order to avoid highly contaminated areas of the sky, the regions near the Galactic centre and plane are masked and we retain only about 50% of the sky. The mask is built by applying a threshold on the 353-GHz map and combined with the Commander confidence mask.
+The end-to-end simulations contain a realistic Galactic contamination and our best knowledge of the HFI detector and analysis chain. The accuracy of the simulation is discussed in {{PlanckPapers|planck2016-l03}}.
+The end-to-end simulations only explore a single CMB realization, but at large scales a CMB swapping procedure can be implemented to explore different cosmological parameter sets (within &Lambda;CDM) and different CMB realizations. The end-to-end realizations are processed in the same way as the data (foreground mitigation, masking, QML) and using the distance between the data and the simulations, an approximation of the log likelihood is produced for each multipole. The final likelihood thus ignore &#8467;-to-&#8467; correlations.
+The likelihood files contains metadata allowing for computation of the approximation for each multipole.
+''' Inputs: '''
+* Planck 30-, 100-, 143- and 353-GHz frequency maps;
+* Commander 2018 confidence mask ({{PlanckPapers|planck2016-l04}}) and a specially designed Galactic mask based on the 353-GHz map
+* 300 single CMB- and foreground-realization end-to-end simulations. 300000 large scale CMB-only realization (300 map realizations for 1000 different random set of cosmological parameters.)
+'''File name and usage'''
+The low ell EEBB likelihood is distributed in
+''plc_3.0/low_l/simall/simall_100x143_offlike5_EEBB_Aplanck_B.clik''.
+When used with the library, this expects a vector of parameters consisting of the
+<i>EE</i> CMB power spectrum from &#8467;=0 to 29 (inclusive), followed by <i>BB</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and by an extra nuisance parameter
+consisting of the overall Planck calibration.  Note that the entries really start at &#8467;=0, although the
+&#8467;=0 and &#8467;=1 values will be null.
+''' High-&#8467; likelihoods '''
+'''TT only - Plik'''
+This file allows for the computation of the CMB TT likelihood in the range &#8467;=30-2508.
+Using the optional tools in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509, and to remove the contribution of any range of multipole from any of the cross-spectra considered in the approximation.
+''' Production process'''
+The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>TT</i> cross-spectra.
+Only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used. Masks and multipole
+ranges for each spectrum are different and described in {{PlanckPapers|planck2016-l05}}.
+Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.
+The file also contains
+templates for the residual foreground contamination of each spectrum. The templates are needed
+to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is
+computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.
+The covariance matrix is computed for a fiducial
+cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.
+The beam matrix computed for the specific masks and data cuts are applied to the 2015 TT &Lambda;CDM best-fit spectra to predict leakage templates.
+Subpixel effect are predicted for the specific masks and data cuts.
+''' Inputs: '''
+* Planck 100-, 143-, and 217-GHz half-mission <i>T</i> maps;
+* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;
+* Planck 545-GHz maps for the dust residual-contamination template;
+* CIB, tSZ, kSZ, and CIB&times;SZ templates;
+* Beam-matrix (effective beams and leakage) and subpixel-effect templates computed for the specific masks and sky fractions retained for the likelihood.
+'''File name and usage'''
+The high-&#8467;, Plik TT likelihood is distributed in
+''plc_3.0/hi_l/plik/plik_rd12_HM_v22_TT.clik''.
+When used with the library, this expects a vector of parameters consisting of the
+<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by a vector of 20 nuisance parameters.
+Those are, in order:
+* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;
+* cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;
+* xi_sz_cib, the SZ&times;CIB cross-correlation;
+* A_sz, the tSZ contamination at 143 GHz;
+* ps_A_100_100, the point-source contribution in 100&times;100;
+* ps_A_143_143, the point-source contribution in 143&times;143;
+* ps_A_143_217, the point-source contribution in 143&times;217;
+* ps_A_217_217, the point-source contribution in 217&times;217;
+* ksz_norm, the kSZ contamination;
+* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100;
+* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143;
+* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217;
+* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217;
+* A_sbpx_100_100_TT, a rescaling amplitude for the subpixel effects at &#8467;=200 in 100&times;100 (default is 1);
+* A_sbpx_143_143_TT, a rescaling amplitude for the subpixel effects at &#8467;=200 in 143&times;143 (default is 1);
+* A_sbpx_143_217_TT, a rescaling amplitude for the subpixel effects at &#8467;=200 in 143&times;217 (default is 1);
+* A_sbpx_217_217_TT, a rescaling amplitude for the subpixel effects at &#8467;=200 in 217&times;217 (default is 1);
+* calib_100T, the relative calibration between the 100 and 143 spectra;
+* calib_217T, the relative calibration between the 217 and 143 spectra;
+* A_planck, the Planck absolute calibration.
+Recommended priors can be found in the file ''plc_3.0/hi_l/plik/plik_recommended_priors.txt''
+For ''cosmomc'' users, a set of initialization files is available in ''plc_3.0/cosmomc''
+'''TT+TE+EE - Plik'''
+This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range &#8467;=30-2508 for TT and &#8467;=30-1996 for TE and EE.
+Using the optional tools in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509, and to remove the contribution of any range of multipole from any of the cross-spectra (in TT, TE EE and any cross-frequencies) considered in the approximation.
+''' Production process'''
+The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>T</i> and <i>E</i> cross-spectra.
+In temperature, only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used, while
+in <i>TE</i> and <i>EE</i> all of them are used. Masks and multipole
+ranges for each spectrum are different and described in {{PlanckPapers|planck2016-l05}}.
+Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point-source part, and on the CO maps.
+The file also contains
+templates for the residual foreground contamination of each spectrum. The templates are needed
+to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is
+computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.
+The covariance matrix is computed for a fiducial
+cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.
+The beam matrix computed for the specific masks and data cuts are applied to the 2015 <i>TT</i> &Lambda;CDM best-fit spectra to predict leakage templates.
+Subpixel effect are predicted for the specific masks and data cuts.
+The 300 end-to-end HFI simulations from the FFP10 suite are used to estimate correlated-noise residuals in the <i>EE</i> auto-spectra at 100, 143, and 217 GHz.
+''' Inputs: '''
+* Planck 100-, 143-, and 217-GHz half-mission T+P maps;
+* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;
+* Planck 545-GHz and 353-GHz maps for the dust residual-contamination template;
+* CIB, tSZ, kSZ, and CIB&times;SZ templates;
+* Beam-matrix (effective beams and leakage) and subpixel-effect templates computed for the specific masks and sky fractions retained for the likelihood;
+* 300 end-to-end HFI simulations and resulting smoothed correlated-noise templates.
+'''File name and usage'''
+The high-&#8467;, plik TTTEEE likelihood is distributed in
+''plc_3.0/hi_l/plik/plik_rd12_HM_v22b_TTTEEE.clik''.
+This file should not be used with any other TT-only high-&#8467; file.
+When used with the library, this expects a vector of parameters consisting of the
+<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed the <i>EE</i> and <i>TE</i> spectra (same range) and by a vector of 47 nuisance parameters.
+Those are, in order:
+* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;
+* cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;
+* xi_sz_cib, the SZ&times;CIB cross-correlation;
+* A_sz, the tSZ contamination at 143 GHz;
+* ps_A_100_100, the point-source contribution in 100&times;100;
+* ps_A_143_143, the point-source contribution in 143&times;143;
+* ps_A_143_217, the point-source contribution in 143&times;217;
+* ps_A_217_217, the point-source contribution in 217&times;217;
+* ksz_norm, the kSZ contamination;
+* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100TT;
+* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143TT;
+* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217TT;
+* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217TT;
+* galf_EE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100EE;
+* galf_EE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143EE;
+* galf_EE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217EE;
+* galf_EE_A_143, the dust residual contamination at &#8467;=500 in 143&times;143EE;
+* galf_EE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217EE;
+* galf_EE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217EE;
+* galf_EE_index, the dust EE template slope, which should be set to -2.4;
+* galf_TE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100TE;
+* galf_TE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143TE;
+* galf_TE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217TE;
+* galf_TE_A_143, the dust residual contamination at &#8467;=500 in 143x143TE;
+* galf_TE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217TE;
+* galf_TE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217TE;
+* galf_TE_index, the dust EE template slope, which should be set to -2.4;
+*A_cnoise_e2e_100_100_EE normalization for the end-to-end empirical correlated-noise template at 100 GHz (should be set to 1, set to 0 to null effect of the template);
+*A_cnoise_e2e_143_143_EE normalization for the end-to-end empirical correlated-noise template at 143 GHz (should be set to 1, set to 0 to null effect of the template);
+*A_cnoise_e2e_217_217_EE normalization for the end-to-end empirical correlated-noise template at 217 GHz (should be set to 1, set to 0 to null effect of the template);
+*A_sbpx_100_100_TT normalization for the subpixel-effect correction at 100$\times$100 TT (should be set to 1);
+*A_sbpx_143_143_TT normalization for the subpixel-effect correction at 143$\times$143 TT (should be set to 1);
+*A_sbpx_143_217_TT normalization for the subpixel-effect correction at 143$\times$217 TT (should be set to 1);
+*A_sbpx_217_217_TT normalization for the subpixel-effect correction at 217$\times$217 TT (should be set to 1);
+*A_sbpx_100_100_EE normalization for the subpixel-effect correction at 100$\times$100 EE (should be set to 1);
+*A_sbpx_100_143_EE normalization for the subpixel-effect correction at 100$\times$143 EE (should be set to 1);
+*A_sbpx_100_217_EE normalization for the subpixel-effect correction at 100$\times$217 EE (should be set to 1);
+*A_sbpx_143_143_EE normalization for the subpixel-effect correction at 143$\times$143 EE (should be set to 1);
+*A_sbpx_143_217_EE normalization for the subpixel-effect correction at 143$\times$217 EE (should be set to 1);
+*A_sbpx_217_217_EE normalization for the subpixel-effect correction at 217$\times$217 EE (should be set to 1);
+* calib_100T, the relative calibration between 100 and 143 TT spectra;
+* calib_217T, the relative calibration between 217 and 143 TT spectra;
+* calib_100P, the calibration of the 100 EE;
+* calib_143P, the calibration of the 143 EE;
+* calib_217P, the calibration of the 217 EE;
+* A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;
+* A_planck, the Planck absolute calibration.
+Recommended priors can be found in the file ''plc_3.0/hi_l/plik/plik_recommended_priors.txt''
+For ''cosmomc'' users, a set of initialization files is available in ''plc_3.0/cosmomc''
+'''TT only - Plik lite'''
+This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range &#8467;=30-2508. It should not be used with the regular high-&#8467; TT or TTTEEE files.
+''' Production process'''
+The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2016-l05}}. The joint posterior of the CMB <i>TT</i> spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-&#8467; likelihood approximation for the
+CMB spectrum only. The nuisance parameters have been marginalized over the priors described above.
+''' Inputs: '''
+* Plik plik_rd12_HM_v22b_TTTEEE likelihood;
+* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ, leakage and subpixel templates.
+'''File name and usage'''
+The high-&#8467;, Plik TT, nuisance-marginalized likelihood is distributed in
+''plc_3.0/hi_l/plik_lite/plik_lite_v22_TT.clik'' .
+When used with the library, this expects a vector of parameters consisting of the
+<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.
+'''TT EE TE - Plik lite'''
+This file allows for the computation of the nuisance-marginalized CMB joint TT, TE, EE likelihood in the range &#8467;=30-2508 for temperature and &#8467;=30-1996 for TE and EE. It should not be used with the regular high-&#8467; TT or TTTEEE files.
+''' Production process'''
+The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2016-l05}}. The joint posterior of the CMB <i>TT<i/>, <i>TE</i>, and <i>EE</i> spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the
+CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.
+''' Inputs: '''
+* Plik plik_rd12_HM_v22b_TTTEEE likelihood;
+* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ leakage, subpixel and correlated noise templates.
+'''File name and usage'''
+The high-&#8467;, Plik TTTEEE, nuisance-marginalized likelihood is distributed in
+''plc_3.0/hi_l/plik_lite/plik_lite_v22_TTTEEE.clik''.
+When used with the library, this expects a vector of parameters consisting of the
+<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the <i>EE</i>, and <i>TE</i> spectra (same range) and by the Planck absolute calibration nuisance parameter.
+''' Lensing likelihoods '''
+'''CMB dependent likelihood'''
+This file allows for the computation of the baseline lensing likelihood, using the SMICA temperature and polarization
+map-based lensing reconstruction. Only the lensing multipole range &#8467;=8-400
+is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes
+the computation of a model-dependent correction to the normalization and
+the "N1 bias". To speed up those computations, both are performed using a linear approximation.
+'''Production process'''
+The SMICA <i>T</i> maps are filtered and correlated to reconstruct an optimal
+lensing-reconstruction map. Biases are corrected using Monte Carlo simulations
+for the dominant "mean field" and "N0" contributions, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned.
+The covariance matrix of this binned spectrum is evaluated using numerical simulations.
+The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.
+''' Inputs: '''
+* SMICA temperature and polarization CMB map;
+* Galactic mask;
+* best-fit Planck CMB model.
+'''File name and usage'''
+The lensing likelihood is distributed in
+''plc_3.0/hi_l/lensing/smicadx12_Dec5_ftl_mv2_ndclpp_p_teb_consext8.clik_lensing''.
+When used with the library, this expects a vector of parameters consisting of the
+&phi;&phi; lensing spectrum for &#8467;=0 to 2500 (inclusive), followed by the
+followed by the
+<i>TT</i> CMB power spectrum for &#8467;=0 to 2500 (inclusive), the <i>EE</i> and <i>TE</i> power spectra (same range) and by the Planck absolute calibration nuisance parameter.
+The <i>TT</i>, <i>EE</i>, and <i>TE</i> spectra are needed to compute the normalization and N1 corrections.
+'''CMB marginalized lensing likelihood'''
+This file allows for the computation of the baseline lensing likelihood, marginalized over the CMB power spectrum. The covariance is enlarged compared to the previous case to account for the change in N0 and N1 dues to possible variations of the CMB power spectrum. As in the previous case, only the lensing multipoles in the range range &#8467;=8-400
+are used.
+''' Production process'''
+The covariance of the CMB dependent likelihood is enlarged, and the theory spectrum is shifted to account for the marginalization over the CMB spectrum, using a Gaussian approximation. The "plik_lite" likelihood is used to provide the CMB spectra and covariances.
+''' Inputs: '''
+* SMICA <i>T</i> and <i>E</i> CMB maps;
+* Galactic mask;
+* best-fit Planck CMB model.
+* ''plik_lite'' likelihood
+'''File name and usage'''
+The CMB marginalized lensing likelihood is distributed in
+''plc_3.0/hi_l/lensing/smicadx12_Dec5_ftl_mv2_ndclpp_p_teb_consext8_CMBmarged.clik_lensing''.
+When used with the library, this expects a vector of parameters consisting of the
+&phi;&phi; lensing spectrum for &#8467;=0 to 2500 (inclusive), followed by the Planck absolute calibration nuisance parameter.
+'''Data sets - Extended data'''
+Five other data files are available.
+Those extend the baseline delivery by adding:
+* The LFI based low-&#8467; likelihood for TEB, ''[https://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_Likelihood_Data-extra-bflike-ext_R3.00.tar.gz COM_Likelihood_Data-extra-bflike-ext_R3.00.tar.gz]'';
+* TE, EE, unbinned and spectrum-model PE correction high-&#8467 Plik likelihoods, ''[https://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_Likelihood_Data-extra-plik-ext_R3.00.tar.gz COM_Likelihood_Data-extra-plik-ext_R3.00.tar.gz]'';
+* TE and EE high-&#8467 foreground- and nuisance-marginalized Plik_lite likelihoods ''[https://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_Likelihood_Data-extra-plik-lite-ext_R3.00.tar.gz COM_Likelihood_Data-extra-plik-lite-ext_R3.00.tar.gz]'';
+* TT, TE, EE, TTTEEE, TTTE, TEEE and TTEE alternative high-&#8467 Camspec likelihoods ''[https://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_Likelihood_Data-extra-camspec-ext_R3.00.tar.gz COM_Likelihood_Data-extra-camspec-ext_R3.00.tar.gz]'';
+* extended &#8467 range lensing likelihood, ''[https://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_Likelihood_Data-extra-lensing-ext_R3.00.tar.gz COM_Likelihood_Data-extra-lensing-ext_R3.00.tar.gz]'' .
+Note that although these products are discussed in the Planck papers, they are not used for the baseline results.
+Each file contains a '''readme.md''' description of the content and the use of the different likelihood files.
+== Previous Releases: (2015) and (2013) CMB spectrum and Likelihood ==
+<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #FFDAB9;width:80%">
+'''2015 CMB spectrum and Likelihood'''
+<div class="mw-collapsible-content">
+'''2015 CMB spectra'''
+'''General description'''
+'''TT'''
+The Planck best-fit CMB temperature power spectrum, shown in the figure below, covers the wide range of multipoles &#8467; = 2-2508. Over the multipole range &#8467; = 2-29, the power spectrum is derived from the "Commander" component-separation algorithm applied to the combination of Planck 2015 temperature data between 30 and 857 GHz, the 9-year WMAP sky maps, and the 408-MHz Haslam et al. (1982) survey, including 93% of the sky ({{PlanckPapers|planck2014-a12}}). The asymmetric error bars associated with this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction.
+For multipoles equal or greater than &#8467; = 30, instead, the spectrum is derived from the "Plik" likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT+lowP &Lambda;CDM run. Associated 1&sigma; errors include beam uncertainties. Both Commander and Plik are described in more detail in the sections below.
+[[File: A15_TT.png|thumb|center|700px|'''Planck 2015 TT power spectrum. The <i>x</i>-axis is logarithmic up to &#8467; = 30 and linear at higher &#8467;. The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of Planck-2015-A15[3]).  Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties.''']]
+'''TE, EE, and TB, EB, BB '''
+The Planck best-fit CMB polarization and temperature-polarization cross-correlation power spectra, shown in the figure below, cover the multipole range &#8467; = 2-1996. The data points relative to the multipole range &#8467; = 2-29 are quadratic maximum likelihood (QML) estimates from foreground-cleaned Planck 70-GHz <i>Q</i> and <i>U</i> Stokes parameter maps using 46% of the sky (the same maps that are used in the "lowP" likelihood, see {{PlanckPapers|planck2014-a13}}). In the range &#8467; = 2-29, we also release the <i>BB</i>, <i>TB</i>, and <i>EB</i> power spectra derived from the same maps (for the cross-spectra involving temperature, the Commander map is always used). Symmetric error bars are given as the 68% confidence intervals as derived from the Fisher information matrix of the estimates.
+Analogously to the <i>TT</i> case, the &#8467; &ge; 30 spectrum is derived from the Plik likelihood {{PlanckPapers|planck2014-a13}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds using the best-fit foreground solution from a Planck TT,TE,EE+lowP &Lambda;CDM run.
 {|style="margin: 0 auto;"
-|[[File: A15_EE.png|thumb|center|500px|'''The Planck 2015 EE power spectrum.  The red line is the Planck best-fit primordial power spectrum (cf Planck TT+lowP in Table 3 of Planck-2015-A15).  Residuals with respect to this model are shown in the lower panel. The error bars show <math>\pm 1\sigma</math> uncertainties. The green lines in the lower panels show the best-fit temperature-to-polarization leakage model of Eqs. (11a) and (11b) in Planck-2015-A15.''']]
+|[[File: A15_EE.png|thumb|center|500px|'''Planck 2015 <i>EE</i> power spectrum.  The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}).  Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]
-|[[File: A15_TE.png|thumb|center|500px|'''The Planck 2015 TE power spectrum.  The red line is the Planck best-fit primordial power spectrum (cf Planck TT+lowP in Table 3 of Planck-2015-A15).  Residuals with respect to this model are shown in the lower panel. The error bars show <math>\pm 1\sigma</math> uncertainties. The green lines in the lower panels show the best-fit temperature-to-polarization leakage model of Eqs. (11a) and (11b) in Planck-2015-A15.''']]
+|[[File: A15_TE.png|thumb|center|500px|'''Planck 2015 <i>TE</i> power spectrum.  The red line is the Planck best-fit primordial power spectrum (cf. Planck TT+lowP in table 3 of {{PlanckPapers|planck2014-a15}}).  Residuals with respect to this model are shown in the lower panel. The error bars show &plusmn;1&sigma; uncertainties. ''']]
 |}
-===Production process===
+'''Production process'''
-The <math>\ell</math> < 30 part of the Planck TT power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters {{PlanckPapers|planck2014-a12}}. The power spectrum at any multipole <math>\ell</math> is given as the maximum probability point for the posterior <math>C_\ell</math> distribution, marginalized over the other multipoles, and the error bars are 68% confidence level; see {{PlanckPapers|planck2014-a12}}.
+The &#8467; &lt; 30 part of the Planck <i>TT</i> power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters ({{PlanckPapers|planck2014-a12}}). The power spectrum at any multipole &#8467; is given as the maximum probability point for the posterior <i>C</i><sub>&#8467;</sub> distribution, marginalized over the other multipoles, and the error bars are from the 68% confidence level; see {{PlanckPapers|planck2014-a12}}. The polarization spectra (<i>EE</i>, <i>TE</i>, <i>BB</i>, <i>TB</i>, <i>EB</i>) are estimated from maps of the Planck 70 GHz channel, cleaned from polarized synchrotron emission using the 30 GHz channel as a template and from polarized dust emission using the 353 GHz channel; see Sect.2 of {{PlanckPapers|planck2014-a13}} for details about the foreground cleaning procedure.  The pixel-pixel (map level) noise covariance matrix has been estimated from the timelines and corrected to account for foreground cleaning. The QML code Bolpol has been used to estimate the power spectra and their Fisher matrix from the cleaned map and covariance matrix, after imposing a Galactic mask that makes 43% of the full sky available to analysis (see again {{PlanckPapers|planck2014-a13}}). The symmetric 68% error bars have been derived from the resulting Fisher matrix and include contributions from cosmic variance, noise, and foreground associated errors.
+The &#8467; &ge; 30 part of the <i>TT</i>, <i>TE</i>, and <i>EE</i> power spectra have been derived by the Plik likelihood, a code that implements a pseudo-<i>C</i><sub>&#8467;</sub> based technique, extensively described in section 2.2 and the appendix of {{PlanckPapers|planck2013-p08}}, and more recently in {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143&times;217, and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for <i>TT</i> we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for <i>TE</i> and <i>EE</i> we use the best fit from Planck+TT+lowP, cf. table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The &#8467; &ge; 30 CMB <i>TT</i> spectrum and associated covariance matrix are available in two formats.
+#Unbinned: TT, 2479 bandpowers (&#8467; = 30-2508); TE or EE, 1697 bandpowers (&#8467; = 30-1996).
+#Binned, in bins of &Delta;&#8467; = 30: TT, 83 bandpowers; TE or EE, 66 bandpowers.
+We bin the <i>C</i><sub>&#8467;</sub> power spectrum with a weight proportional to &#8467;(&#8467;+1), so that the <i>C</i><sub>&#8467;<sub><i>b</i></sub></sub> binned bandpower centred on &#8467;<sub><i>b</i></sub> is
+<math>\\ C_{\ell_b}=\Sigma_{\ell \in b}  w_{\ell_b\ell} C_\ell, \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}.\\</math>
+Equivalently, using the matrix formalism, we can construct the binning matrix <i>B</i> as
+<math>\\ B_{\ell_b \ell}=w_{\ell_b\ell}, \\ </math>
+where <i>B</i> is an <i>n</i><sub>b</sub>&times;<i>n</i><sub>&#8467;</sub> matrix, with <i>n<sub>b</sub></i>=83 being the number of bins and <i>n</i><sub>&#8467;</sub>=2479 the number of unbinned multipoles. Thus
+<math> \\ {\bf C}_\mathrm{binned}=B \, {\bf C}, \\
+\mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^{\rm T}, \\
+\ell_b=B\, \ell .\\ </math>
+Here, <math> {\bf C}_{\rm binned}\, ({\bf C})</math> is the vector containing all the binned (unbinned) <i>C</i><sub>&#8467;</sub> bandpowers, <math>\mathrm{cov}</math> is the covariance matrix, and &#8467;<sub><i>b</i></sub> is the weighted average multipole in each bin. Note that following this definition, &#8467;<sub><i>b</i></sub> can be a non-integer. The binned <i>D</i><sub>&#8467;<sub><i>b</i></sub></sub> power spectrum is then calculated as
+<math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b}. </math>
-The <math>\ell \ge 30</math>   part of the TT, TE and EE power spectra have been derived by the Plik likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of {{PlanckPapers|planck2013-p08}} and {{PlanckPapers|planck2014-a13}}. Frequency spectra are computed as cross-spectra between half-mission maps. Mask and multipole range choices for each frequency spectrum are summarized in Section 3.3 of {{PlanckPapers|planck2014-a15}} and in {{PlanckPapers|planck2014-a13}}. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (for TT we use the best-fit solutions for the nuisance parameters from the Planck+TT+lowP data combination, while for TE and EE we use the best fit from Planck+TT+lowP, cf Table 3 of {{PlanckPapers|planck2014-a15}}). A thorough description of the models of unresolved foregrounds is given in {{PlanckPapers|planck2014-a13}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with beam uncertainties. The <math>\ell  \ge 30</math>  CMB TT spectrum and associated covariance matrix are available in two formats:
+'''Inputs'''
-#Unbinned. TT: 2479 bandpowers (<math>\ell=30-2508</math>); TE or EE: 1697 bandpowers (<math>\ell=30-1996</math>).
-#Binned, in bins of <math> \Delta\ell=30 </math>. TT: 83 bandpowers. TE or EE: 66 bandpowers. We bin the <math> C_\ell </math> power spectrum with a weight proportional to <math> \ell (\ell+1) </math>, so that the <math> C_{\ell_b} </math> binned bandpower centered in <math> \ell_b </math> is: <math> \\ C_{\ell_b}=\Sigma_{\ell \in b}  w_{\ell_b\ell} C_\ell \quad \text{with} \quad w_{\ell_b\ell}=\frac{\ell (\ell+1)}{\Sigma_{\ell \in b} \ell (\ell+1)}. \\</math> Equivalently, using the matrix formalism, we can construct the binning matrix B as: <math>\\ B_{\ell_b \ell}=w_{\ell_b\ell} \\ </math> where B is a <math> n_b\times n_\ell</math> matrix, with <math>n_b=83</math> the number of bins and <math>n_\ell=2479</math> the number of unbinned multipoles. Thus:  <math> \\ \vec{C}_\mathrm{binned}=B \, \vec{C} \\ \mathrm{cov_\mathrm{binned}}= B\, \mathrm{cov}\, B^T \\ \ell_b=B\, \ell \\ </math> Here, <math> \vec{C}_{binned}\, (\vec{C}) </math>  is the vector containing all the binned (unbinned) <math>C_\ell</math> bandpowers, <math>\mathrm{cov} </math> is the covariance matrix and <math>\ell_b</math> is  the weighted average multipole  in each bin. Note that following this definition, <math>\ell_b</math> can be a non-integer. The binned <math>D_{\ell_B}</math> power spectrum is then calculated as: <math> \\ D_{\ell_b}=\frac{\ell_b (\ell_b+1)}{2\pi} C_{\ell_b} </math>.
-===Inputs===
+; Low-&#8467; spectrum (&#8467;&lt;30)<nowiki>:</nowiki>
-; Low-l spectrum (<math>\ell  < 30</math>):
+* Planck 30 and 44 GHz frequency maps;
-* Planck 30 and 44 GHz frequency maps
+* Planck 70 to 857 GHz detector and detector-set maps;
-* Planck 70 to 857 GHz detector and detector set maps
+* 9-year WMAP temperature sky maps between 23 and 94 GHz;
-* 9-year WMAP temperature sky maps between 23 and 94 GHz
+* 408-MHz survey of Haslam et al. (1982);
-* 408 MHz survey by Haslam et al. (1982)
+* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).
-* Commander <math>\chi^2</math> based LM93 confidence mask {{PlanckPapers|planck2014-a12}}
-; High-l spectrum (<math>30 \le  \ell \le 2508</math>):
+; High-&#8467; spectrum (30&le;&#8467;&le;2508)<nowiki>:</nowiki>
-* 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 3.3 {{PlanckPapers|planck2014-a15}})
+* 100, 143, 143&times;217 and 217 GHz spectra and their covariance matrix (setion 3.3 of {{PlanckPapers|planck2014-a15}});
-* best-fit foreground templates and inter-frequency calibration factors (Table 3 of {{PlanckPapers|planck2014-a15}})
+* best-fit foreground templates and inter-frequency calibration factors (table 3 of {{PlanckPapers|planck2014-a15}});
-* Beam transfer function uncertainties {{PlanckPapers|planck2014-a08}}
+* beam transfer function uncertainties ({{PlanckPapers|planck2014-a08}}).
-=== File names and Meta data ===
+''' File names and meta-data '''
-The CMB spectrum and its covariance matrix are distributed in a single FITS file named
+The CMB spectra and their uncertainties are distributed in a single multi-extension FITS file named ''COM_PowerSpect_CMB_R2.nn.fits''.
-<!--- * ''{{PLASingleFile | fileType=cosmo | name=COM_PowerSpect_CMB_R2.00.fits | link=COM_PowerSpect_CMB_R1.10.fits}}''  --->
+* R2.00 contains (unbinned) TT spectra for low &#8467; and TT, TE and EE spectra at high &#8467;, both binned and unbinned (7 extensions).
-* ''COM_PowerSpect_CMB_R2.nn.fits''
+* R2.01 corrects a small error in the <i>effective</i>  &#8467; of the bin of the binned data, which was truncated to an integer.  Since these are weighted averages of the &#8467;'s used in a particular bin, they should be a reals.
-which contains 7 ''BINTABLE'' extensions
+* R2.02 contains  low &#8467; *E and *B spectra in addition to the TT spectra (5 additional extensions for a total of 12 extensions).
-; 1. TT low-ell, unbinned (TTLOLUNB)
+Further details on the data columns are given below (the extension numbers correspond to the R2.02 release).
-: with the low ell part of the spectrum, not binned, and for l=2-29.  The table columns are
-# ''ELL'' (integer): multipole number
-# ''D_ELL'' (float): <math>D_ell</math> as described above
-# ''ERRUP'' (float): the upward uncertainty
-# ''ERRDOWN'' (float): the downward uncertainty
-; 2. TE low-ell, unbinned (TTLOLUNB)
+; 1. TT low-&#8467;, unbinned (TTLOLUNB)
-: with the low ell part of the spectrum, not binned, and for l=2-29.  The table columns are
+: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29.  The table columns are:
-# ''ELL'' (integer): multipole number
+# ''ELL'' (integer), multipole number;
-# ''D_ELL'' (float): <math>D_ell</math> as described above
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
-# ''ERRUP'' (float): the upward uncertainty
+# ''ERRUP'' (float), the upward uncertainty;
-# ''ERRDOWN'' (float): the downward uncertainty
+# ''ERRDOWN'' (float), the downward uncertainty.
-; 3. EE low-ell, unbinned (TTLOLUNB)
+; 2. TE low-&#8467;, unbinned (TTLOLUNB)
-: with the low ell part of the spectrum, not binned, and for l=2-29.  The table columns are
+: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29.  The table columns are:
-# ''ELL'' (integer): multipole number
+# ''ELL'' (integer), multipole number;
-# ''D_ELL'' (float): <math>D_ell</math> as described above
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
-# ''ERRUP'' (float): the upward uncertainty
+# ''ERRUP'' (float), the upward uncertainty;
-# ''ERRDOWN'' (float): the downward uncertainty
+# ''ERRDOWN'' (float), the downward uncertainty.
-; 4. TB low-ell, unbinned (TTLOLUNB)
+; 3. EE low-&#8467;, unbinned (TTLOLUNB)
-: with the low ell part of the spectrum, not binned, and for l=2-29.  The table columns are
+: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29.  The table columns are:
-# ''ELL'' (integer): multipole number
+# ''ELL'' (integer), multipole number;
-# ''D_ELL'' (float): <math>D_ell</math> as described above
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
-# ''ERRUP'' (float): the upward uncertainty
+# ''ERRUP'' (float), the upward uncertainty;
-# ''ERRDOWN'' (float): the downward uncertainty
+# ''ERRDOWN'' (float), the downward uncertainty.
-; 5. EB low-ell, unbinned (TTLOLUNB)
+; 4. TB low-&#8467;, unbinned (TTLOLUNB)
-: with the low ell part of the spectrum, not binned, and for l=2-29.  The table columns are
+: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29.  The table columns are:
-# ''ELL'' (integer): multipole number
+# ''ELL'' (integer), multipole number;
-# ''D_ELL'' (float): <math>D_ell</math> as described above
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
-# ''ERRUP'' (float): the upward uncertainty
+# ''ERRUP'' (float), the upward uncertainty;
-# ''ERRDOWN'' (float): the downward uncertainty
+# ''ERRDOWN'' (float), the downward uncertainty.
-; 6. BB low-ell, unbinned (TTLOLUNB)
+; 5. EB low-&#8467;, unbinned (TTLOLUNB)
-: with the low ell part of the spectrum, not binned, and for l=2-29.  The table columns are
+: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29.  The table columns are:
-# ''ELL'' (integer): multipole number
+# ''ELL'' (integer), multipole number;
-# ''D_ELL'' (float): <math>D_ell</math> as described above
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
-# ''ERRUP'' (float): the upward uncertainty
+# ''ERRUP'' (float), the upward uncertainty;
-# ''ERRDOWN'' (float): the downward uncertainty
+# ''ERRDOWN'' (float), the downward uncertainty.
-; 7. TT high-ell, binned (TTHILBIN)
+; 6. BB low-&#8467;, unbinned (TTLOLUNB)
-: with the high-ell part of the spectrum, binned into 83 bins covering <math>\langle l \rangle = 47-2499\ </math> in bins of width <math>l=30</math> (with the exception of the last bin that is smaller). The table columns are as follows:
+: with the low-&#8467; part of the spectrum, not binned, and for &#8467;=2-29.  The table columns are:
-# ''ELL'' (float): mean multipole number of bin
+# ''ELL'' (integer), multipole number;
-# ''L_MIN'' (integer): lowest multipole of bin
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
-# ''L_MAX'' (integer): highest multipole of bin
+# ''ERRUP'' (float), the upward uncertainty;
-# ''D_ELL'' (float): <math>D_\ell</math> as described above
+# ''ERRDOWN'' (float), the downward uncertainty.
-# ''ERR'' (float): the uncertainty
-; 8. TT high-ell unbinned (TTHILUNB)
+; 7. TT high-&#8467;, binned (TTHILBIN)
-: with the high-ell part of the spectrum, unbinned, in 2979 bins covering <math>\langle l \rangle = 30-2508\ </math>. The table columns are as follows:
+: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-2499 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:
-# ''ELL'' (integer):  multipole
+# ''ELL'' (float), mean multipole number of bin;
-# ''D_ELL'' (float): <math>D_\ell</math> as described above
+# ''L_MIN'' (integer), lowest multipole of bin;
-# ''ERR'' (float): the uncertainty
+# ''L_MAX'' (integer), highest multipole of bin;
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
+# ''ERR'' (float), the uncertainty.
-; 9. TE high-ell, binned (TEHILBIN)
+; 8. TT high-&#8467; unbinned (TTHILUNB)
-: with the high-ell part of the spectrum, binned into 83 bins covering <math>\langle l \rangle = 47-1988\ </math> in bins of width <math>l=30</math> (with the exception of the last bin that is smaller). The table columns are as follows:
+: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-2508. The table columns are:
-# ''ELL'' (float): mean multipole number of bin
+# ''ELL'' (integer), multipole;
-# ''L_MIN'' (integer): lowest multipole of bin
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
-# ''L_MAX'' (integer): highest multipole of bin
+# ''ERR'' (float), the uncertainty.
-# ''D_ELL'' (float): <math>D_\ell</math> as described above
-# ''ERR'' (float): the uncertainty
-; 10. TE high-ell, unbinned (TEHILUNB)
+; 9. TE high-&#8467;, binned (TEHILBIN)
-: with the high-ell part of the spectrum, unbinned, in 2979 bins covering <math>\langle l \rangle = 30-1996\ </math>. The table columns are as follows:
+: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:
-# ''ELL'' (integer):  multipole
+# ''ELL'' (float), mean multipole number of bin;
-# ''D_ELL'' (float): <math>D_\ell</math> as described above
+# ''L_MIN'' (integer), lowest multipole of bin;
-# ''ERR'' (float): the uncertainty
+# ''L_MAX'' (integer), highest multipole of bin;
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
+# ''ERR'' (float), the uncertainty.
-; 11. EE high-ell, binned (EEHILBIN)
+; 10. TE high-&#8467;, unbinned (TEHILUNB)
-: with the high-ell part of the spectrum, binned into 83 bins covering <math>\langle l \rangle = 47-1988\ </math> in bins of width <math>l=30</math> (with the exception of the last bin that is smaller). The table columns are as follows:
+: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:
-# ''ELL'' (float): mean multipole number of bin
+# ''ELL'' (integer), multipole;
-# ''L_MIN'' (integer): lowest multipole of bin
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
-# ''L_MAX'' (integer): highest multipole of bin
+# ''ERR'' (float), the uncertainty.
-# ''D_ELL'' (float): <math>D_\ell</math> as described above
-# ''ERR'' (float): the uncertainty
-; 12. EE high-ell, unbinned (EEHILUNB)
+; 11. EE high-&#8467;, binned (EEHILBIN)
-: with the high-ell part of the spectrum, unbinned, in 2979 bins covering <math>\langle l \rangle = 30-1996\ </math>. The table columns are as follows:
+: with the high-&#8467; part of the spectrum, binned into 83 bins covering &lang;&#8467;&rang;= 47-1988 in bins of width &#8467;=30 (with the exception of the last bin that is smaller). The table columns are:
-# ''ELL'' (integer):  multipole
+# ''ELL'' (float), mean multipole number of bin;
-# ''D_ELL'' (float): <math>D_\ell</math> as described above
+# ''L_MIN'' (integer), lowest multipole of bin;
-# ''ERR'' (float): the uncertainty
+# ''L_MAX'' (integer), highest multipole of bin;
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
+# ''ERR'' (float), the uncertainty.
-Note that R2.00 of these files contained a small error in that the ''effective'' <math>\ell</math> of the bin in the binned data was truncated to an integer.  While the <math>\ell</math> values of the unbinned (full) data are indeed integer, the ''effective'' <math>\ell</math> of the binned data is a weighted average of the <math>\ell</math>'s used in the bin and it should be a real number.  This is corrected in R2.01.
+; 12. EE high-&#8467;, unbinned (EEHILUNB)
+: with the high-&#8467; part of the spectrum, unbinned, in 2979 bins covering &lang;&#8467;&rang;= 30-1996. The table columns are:
+# ''ELL'' (integer), multipole;
+# ''D_ELL'' (float), <i>D</i><sub>&#8467;</sub> as described above;
+# ''ERR'' (float), the uncertainty.
-The spectra give <math>D_\ell = \ell(\ell+1)C_\ell / 2\pi </math> in units of <math>\mu\, K^2</math>. The covariance matrices of the spectra will be released at a later time.
+The spectra give <i>D</i><sub>&#8467;</sub> = &#8467;(&#8467;+1)<i>C</i><sub>&#8467;</sub> / 2&pi; in units of &mu;K<sup>2</sup>. The covariance matrices of the spectra will be released at a later time.
 The CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.
-==Likelihood==
+'''Likelihood'''
+The 2015 baseline likelihood release consists of a code package and a single data package. Four extended data packages are also available enabling exploration of alternatives to the baseline results.
+The code compiles to a library allowing for the computation of log likelihoods for a given data set. Each data package contains multiple data sets.  A data set permits the computation of a single likelihood among:
+* the high-&#8467; temperature and polarization CMB (jointly or separately);
+* the low-&#8467; temperature and polarization CMB (jointly or separately);
+* the CMB lensing reconstruction.
+By combining the results from different data sets (possibly from different data packages), one can compute the likelihood of different subsets of the Planck data.
-The 2015 likelihood release consists of a code package and a small number of data packages. The code compiles to a library allowing for the computation of log likelihoods for a given dataset. Each data package contains multiple datasets.  Each dataset allow for the computation of a single likelihood among the following
+Only the baseline data package, ''COM_Likelihood_Data-baseline_R2.00.tar.gz'', will be fully described on this page. It contains six data sets, which are enough to compute all of the baseline Planck results that are discussed in {{PlanckPapers|planck2014-a14}}. In particular it allows for the computation of the CMB and lensing likelihood from either the Temperature data only, or the Temperature + Polarization combination.
-* the high-<math>\ell</math> temperature and polarization CMB (jointly or separately)
-* the low-<math>\ell</math> temperature and polarization CMB (jointly or separately)
-* the CMB lensing reconstruction
-By combining the results from different datasets, one can compute the likelihood for different subsets of the Planck data.
-Only one data package,  '''COM_Likelihood_Data-baseline_R2.00.tar.gz''', will be fully described in this page. It contains 6 datasets that are enough to compute all of the baseline Planck results that are discussed in  {{PlanckPapers|planck2014-a14}}.
+The other data packages contain data sets that extend the baseline results, enabling the exploration of different regimes, which are discussed in {{PlanckPapers|planck2014-a13}} and  {{PlanckPapers|planck2014-a17}}. Their full description is contained in the documentation included in each of the extended data packages.
-The other data packages contains datasets that extend the baseline results, allowing to explore different regimes that are discussed in {{PlanckPapers|planck2014-a13}} and  {{PlanckPapers|planck2014-a17}}. There full description is included in the documentation included in the data package.
-===Library and tools===
+'''Library and tools'''
-====Description====
+'''Description'''
 The library consists of code written in C and Fortran 90. It can be called from both of
 those languages. Optionally, a python wrapper can be built as well. Scripts to
 simplify the linking of the library with other codes are part of the package, as
 well as some example codes that can be used to test the correct installation of
-the code and the integrity of the data packages. Optionally, a script allowing
+the code and the integrity of the data packages. Optionally, a script is also available, allowing
 the user to modify the multipole range of the TT likelihoods and reproduce the hybridization
-test performed in the paper is also available.
+test performed in the paper.
 A description of the tool, the API of the library, as well as different
-installation procedure are detailed in the readme.md file in the code package.
+installation procedure are detailed in the ''readme.md'' file in the code package.
-====File name====
+'''File name'''
 The code can be extracted from
-'''COM_Likelihood_Code-v2.0.R2.00.tar.bz2'''
+''COM_Likelihood_Code-v2.0_R2.00.tar.bz2''.
 Please read the file ''readme.md'' for installation instructions.
-===Datasets - Baseline data===
+'''Data sets - Baseline data'''
-All of the baseline data release are distributed within a single file.
+All of the released baseline data are distributed within a single file,
-'''COM_Likelihood_Data-baseline_R2.00.tar.gz'''.
+''COM_Likelihood_Data-baseline_R2.00.tar.gz''.
-This files extract to a hierarchy of directory containing the different datasets needed to compute different likelihoods.
+This file extracts to a directory hierarchy, containing the different data sets needed to compute different likelihoods.
-Each dataset is stored in its own directory. The directory structure follows similar rules
+Each data set is stored in its own directory. The directory structure follows similar rules
-for each dataset, and stores data, template and metadata for each particular likelihood.
+for each data set, and stores data, template, and meta-data for each particular likelihood.
-As in 2013, the CMB likelihood is cut into a low-ell and high-ell part. Moreover,
+As in 2013, the CMB likelihood is cut into low-&#8467; and high-&#8467; parts. Moreover,
-for each of those, we distribute both a TT only datafile and a joint T+P one. In the case
+for each of those, we distribute both a T-only datafile and a joint T+P one. In the case
-of the high-ell part, we also distribute two specific versions of the likelihood,
+of the high-&#8467; part, we also distribute two specific versions of the likelihood,
-that allow for estimate of the TT and T+P marginalized over the nuisance parameters.
+that allow for estimate of T and T+P marginalized over the nuisance parameters.
-Combining both the low-ell and high-ell files, one can compute the likelihood over the
+Combining both the low-&#8467; and high-&#8467; files, one can compute the likelihood over the
-range <math>\ell=2-2508</math> in TT and <math>\ell=2-1996</math> in TE and EE. Full description of the low-ell
+range &#8467;=2-2508 in TT and &#8467;=2-1996 in TE and EE. A full description of the low-&#8467;
-and high-ell likelihood is available in {{PlanckPapers|planck2014-a13}}.
+and high-&#8467; likelihood is available in {{PlanckPapers|planck2014-a13}}.
-Similarly, in the case of lensing, we also distribute both the likelihood using either
+Similarly, for the case of lensing, we also distribute the likelihood using both
-the reconstruction based on the temperature map only, or on T+P maps.
+the reconstruction based on the <i>T</i> map only, or on <i>T</i>+<i>P</i> maps.
-Full description of the lensing likelihood is available in {{PlanckPapers|planck2014-a17}}.
+A full description of the lensing likelihood is available in {{PlanckPapers|planck2014-a17}}.
-All of the likelihood files have at least one nuisance parameter allowing to explore the Planck absolute calibration. We recommend that his parameter is explored in the gaussian prior 1±0.0025
+All of the likelihood files have at least one nuisance parameter, allowing users to investigate the Planck absolute calibration. We recommend that his parameter is explored in the Gaussian prior 1.0000&plusmn;0.0025.
-==== Low ell likelihoods ====
+''' Low-&#8467; likelihoods '''
-=====TT only - commander=====
+'''TT only - commander'''
-This file allows for the computation of the CMB TT likelihood in the range <math>\ell=2-29</math>.
+This file allows for the computation of the CMB TT likelihood in the range &#8467;=2-29.
-Using the optional tool in the code package it can be modified to cover any l range
+Using the optional tool in the code package, it can be modified to cover any multipole range
-up to <math>\ell<200</math>
+up to &#8467;&lt;200.
-====== Production process======
+''' Production process'''
-The likelihood is based on the result of the Commander approach which implements a
+The likelihood is based on the results of the Commander approach, which implements a
-Bayesian component separation in pixel space, sampling the posterior distribution
+Bayesian component separation method in pixel space, sampling the posterior distribution
-of the parameter of a model that describes both the CMB and the foreground emissions
+of the parameters of a model that describes both the CMB and the foreground emissions
-in a combination of the Planck maps, the WMAP map and the 408 MHz survey. The samples
+in a combination of the Planck maps, the WMAP map, and the 408-MHz survey. The samples
-of this exploration are used to infer the foreground marginalized low-ell likelihood
+of this exploration are used to infer the foreground marginalized low-&#8467; likelihood
-for any TT CMB spectrum.
+for any <i>TT</i> CMB spectrum.
-====== Inputs ======
+''' Inputs: '''
-* Planck 30 and 44 GHz frequency maps
+* Planck 30- and 44-GHz frequency maps;
-* Planck 70 to 857 GHz detector and detector set maps
+* Planck 70- to 857-GHz detector and detector-set maps;
-* 9-year WMAP temperature sky maps between 23 and 94 GHz
+* 9-year WMAP temperature sky maps between 23 and 94 GHz;
-* 408 MHz survey by Haslam et al. (1982)
+* 408-MHz survey of Haslam et al. (1982);
-* Commander <math>\chi^2</math> based LM93 confidence mask {{PlanckPapers|planck2014-a12}}
+* Commander &chi;<sup>2</sup>-based LM93 confidence mask ({{PlanckPapers|planck2014-a12}}).
+'''File name and usage'''
-======File name and usage======
 The commander likelihood is distributed in
 ''plc_2.0/low_l/commander/commander_rc2_v1.1_l2_29_B.clik''
-When used with the library, it expects a vector of parameters consisting in the
+When used with the library, this expects a vector of parameters consisting of the
-TT CMB power spectrum from <math>\ell=0</math> to <math>\ell=29</math> (included) and an extra nuisance parameter
+<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive) and an extra nuisance parameter
-consisting of the overall planck calibration.
+consisting of the overall Planck calibration.  Note that the vector really starts at &#8467;=0, although
+the first two entries are null.
-=====TEB =====
+'''TEB '''
 This file allows for the computation of the CMB joint TT,EE, BB and TE  likelihood
-in the range <math>\ell=2-29</math>. It should not be used with the low-ell TT only likelihood.
+in the range &#8467;=2-29. It should not be used with the low-&#8467; TT-only likelihood.
-====== Production process======
+''' Production process'''
-The file allows for the computation of the pixel based likelihood of T, E and B
+The file allows for the computation of the pixel based likelihood of <i>T</i>, <i>E</i>, and <i>B</i>
-maps. The T map is the best fit map obtained from the commander algorithm as above,
+maps. The <i>T</i> map is the best-fit map obtained from the commander algorithm, as described above,
-while the E and B maps are obtained from the 70GHz LFI instrument, using data from the full mission but excluding the second and fourth surveys. Foreground contamination are
+while the <i>E</i> and <i>B</i> maps are obtained from the 70GHz LFI full mission data, but excluding the second and fourth surveys. Foreground contamination is
-dealt with by marginalizing over templates based on the 30GHz LFI and 353GHz HFI maps.
+dealt with by marginalizing over templates based on the 30-GHz LFI and 353-GHz HFI maps.
-The covariance matrix is based on the Planck detector sensitivity modulated on the
+The covariance matrix comes from the Planck detector sensitivity modulated on the
 sky by the scanning strategy. The covariance matrix is further enlarged to account
 for the foreground template removal.
 To speed up the computation by about an order of magnitude, the problem is
-projected in Cl space using the Sherman-Morrison-Woodbury identity. Only the
+projected into <i>C</i><sub>&#8467;</sub> space using the Sherman-Morrison-Woodbury identity. Only the
 projected quantities are stored in the data package.
-====== Inputs ======
+''' Inputs: '''
-* Planck 30 and 44 GHz frequency maps
+* Planck 30- and 44-GHz frequency maps;
-* Planck 70 to 857 GHz detector and detector set maps
+* Planck 70- to 857-GHz detector and detector-set maps;
-* 9-year WMAP temperature sky maps between 23 and 94 GHz
+* 9-year WMAP temperature sky maps between 23 and 94 GHz;
-* 408 MHz survey by Haslam et al. (1982)
+* 408-MHz survey of Haslam et al. (1982);
-* Commander <math>\chi^2</math> based LM93 confidence mask {{PlanckPapers|planck2014-a12}}
+* Commander &chi;<sup>2</sup>-based LM93 confidence mask {{PlanckPapers|planck2014-a12}}.
-======File name and usage======
+'''File name and usage'''
 The low ell TEB likelihood is distributed in
-''plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik''
+''plc_2.0/low_l/bflike/lowl_SMW_70_dx11d_2014_10_03_v5c_Ap.clik''.
-When used with the library, it expects a vector of parameters consisting in the
-TT CMB power spectrum from <math>\ell=0</math> to <math>\ell=29</math> (included), followed by the EE (<math>\ell=0</math> to 29),
-BB  (<math>\ell=0</math> to 29) and TE  (<math>\ell=0</math> to 29) spectra, and by an extra nuisance parameter
-consisting of the overall planck calibration.
+When used with the library, this expects a vector of parameters consisting of the
+<i>TT</i> CMB power spectrum from &#8467;=0 to 29 (inclusive), followed by the <i>EE</i> (&#8467;=0 to 29),
+<i>BB</i>  (&#8467;=0 to 29) and <i>TE</i>  (&#8467;=0 to 29) spectra, and by an extra nuisance parameter
+consisting of the overall Planck calibration.  Note that the entries really start at &#8467;=0, although the
+&#8467;=0 and &#8467;=1 values will be null.
-==== High ell likelihoods ====
+''' High-&#8467; likelihoods '''
-=====TT only - plik=====
+'''TT only - Plik'''
-This file allows for the computation of the CMB TT likelihood in the range  <math>\ell=30-2508</math>.
+This file allows for the computation of the CMB TT likelihood in the range &#8467;=30-2508.
-Using the optional tool in the code package it can be modified to cover any l range in  <math>29<\ell<2509</math>.
+Using the optional tool in the code package it can be modified to cover any multipole range within 29&lt;&#8467;&lt;2509.
-====== Production process======
+''' Production process'''
-The file contains the 100GHz, 143GHz, and 217GHz binned half mission TT cross spectra.
+The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>TT</i> cross-spectra.
-Only the 100x100, 143x143, 143x217 and 217x217 are actually used. Masks and multipole
+Only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used. Masks and multipole
-ranges for each spectra are different and described in {{PlanckPapers|planck2014-a13}}.
+ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.
-Masks are based on CMB cleaned 353GHz map for the dust component, on the Planck catalogs for the point source part, and on the CO maps.
+Masks are based on the CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.
 The file also contains
-templates for the residual foreground contamination of each spectra. The templates are needed
+templates for the residual foreground contamination of each spectrum. The templates are needed
-to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is
+to allow for computation of the joint CMB and nuisance likelihood. The covariance matrix is
-computed using an analytical approximation, and corrected by Monte-Carlo estimates
+computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.
-for the effect of point sources. The covariance matrix is computed for a fiducial
+The covariance matrix is computed for a fiducial
-cosmology and nuisance model that has been obtained using a first, less optimal
+cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.
-estimate of the parameters.
-====== Inputs ======
+''' Inputs: '''
-* Planck 100, 143 and 217GHz half mission Temperature maps
+* Planck 100-, 143-, and 217-GHz half-mission <i>T</i> maps;
-* CMB cleaned (using the smica map) 353GHz map, CO emission maps, and planck catalogs for the masks.
+* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;
-* Planck 545GHz maps for the dust residual contamination template
+* Planck 545-GHz maps for the dust residual contamination template;
-* CIB, tSZ, kSZ, CIBxSZ templates
+* CIB, tSZ, kSZ, and CIB&times;SZ templates.
-======File name and usage======
+'''File name and usage'''
-The high ell, plik TT likelihood is distributed in
+The high-&#8467;, Plik TT likelihood is distributed in
-''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik''
+''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TT.clik''.
-When used with the library, it expects a vector of parameters consisting in the
+When used with the library, this expects a vector of parameters consisting of the
-TT CMB power spectrum from <math>\ell=0</math> to <math>\ell=2508</math> (included), followed by a vector of 16 nuisance parameters.
+<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by a vector of 16 nuisance parameters.
-Those are, in that order
+Those are, in order:
-* A_cib_217, The CIB contamination at l=3000 in the 217GHz Planck map.
+* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;
-* cib_index, The effective slope of the CIB spectrum. This parameter should be set to -1.3
+* cib_index, the effective slope of the CIB spectrum, a parameter that should be set to -1.3;
-* xi_sz_cib, The szXcib cross correlation
+* xi_sz_cib, the SZ&times;CIB cross-correlation;
-* A_sz, the tSZ contamination at 143GHz
+* A_sz, the tSZ contamination at 143GHz;
-* ps_A_100_100, the point source contribution in 100x100
+* ps_A_100_100, the point source contribution in 100&times;100;
-* ps_A_143_143, the point source contribution in 143x143
+* ps_A_143_143, the point source contribution in 143&times;143;
-* ps_A_143_217, the point source contribution in 143x217
+* ps_A_143_217, the point source contribution in 143&times;217;
-* ps_A_217_217, the point source contribution in 217x217
+* ps_A_217_217, the point source contribution in 217&times;217;
-* ksz_norm, the ksz contamination
+* ksz_norm, the kSZ contamination;
-* gal545_A_100, the dust residual contamination at l=200 in 100x100
+* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100;
-* gal545_A_143, the dust residual contamination at l=200 in 143x143
+* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143;
-* gal545_A_143_217, the dust residual contamination at l=200 in 143x217
+* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217;
-* gal545_A_217, the dust residual contamination at l=200 in 217x217
+* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217;
-* calib_100T, the relative calibration between the 100 and 143 spectra
+* calib_100T, the relative calibration between the 100 and 143 spectra;
-* calib_217T, the relative calibration between the 217 and 143 spectra
+* calib_217T, the relative calibration between the 217 and 143 spectra;
-* A_planck, the planck absolute calibration
+* A_planck, the Planck absolute calibration.
-We recommend using the following gaussian priors:
+We recommend using the following Gaussian priors:
-* ksz_norm + 1.6 * A_sz = 9.5 ± 3
+* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;
-* cib_index             = -1.3
+* cib_index             = -1.3;
-* gal545_A_100          = 7±2
+* gal545_A_100          = 7&plusmn;2;
-* gal545_A_143          = 9±2
+* gal545_A_143          = 9&plusmn;2;
-* gal545_A_143_217      = 21±8.5
+* gal545_A_143_217      = 21.0&plusmn;8.5;
-* gal545_A_217          = 80±20
+* gal545_A_217          = 80&plusmn;20;
-* calib_100T            = 0.999±0.001
+* calib_100T            = 0.999&plusmn;0.001;
-* calib_217T            = 0.995±0.002
+* calib_217T            = 0.995&plusmn;0.002;
-* A_planck              = 1±0.0025
+* A_planck              = 1.0000&plusmn;0.0025.
-=====TT+TE+EE - plik=====
+'''TT+TE+EE - Plik'''
-This file allows for the computation of the CMB joint TT, TE and EE likelihood in the range <math>\ell=30-2508</math> for TT and <math>\ell=30-1996</math> for TE and EE.
+This file allows for the computation of the CMB joint TT, TE, and EE likelihood in the range &#8467;=30-2508 for TT and &#8467;=30-1996 for TE and EE.
-====== Production process======
+''' Production process'''
-The file contains the 100GHz, 143GHz, and 217GHz binned half mission T and E cross spectra.
+The file contains the 100-GHz, 143-GHz, and 217-GHz binned half-mission <i>T</i> and <i>E</i> cross-spectra.
-In temperature, only the 100x100, 143x143, 143x217 and 217x217 are actually used, while
+In temperature, only the 100&times;100, 143&times;143, 143&times;217, and 217&times;217 spectra are actually used, while
-in TE and EE all of them are. Masks and multipole
+in <i>TE</i> and <i>EE</i> all of them are used. Masks and multipole
-ranges for each spectra are different and described in {{PlanckPapers|planck2014-a13}}.
+ranges for each spectrum are different and described in {{PlanckPapers|planck2014-a13}}.
-Masks are based on CMB cleaned 353GHz map for the dust component, on the Planck catalogs for the point source part, and on the CO maps.
+Masks are based on CMB-cleaned 353-GHz map for the dust component, on the Planck catalogues for the point source part, and on the CO maps.
 The file also contains
-templates for the residual foreground contamination of each spectra. The templates are needed
+templates for the residual foreground contamination of each spectrum. The templates are needed
 to allow the computation of the joint CMB and nuisance likelihood. The covariance matrix is
-computed using an analytical approximation, and corrected by Monte-carlo estimates
+computed using an analytical approximation, and corrected for the effect of point sources through Monte Carlo estimates.
-for the effect of point sources. The covariance matrix is computed for a fiducial
+The covariance matrix is computed for a fiducial
-cosmology and nuisance model that has been obtained using a first, less optimal
+cosmology and nuisance model that has been obtained using a first, less optimal estimate of the parameters.
-estimate of the parameters.
-====== Inputs ======
+''' Inputs: '''
-* Planck 100, 143 and 217GHz half mission T+P maps
+* Planck 100-, 143-, and 217-GHz half-mission T+P maps;
-* CMB cleaned (using the smica map) 353GHz map, CO emission maps, and planck catalogs for the masks.
+* CMB-cleaned (using the SMICA map) 353-GHz map, CO emission maps, and Planck catalogues for the masks;
-* Planck 545GHz and 353GHz maps for the dust residual contamination template
+* Planck 545-GHz and 353-GHz maps for the dust residual contamination template;
-* CIB, tSZ, kSZ, CIBxSZ templates
+* CIB, tSZ, kSZ, and CIB&times;SZ templates;
-* best fit CMB+fg model for the beam leakage template
+* best-fit CMB+foreground model for the beam-leakage template.
-======File name and usage======
+'''File name and usage'''
-The high ell, plik TTTEEE likelihood is distributed in
+The high-&#8467;, plik TTTEEE likelihood is distributed in
-''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik''
+''plc_2.0/hi_l/plik/plik_dx11dr2_HM_v18_TTTEEE.clik''.
-This file should not be used with any other TT only high ell file.
+This file should not be used with any other TT-only high-&#8467; file.
-When used with the library, it expects a vector of parameters consisting in the
+When used with the library, this expects a vector of parameters consisting of the
-TT CMB power spectrum from <math>\ell=0</math> to <math>\ell=2508</math> (included), followed the EE and TE spectra (same range) and by a vector of 94 nuisance parameters.
+<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed the <i>EE</i> and <i>TE</i> spectra (same range) and by a vector of 94 nuisance parameters.
-Those are, in that order
+Those are, in g:
-* A_cib_217, The CIB contamination at l=3000 in the 217GHz Planck map.
+* A_cib_217, the CIB contamination at &#8467;=3000 in the 217-GHz Planck map;
-* cib_index, The effective slope of the CIB spectrum. This parameter should be set to -1.3
+* cib_index, the effective slope of the CIB spectrum, which should be set to -1.3;
-* xi_sz_cib, The szXcib cross correlation
+* xi_sz_cib, the SZ&times;CIB cross-correlation;
-* A_sz, the tSZ contamination at 143GHz
+* A_sz, the tSZ contamination at 143GHz;
-* ps_A_100_100, the point source contribution in 100x100
+* ps_A_100_100, the point source contribution in 100&times;100;
-* ps_A_143_143, the point source contribution in 143x143
+* ps_A_143_143, the point source contribution in 143&times;143;
-* ps_A_143_217, the point source contribution in 143x217
+* ps_A_143_217, the point source contribution in 143&times;217;
-* ps_A_217_217, the point source contribution in 217x217
+* ps_A_217_217, the point source contribution in 217&times;217;
-* ksz_norm, the ksz contamination
+* ksz_norm, the kSZ contamination;
-* gal545_A_100, the dust residual contamination at l=200 in 100x100TT
+* gal545_A_100, the dust residual contamination at &#8467;=200 in 100&times;100TT;
-* gal545_A_143, the dust residual contamination at l=200 in 143x143TT
+* gal545_A_143, the dust residual contamination at &#8467;=200 in 143&times;143TT;
-* gal545_A_143_217, the dust residual contamination at l=200 in 143x217TT
+* gal545_A_143_217, the dust residual contamination at &#8467;=200 in 143&times;217TT;
-* gal545_A_217, the dust residual contamination at l=200 in 217x217TT
+* gal545_A_217, the dust residual contamination at &#8467;=200 in 217&times;217TT;
-* galf_EE_A_100, The dust residual contamination at l=500 in 100x100EE
+* galf_EE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100EE;
-* galf_EE_A_100_143, The dust residual contamination at l=500 in 100x143EE
+* galf_EE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143EE;
-* galf_EE_A_100_217, The dust residual contamination at l=500 in 100x217EE
+* galf_EE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217EE;
-* galf_EE_A_143, The dust residual contamination at l=500 in 143x143EE
+* galf_EE_A_143, the dust residual contamination at &#8467;=500 in 143&times;143EE;
-* galf_EE_A_143_217, The dust residual contamination at l=500 in 143x217EE
+* galf_EE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217EE;
-* galf_EE_A_217, The dust residual contamination at l=500 in 217x217EE
+* galf_EE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217EE;
-* galf_EE_index, the dust EE template slope, should be set to -2.4
+* galf_EE_index, the dust EE template slope, which should be set to -2.4;
-* galf_TE_A_100, The dust residual contamination at l=500 in 100x100TE
+* galf_TE_A_100, the dust residual contamination at &#8467;=500 in 100&times;100TE;
-* galf_TE_A_100_143, The dust residual contamination at l=500 in 100x143TE
+* galf_TE_A_100_143, the dust residual contamination at &#8467;=500 in 100&times;143TE;
-* galf_TE_A_100_217, The dust residual contamination at l=500 in 100x217TE
+* galf_TE_A_100_217, the dust residual contamination at &#8467;=500 in 100&times;217TE;
-* galf_TE_A_143, The dust residual contamination at l=500 in 143x143TE
+* galf_TE_A_143, the dust residual contamination at &#8467;=500 in 143x143TE;
-* galf_TE_A_143_217, The dust residual contamination at l=500 in 143x217TE
+* galf_TE_A_143_217, the dust residual contamination at &#8467;=500 in 143&times;217TE;
-* galf_TE_A_217, The dust residual contamination at l=500 in 217x217TE
+* galf_TE_A_217, the dust residual contamination at &#8467;=500 in 217&times;217TE;
-* galf_TE_index, the dust EE template slope, should be set to -2.4
+* galf_TE_index, the dust EE template slope, which should be set to -2.4;
-* bleak_epsilon_0_0T_0E, Beam leakage parameters, espilon_0, 100x100 TE
+* bleak_epsilon_0_0T_0E, beam-leakage parameter, espilon_0, 100&times;100 TE;
-* bleak_epsilon_1_0T_0E, Beam leakage parameters, espilon_1, 100x100 TE
+* bleak_epsilon_1_0T_0E, beam-leakage parameter, espilon_1, 100&times;100 TE;
-* bleak_epsilon_2_0T_0E, Beam leakage parameters, espilon_2, 100x100 TE
+* bleak_epsilon_2_0T_0E, beam-leakage parameter, espilon_2, 100&times;100 TE;
-* bleak_epsilon_3_0T_0E, Beam leakage parameters, espilon_3, 100x100 TE
+* bleak_epsilon_3_0T_0E, beam-leakage parameter, espilon_3, 100&times;100 TE;
-* bleak_epsilon_4_0T_0E, Beam leakage parameters, espilon_4, 100x100 TE
+* bleak_epsilon_4_0T_0E, beam-leakage parameter, espilon_4, 100&times;100 TE;
-* bleak_epsilon_0_0T_1E, Beam leakage parameters, espilon_0, 100x143 TE
+* bleak_epsilon_0_0T_1E, beam-leakage parameter, espilon_0, 100&times;143 TE;
-* bleak_epsilon_1_0T_1E, Beam leakage parameters, espilon_1, 100x143 TE
+* bleak_epsilon_1_0T_1E, beam-leakage parameter, espilon_1, 100&times;143 TE;
-* bleak_epsilon_2_0T_1E, Beam leakage parameters, espilon_2, 100x143 TE
+* bleak_epsilon_2_0T_1E, beam-leakage parameter, espilon_2, 100&times;143 TE;
-* bleak_epsilon_3_0T_1E, Beam leakage parameters, espilon_3, 100x143 TE
+* bleak_epsilon_3_0T_1E, beam-leakage parameter, espilon_3, 100&times;143 TE;
-* bleak_epsilon_4_0T_1E, Beam leakage parameters, espilon_4, 100x143 TE
+* bleak_epsilon_4_0T_1E, beam-leakage parameter, espilon_4, 100&times;143 TE;
-* bleak_epsilon_0_0T_2E, Beam leakage parameters, espilon_0, 100x217 TE
+* bleak_epsilon_0_0T_2E, beam-leakage parameter, espilon_0, 100&times;217 TE;
-* bleak_epsilon_1_0T_2E, Beam leakage parameters, espilon_1, 100x217 TE
+* bleak_epsilon_1_0T_2E, beam-leakage parameter, espilon_1, 100&times;217 TE;
-* bleak_epsilon_2_0T_2E, Beam leakage parameters, espilon_2, 100x217 TE
+* bleak_epsilon_2_0T_2E, beam-leakage parameter, espilon_2, 100&times;217 TE;
-* bleak_epsilon_3_0T_2E, Beam leakage parameters, espilon_3, 100x217 TE
+* bleak_epsilon_3_0T_2E, beam-leakage parameter, espilon_3, 100&times;217 TE;
-* bleak_epsilon_4_0T_2E, Beam leakage parameters, espilon_4, 100x217 TE
+* bleak_epsilon_4_0T_2E, beam-leakage parameter, espilon_4, 100&times;217 TE;
-* bleak_epsilon_0_1T_1E, Beam leakage parameters, espilon_0, 143x143 TE
+* bleak_epsilon_0_1T_1E, beam-leakage parameter, espilon_0, 143&times;143 TE;
-* bleak_epsilon_1_1T_1E, Beam leakage parameters, espilon_1, 143x143 TE
+* bleak_epsilon_1_1T_1E, beam-leakage parameter, espilon_1, 143&times;143 TE;
-* bleak_epsilon_2_1T_1E, Beam leakage parameters, espilon_2, 143x143 TE
+* bleak_epsilon_2_1T_1E, beam-leakage parameter, espilon_2, 143&times;143 TE;
-* bleak_epsilon_3_1T_1E, Beam leakage parameters, espilon_3, 143x143 TE
+* bleak_epsilon_3_1T_1E, beam-leakage parameter, espilon_3, 143&times;143 TE;
-* bleak_epsilon_4_1T_1E, Beam leakage parameters, espilon_4, 143x143 TE
+* bleak_epsilon_4_1T_1E, beam-leakage parameter, espilon_4, 143&times;143 TE;
-* bleak_epsilon_0_1T_2E, Beam leakage parameters, espilon_0, 143x217 TE
+* bleak_epsilon_0_1T_2E, beam-leakage parameter, espilon_0, 143&times;217 TE;
-* bleak_epsilon_1_1T_2E, Beam leakage parameters, espilon_1, 143x217 TE
+* bleak_epsilon_1_1T_2E, beam-leakage parameter, espilon_1, 143&times;217 TE;
-* bleak_epsilon_2_1T_2E, Beam leakage parameters, espilon_2, 143x217 TE
+* bleak_epsilon_2_1T_2E, beam-leakage parameter, espilon_2, 143&times;217 TE;
-* bleak_epsilon_3_1T_2E, Beam leakage parameters, espilon_3, 143x217 TE
+* bleak_epsilon_3_1T_2E, beam-leakage parameter, espilon_3, 143&times;217 TE;
-* bleak_epsilon_4_1T_2E, Beam leakage parameters, espilon_4, 143x217 TE
+* bleak_epsilon_4_1T_2E, beam-leakage parameter, espilon_4, 143&times;217 TE;
-* bleak_epsilon_0_2T_2E, Beam leakage parameters, espilon_0, 217x217 TE
+* bleak_epsilon_0_2T_2E, beam-leakage parameter, espilon_0, 217&times;217 TE;
-* bleak_epsilon_1_2T_2E, Beam leakage parameters, espilon_1, 217x217 TE
+* bleak_epsilon_1_2T_2E, beam-leakage parameter, espilon_1, 217&times;217 TE;
-* bleak_epsilon_2_2T_2E, Beam leakage parameters, espilon_2, 217x217 TE
+* bleak_epsilon_2_2T_2E, beam-leakage parameter, espilon_2, 217&times;217 TE;
-* bleak_epsilon_3_2T_2E, Beam leakage parameters, espilon_3, 217x217 TE
+* bleak_epsilon_3_2T_2E, beam-leakage parameter, espilon_3, 217&times;217 TE;
-* bleak_epsilon_4_2T_2E, Beam leakage parameters, espilon_4, 217x217 TE
+* bleak_epsilon_4_2T_2E, beam-leakage parameter, espilon_4, 217&times;217 TE;
-* bleak_epsilon_0_0E_0E, Beam leakage parameters, espilon_0, 100x100 EE
+* bleak_epsilon_0_0E_0E, beam-leakage parameter, espilon_0, 100&times;100 EE;
-* bleak_epsilon_1_0E_0E, Beam leakage parameters, espilon_1, 100x100 EE
+* bleak_epsilon_1_0E_0E, beam-leakage parameter, espilon_1, 100&times;100 EE;
-* bleak_epsilon_2_0E_0E, Beam leakage parameters, espilon_2, 100x100 EE
+* bleak_epsilon_2_0E_0E, beam-leakage parameter, espilon_2, 100&times;100 EE;
-* bleak_epsilon_3_0E_0E, Beam leakage parameters, espilon_3, 100x100 EE
+* bleak_epsilon_3_0E_0E, beam-leakage parameter, espilon_3, 100&times;100 EE;
-* bleak_epsilon_4_0E_0E, Beam leakage parameters, espilon_4, 100x100 EE
+* bleak_epsilon_4_0E_0E, beam-leakage parameter, espilon_4, 100&times;100 EE;
-* bleak_epsilon_0_0E_1E, Beam leakage parameters, espilon_0, 100x143 EE
+* bleak_epsilon_0_0E_1E, beam-leakage parameter, espilon_0, 100&times;143 EE;
-* bleak_epsilon_1_0E_1E, Beam leakage parameters, espilon_1, 100x143 EE
+* bleak_epsilon_1_0E_1E, beam-leakage parameter, espilon_1, 100&times;143 EE;
-* bleak_epsilon_2_0E_1E, Beam leakage parameters, espilon_2, 100x143 EE
+* bleak_epsilon_2_0E_1E, beam-leakage parameter, espilon_2, 100&times;143 EE;
-* bleak_epsilon_3_0E_1E, Beam leakage parameters, espilon_3, 100x143 EE
+* bleak_epsilon_3_0E_1E, beam-leakage parameter, espilon_3, 100&times;143 EE;
-* bleak_epsilon_4_0E_1E, Beam leakage parameters, espilon_4, 100x143 EE
+* bleak_epsilon_4_0E_1E, beam-leakage parameter, espilon_4, 100&times;143 EE;
-* bleak_epsilon_0_0E_2E, Beam leakage parameters, espilon_0, 100x217 EE
+* bleak_epsilon_0_0E_2E, beam-leakage parameter, espilon_0, 100&times;217 EE;
-* bleak_epsilon_1_0E_2E, Beam leakage parameters, espilon_1, 100x217 EE
+* bleak_epsilon_1_0E_2E, beam-leakage parameter, espilon_1, 100&times;217 EE;
-* bleak_epsilon_2_0E_2E, Beam leakage parameters, espilon_2, 100x217 EE
+* bleak_epsilon_2_0E_2E, beam-leakage parameter, espilon_2, 100&times;217 EE;
-* bleak_epsilon_3_0E_2E, Beam leakage parameters, espilon_3, 100x217 EE
+* bleak_epsilon_3_0E_2E, beam-leakage parameter, espilon_3, 100&times;217 EE;
-* bleak_epsilon_4_0E_2E, Beam leakage parameters, espilon_4, 100x217 EE
+* bleak_epsilon_4_0E_2E, beam-leakage parameter, espilon_4, 100&times;217 EE;
-* bleak_epsilon_0_1E_1E, Beam leakage parameters, espilon_0, 143x143 EE
+* bleak_epsilon_0_1E_1E, beam-leakage parameter, espilon_0, 143&times;143 EE;
-* bleak_epsilon_1_1E_1E, Beam leakage parameters, espilon_1, 143x143 EE
+* bleak_epsilon_1_1E_1E, beam-leakage parameter, espilon_1, 143&times;143 EE;
-* bleak_epsilon_2_1E_1E, Beam leakage parameters, espilon_2, 143x143 EE
+* bleak_epsilon_2_1E_1E, beam-leakage parameter, espilon_2, 143&times;143 EE;
-* bleak_epsilon_3_1E_1E, Beam leakage parameters, espilon_3, 143x143 EE
+* bleak_epsilon_3_1E_1E, beam-leakage parameter, espilon_3, 143&times;143 EE;
-* bleak_epsilon_4_1E_1E, Beam leakage parameters, espilon_4, 143x143 EE
+* bleak_epsilon_4_1E_1E, beam-leakage parameter, espilon_4, 143&times;143 EE;
-* bleak_epsilon_0_1E_2E, Beam leakage parameters, espilon_0, 143x217 EE
+* bleak_epsilon_0_1E_2E, beam-leakage parameter, espilon_0, 143&times;217 EE;
-* bleak_epsilon_1_1E_2E, Beam leakage parameters, espilon_1, 143x217 EE
+* bleak_epsilon_1_1E_2E, beam-leakage parameter, espilon_1, 143&times;217 EE;
-* bleak_epsilon_2_1E_2E, Beam leakage parameters, espilon_2, 143x217 EE
+* bleak_epsilon_2_1E_2E, beam-leakage parameter, espilon_2, 143&times;217 EE;
-* bleak_epsilon_3_1E_2E, Beam leakage parameters, espilon_3, 143x217 EE
+* bleak_epsilon_3_1E_2E, beam-leakage parameter, espilon_3, 143&times;217 EE;
-* bleak_epsilon_4_1E_2E, Beam leakage parameters, espilon_4, 143x217 EE
+* bleak_epsilon_4_1E_2E, beam-leakage parameter, espilon_4, 143&times;217 EE;
-* bleak_epsilon_0_2E_2E, Beam leakage parameters, espilon_0, 217x217 EE
+* bleak_epsilon_0_2E_2E, beam-leakage parameter, espilon_0, 217&times;217 EE;
-* bleak_epsilon_1_2E_2E, Beam leakage parameters, espilon_1, 217x217 EE
+* bleak_epsilon_1_2E_2E, beam-leakage parameter, espilon_1, 217&times;217 EE;
-* bleak_epsilon_2_2E_2E, Beam leakage parameters, espilon_2, 217x217 EE
+* bleak_epsilon_2_2E_2E, beam-leakage parameter, espilon_2, 217&times;217 EE;
-* bleak_epsilon_3_2E_2E, Beam leakage parameters, espilon_3, 217x217 EE
+* bleak_epsilon_3_2E_2E, beam-leakage parameter, espilon_3, 217&times;217 EE;
-* bleak_epsilon_4_2E_2E, Beam leakage parameters, espilon_4, 217x217 EE
+* bleak_epsilon_4_2E_2E, beam-leakage parameter, espilon_4, 217&times;217 EE;
-* calib_100T, the relative calibration between the 100 and 143 TT spectra
+* calib_100T, the relative calibration between 100 and 143 TT spectra;
-* calib_217T, the relative calibration between the 217 and 143 TT spectra
+* calib_217T, the relative calibration between 217 and 143 TT spectra;
-* calib_100P, the calibration of the 100 EE spectra, This should be set to 1
+* calib_100P, the calibration of the 100 EE spectra, which should be set to 1;
-* calib_143P, the calibration of the 143 EE spectra, This should be set to 1
+* calib_143P, the calibration of the 143 EE spectra, which should be set to 1;
-* calib_217P, the calibration of the 217 EE spectra, This should be set to 1
+* calib_217P, the calibration of the 217 EE spectra, which should be set to 1;
-* A_pol, the calibration of the polarization relative to the temperature, this should be set to 1
+* A_pol, the calibration of the polarization relative to the temperature, which should be set to 1;
-* A_planck, the planck absolute calibration
+* A_planck, the Planck absolute calibration.
-We recommend using the following gaussian priors:
+We recommend using the following Gaussian priors:
-* ksz_norm + 1.6 * A_sz = 9.5 ± 3)
+* ksz_norm + 1.6 &times; A_sz = 9.5&plusmn;3.0;
-* cib_index             = -1.3
+* cib_index             = -1.3;
-* gal545_A_100          = 7±2
+* gal545_A_100          = 7&plusmn;2;
-* gal545_A_143          = 9±2
+* gal545_A_143          = 9&plusmn;2;
-* gal545_A_143_217      = 21±8.5
+* gal545_A_143_217      = 21.0&plusmn;8.5;
-* gal545_A_217          = 80±20
+* gal545_A_217          = 80&plusmn;20;
-* galf_EE_A_100         = 0.06±0.012
+* galf_EE_A_100         = 0.060&plusmn;0.012;
-* galf_EE_A_100_143     = 0.05±0.015
+* galf_EE_A_100_143     = 0.050&plusmn;0.015;
-* galf_EE_A_100_217     = 0.11±0.033
+* galf_EE_A_100_217     = 0.110&plusmn;0.033;
-* galf_EE_A_143         = 0.1±0.02
+* galf_EE_A_143         = 0.10&plusmn;0.02;
-* galf_EE_A_143_217     = 0.24±0.048
+* galf_EE_A_143_217     = 0.240&plusmn;0.048;
-* galf_EE_A_217         = 0.72±0.14
+* galf_EE_A_217         = 0.72&plusmn;0.14;
-* galf_EE_index         = -2.4
+* galf_EE_index         = -2.4;
-* galf_TE_A_100         = 0.14±0.042
+* galf_TE_A_100         = 0.140&plusmn;0.042;
-* galf_TE_A_100_143     = 0.12±0.036
+* galf_TE_A_100_143     = 0.120&plusmn;0.036;
-* galf_TE_A_100_217     = 0.3±0.09
+* galf_TE_A_100_217     = 0.30&plusmn;0.09;
-* galf_TE_A_143         = 0.24±0.072
+* galf_TE_A_143         = 0.240&plusmn;0.072;
-* galf_TE_A_143_217     = 0.6±0.018
+* galf_TE_A_143_217     = 0.60&plusmn;0.018;
-* galf_TE_A_217         = 1.8±0.54
+* galf_TE_A_217         = 1.80&plusmn;0.54;
-* galf_TE_index         = -2.4
+* galf_TE_index         = -2.4;
-* bleak_epsilon_0_0T_0E = 0
+* bleak_epsilon_0_0T_0E = 0;
-* bleak_epsilon_1_0T_0E = 0
+* bleak_epsilon_1_0T_0E = 0;
-* bleak_epsilon_2_0T_0E = 0
+* bleak_epsilon_2_0T_0E = 0;
-* bleak_epsilon_3_0T_0E = 0
+* bleak_epsilon_3_0T_0E = 0;
-* bleak_epsilon_4_0T_0E = 0
+* bleak_epsilon_4_0T_0E = 0;
-* bleak_epsilon_0_0T_1E = 0
+* bleak_epsilon_0_0T_1E = 0;
-* bleak_epsilon_1_0T_1E = 0
+* bleak_epsilon_1_0T_1E = 0;
-* bleak_epsilon_2_0T_1E = 0
+* bleak_epsilon_2_0T_1E = 0;
-* bleak_epsilon_3_0T_1E = 0
+* bleak_epsilon_3_0T_1E = 0;
-* bleak_epsilon_4_0T_1E = 0
+* bleak_epsilon_4_0T_1E = 0;
-* bleak_epsilon_0_0T_2E = 0
+* bleak_epsilon_0_0T_2E = 0;
-* bleak_epsilon_1_0T_2E = 0
+* bleak_epsilon_1_0T_2E = 0;
-* bleak_epsilon_2_0T_2E = 0
+* bleak_epsilon_2_0T_2E = 0;
-* bleak_epsilon_3_0T_2E = 0
+* bleak_epsilon_3_0T_2E = 0;
-* bleak_epsilon_4_0T_2E = 0
+* bleak_epsilon_4_0T_2E = 0;
-* bleak_epsilon_0_1T_1E = 0
+* bleak_epsilon_0_1T_1E = 0;
-* bleak_epsilon_1_1T_1E = 0
+* bleak_epsilon_1_1T_1E = 0;
-* bleak_epsilon_2_1T_1E = 0
+* bleak_epsilon_2_1T_1E = 0;
-* bleak_epsilon_3_1T_1E = 0
+* bleak_epsilon_3_1T_1E = 0;
-* bleak_epsilon_4_1T_1E = 0
+* bleak_epsilon_4_1T_1E = 0;
-* bleak_epsilon_0_1T_2E = 0
+* bleak_epsilon_0_1T_2E = 0;
-* bleak_epsilon_1_1T_2E = 0
+* bleak_epsilon_1_1T_2E = 0;
-* bleak_epsilon_2_1T_2E = 0
+* bleak_epsilon_2_1T_2E = 0;
-* bleak_epsilon_3_1T_2E = 0
+* bleak_epsilon_3_1T_2E = 0;
-* bleak_epsilon_4_1T_2E = 0
+* bleak_epsilon_4_1T_2E = 0;
-* bleak_epsilon_0_2T_2E = 0
+* bleak_epsilon_0_2T_2E = 0;
-* bleak_epsilon_1_2T_2E = 0
+* bleak_epsilon_1_2T_2E = 0;
-* bleak_epsilon_2_2T_2E = 0
+* bleak_epsilon_2_2T_2E = 0;
-* bleak_epsilon_3_2T_2E = 0
+* bleak_epsilon_3_2T_2E = 0;
-* bleak_epsilon_4_2T_2E = 0
+* bleak_epsilon_4_2T_2E = 0;
-* bleak_epsilon_0_0E_0E = 0
+* bleak_epsilon_0_0E_0E = 0;
-* bleak_epsilon_1_0E_0E = 0
+* bleak_epsilon_1_0E_0E = 0;
-* bleak_epsilon_2_0E_0E = 0
+* bleak_epsilon_2_0E_0E = 0;
-* bleak_epsilon_3_0E_0E = 0
+* bleak_epsilon_3_0E_0E = 0;
-* bleak_epsilon_4_0E_0E = 0
+* bleak_epsilon_4_0E_0E = 0;
-* bleak_epsilon_0_0E_1E = 0
+* bleak_epsilon_0_0E_1E = 0;
-* bleak_epsilon_1_0E_1E = 0
+* bleak_epsilon_1_0E_1E = 0;
-* bleak_epsilon_2_0E_1E = 0
+* bleak_epsilon_2_0E_1E = 0;
-* bleak_epsilon_3_0E_1E = 0
+* bleak_epsilon_3_0E_1E = 0;
-* bleak_epsilon_4_0E_1E = 0
+* bleak_epsilon_4_0E_1E = 0;
-* bleak_epsilon_0_0E_2E = 0
+* bleak_epsilon_0_0E_2E = 0;
-* bleak_epsilon_1_0E_2E = 0
+* bleak_epsilon_1_0E_2E = 0;
-* bleak_epsilon_2_0E_2E = 0
+* bleak_epsilon_2_0E_2E = 0;
-* bleak_epsilon_3_0E_2E = 0
+* bleak_epsilon_3_0E_2E = 0;
-* bleak_epsilon_4_0E_2E = 0
+* bleak_epsilon_4_0E_2E = 0;
-* bleak_epsilon_0_1E_1E = 0
+* bleak_epsilon_0_1E_1E = 0;
-* bleak_epsilon_1_1E_1E = 0
+* bleak_epsilon_1_1E_1E = 0;
-* bleak_epsilon_2_1E_1E = 0
+* bleak_epsilon_2_1E_1E = 0;
-* bleak_epsilon_3_1E_1E = 0
+* bleak_epsilon_3_1E_1E = 0;
-* bleak_epsilon_4_1E_1E = 0
+* bleak_epsilon_4_1E_1E = 0;
-* bleak_epsilon_0_1E_2E = 0
+* bleak_epsilon_0_1E_2E = 0;
-* bleak_epsilon_1_1E_2E = 0
+* bleak_epsilon_1_1E_2E = 0;
-* bleak_epsilon_2_1E_2E = 0
+* bleak_epsilon_2_1E_2E = 0;
-* bleak_epsilon_3_1E_2E = 0
+* bleak_epsilon_3_1E_2E = 0;
-* bleak_epsilon_4_1E_2E = 0
+* bleak_epsilon_4_1E_2E = 0;
-* bleak_epsilon_0_2E_2E = 0
+* bleak_epsilon_0_2E_2E = 0;
-* bleak_epsilon_1_2E_2E = 0
+* bleak_epsilon_1_2E_2E = 0;
-* bleak_epsilon_2_2E_2E = 0
+* bleak_epsilon_2_2E_2E = 0;
-* bleak_epsilon_3_2E_2E = 0
+* bleak_epsilon_3_2E_2E = 0;
-* bleak_epsilon_4_2E_2E = 0
+* bleak_epsilon_4_2E_2E = 0;
-* calib_100T            = 0.999±0.001
+* calib_100T            = 0.999&plusmn;0.001;
-* calib_217T            = 0.995±0.002
+* calib_217T            = 0.995&plusmn;0.002;
-* calib_100P            = 1
+* calib_100P            = 1;
-* calib_143P            = 1
+* calib_143P            = 1;
-* calib_217P            = 1
+* calib_217P            = 1;
-* A_pol                 = 1
+* A_pol                 = 1;
-* A_planck              = 1±0.0025
+* A_planck              = 1.0000&plusmn;0.0025.
+'''TT only - Plik lite'''
+This file allows for the computation of the nuisance-marginalized CMB TT likelihood in the range &#8467;=30-2508. It should not be used with the regular high-&#8467; TT or TTTEEE files.
-=====TT only - plik lite=====
-This file allows for the computation of the nuisance marginalized CMB TT likelihood in the range <math>\ell=30-2508</math>. It should not be used with the regular high ell TT  or TTTEEE files.
+''' Production process'''
-====== Production process======
+The Plik likelihood files described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT</i> spectrum, marginalized over the nuisance parameters, has been extracted from this analysis to build a high-&#8467; likelihood approximation for the
-The plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB TT spectrum, marginalized over the nuisance parameters has been extracted from this exploration to build a high ell likelihood approximation for the
 CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.
+''' Inputs: '''
+* Plik plik_dx11dr2_HM_v18_TT likelihood;
+* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.
-====== Inputs ======
+'''File name and usage'''
-* plik plik_dx11dr2_HM_v18_TT likelihood
+The high-&#8467;, Plik TT, nuisance-marginalized likelihood is distributed in
-* dust residual, CIB, tSZ, kSZ, CIBxSZ templates
+''plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik''.
-======File name and usage======
-The high ell, plik TT, nuisance marginalized likelihood is distributed in
-''plc_2.0/hi_l/plik_lite/plik_lite_v18_TT.clik''
-When used with the library, it expects a vector of parameters consisting in the
+When used with the library, this expects a vector of parameters consisting of the
-TT CMB power spectrum from <math>\ell=0</math> to <math>\ell=2508</math> (included), followed by the planck absolute calibration nuisance parameter.
+<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the Planck absolute calibration nuisance parameter.
-=====TT EE TE - plik lite=====
+'''TT EE TE - Plik lite'''
-This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range <math>\ell=30-2508</math> for temperature and <math>\ell=30-1996</math> for TE and EE. It should not be used with the regular high ell TT  or TTTEEE files.
+This file allows for the computation of the nuisance marginalized CMB joint TT, TE, EE likelihood in the range &#8467;=30-2508 for temperature and &#8467;=30-1996 for TE and EE. It should not be used with the regular high-&#8467; TT or TTTEEE files.
-====== Production process======
+''' Production process'''
-The plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB TT, TE and EE spectra, marginalized over the nuisance parameters has been extracted from this exploration to build a high ell likelihood approximation for the
+The Plik likelihood file described above have been explored using a Bayesian algorithm described in {{PlanckPapers|planck2014-a13}}. The joint posterior of the CMB <i>TT<i/>, <i>TE</i>, and <i>EE</i> spectra, marginalized over the nuisance parameters has been extracted from this analysis to build a high-&#8467 likelihood approximation for the
 CMB spectrum only. The nuisance parameters have been marginalized in the priors described above.
-====== Inputs ======
+''' Inputs: '''
-* plik plik_dx11dr2_HM_v18_TTTEEE likelihood
+* Plik plik_dx11dr2_HM_v18_TTTEEE likelihood;
-* dust residual, CIB, tSZ, kSZ, CIBxSZ templates
+* dust residual, CIB, tSZ, kSZ, and CIB&times;SZ templates.
-======File name and usage======
+'''File name and usage'''
-The high ell, plik TTTEEE, nuisance marginalized likelihood is distributed in
+The high-&#8467;, Plik TTTEEE, nuisance-marginalized likelihood is distributed in
-''plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik''
+''plc_2.0/hi_l/plik_lite/plik_lite_v18_TTTEEE.clik''.
-When used with the library, it expects a vector of parameters consisting in the
+When used with the library, this expects a vector of parameters consisting of the
-TT CMB power spectrum from <math>\ell=0</math> to <math>\ell=2508</math> (included), followed by the EE, and TE spectra (same range) and by the planck absolute calibration nuisance parameter.
+<i>TT</i> CMB power spectrum from &#8467;=0 to 2508 (inclusive), followed by the <i>EE</i>, and <i>TE</i> spectra (same range) and by the Planck absolute calibration nuisance parameter.
-==== lensing likelihoods ====
+''' Lensing likelihoods '''
-=====T only=====
+'''T only'''
-This file allows for the computation of baseline lensing likelihood, using only the
+This file allows for the computation of the baseline lensing likelihood, using only the SMICA <i>T</i>
-Temperature smica map based lensing reconstruction. Only the lensing multipole range <math>\ell=40-400</math>.
+map-based lensing reconstruction. Only the lensing multipole range &#8467;=40-400
-is used. Covariance matrix for the likelihood are based on Monte Carlo. The likelihood includes
+is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes
-the computation of model dependent correction to the  normalization and
+the computation of a model-dependent correction to the normalization and
-the N1 bias. To speed up those computation, both are performed using a linear approximation.
+the "N1 bias." To speed up those computations, both are performed using a linear approximation.
-====== Production process======
+''' Production process'''
-The smica temperature maps are filtered and correlated to reconstruct an optimal
+The SMICA <i>T</i> maps are filtered and correlated to reconstruct an optimal
-lensing reconstruction map. Biases are corrected using Monte-Carlo simulations
+lensing reconstruction map. Biases are corrected using Monte Carlo simulations
-for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB based best fit model. The power spectrum of this map is measured out of a large mask, and binned.
+for the dominant "mean field" and "N0" contribution, while the "N1" bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured out of a large mask, and binned.
 The covariance matrix of this binned spectrum is evaluated using numerical simulations.
-The model dependent corrections to the normalization and N1 biases are linearized and precomputed.
+The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.
-====== Inputs ======
+''' Inputs: '''
-* smica T CMB map
+* SMICA <i>T</i> CMB map;
-* 60% galactic mask
+* 60% Galactic mask;
-* best fit Planck CMB model
+* best-fit Planck CMB model.
-======File name and usage======
+'''File name and usage'''
-The T only  lensing likelihood is distributed in
+The T-only lensing likelihood is distributed in
-''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing''
+''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pttptt.clik_lensing''.
-When used with the library, it expects a vector of parameters consisting in the
+When used with the library, this expects a vector of parameters consisting of the
-phiphi lensing spectrum (<math>\ell=0</math> to <math>\ell=2048</math> included), followed by the
+&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the
-TT CMB power spectrum (<math>\ell=0</math> to <math>\ell=2048</math> included) and by the planck absolute calibration nuisance parameter.
+<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive) and by the Planck absolute calibration nuisance parameter.
-The TT spectrum is needed to compute the normalization and N1 corrections.
+The <i>TT</i> spectrum is needed to compute the normalization and N1 corrections.
-=====T+P=====
+'''T+P'''
-This file allows for the computation of baseline lensing likelihood, using both the
+This file allows for the computation of the baseline lensing likelihood, using both the
-Temperature and polarization smica map based lensing reconstruction. Only the lensing multipole range<math>\ell=40-400</math>.
+<i>T</i> and <i>P</i> SMICA map-based lensing reconstruction. Only the lensing multipole range&#8467;=40-400
-is used. Covariance matrix for the likelihood are based on Monte Carlo. The likelihood includes
+is used. The covariance matrix for the likelihood is based on Monte Carlos. The likelihood includes
 the computation of model dependent correction to the  normalization and
-the N1 bias. To speed up those computation, both are performed using a linear approximation.
+the N1 bias. To speed up those computations, both are performed using a linear approximation.
-====== Production process======
+''' Production process'''
-The smica temperature and polarization maps are filtered and correlated to reconstruct an optimal
+The SMICA <i>T</i> and <i>P</i> maps are filtered and correlated to reconstruct an optimal
-lensing reconstruction map. Biases are corrected using Monte-Carlo simulations
+lensing reconstruction map. Biases are corrected using Monte Carlo simulations
-for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB based best fit model. The power spectrum of this map is measured out of a large mask, and binned.
+for the dominant mean field and N0 contribution, while the N1 bias is computed using the CMB-based best-fit model. The power spectrum of this map is measured outside a large mask, and binned.
 The covariance matrix of this binned spectrum is evaluated using numerical simulations.
-The model dependent corrections to the normalization and N1 biases are linearized and precomputed.
+The model-dependent corrections to the normalization and N1 biases are linearized and precomputed.
-====== Inputs ======
+''' Inputs: '''
-* smica T and E CMB map
+* SMICA <i>T</i> and <i>E</i> CMB maps;
-* 60% galactic mask
+* 60% Galactic mask;
-* best fit Planck CMB model
+* best-fit Planck CMB model.
-======File name and usage======
+'''File name and usage'''
-The T+P only  lensing likelihood is distributed in
+The T+P-only  lensing likelihood is distributed in
-''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing''
+''plc_2.0/hi_l/lensing/smica_g30_ftl_full_pp.clik_lensing''.
-When used with the library, it expects a vector of parameters consisting in the
+When used with the library, this expects a vector of parameters consisting of the
-phiphi lensing spectrum (<math>\ell=0</math> to <math>\ell=2048</math> included), followed by the
+&phi;&phi; lensing spectrum for &#8467;=0 to 2048 (inclusive), followed by the
-TT CMB power spectrum (<math>\ell=0</math> to <math>\ell=2048</math> included), the EE and TE power spectra(same range) and by the planck absolute calibration nuisance parameter.
+<i>TT</i> CMB power spectrum for &#8467;=0 to 2048 (inclusive), the <i>EE</i> and <i>TE</i> power spectra (same range) and by the Planck absolute calibration nuisance parameter.
-The TT, EE and TE spectra are needed to compute the normalization and N1 corrections.
+The <i>TT</i>, <i>EE</i>, and <i>TE</i> spectra are needed to compute the normalization and N1 corrections.
-===Datasets - Extended data===
+'''Data sets - Extended data'''
 Four other data files are available.
-Those extend the baseline delivery by adding
+Those extend the baseline delivery by adding:
-* TE, EE and other joint high-<math>\ell</math> plik likelihoods. '''COM_Likelihood_Data-extra-plik-HM-ext.R2.00.tar.gz'''
+* TE, EE and other joint high-&#8467 Plik likelihoods, ''COM_Likelihood_Data-extra-plik-HM-ext_R2.00.tar.gz'';
-* TT and TTTEEE unbinned high-<math>\ell</math> plik likelihood. '''COM_Likelihood_Data-extra-plik-unbinned.R2.00.tar.gz'''
+* TT and TTTEEE unbinned high-&#8467 Plik likelihood, ''COM_Likelihood_Data-extra-plik-unbinned_R2.00.tar.gz'';
-* TT, TE, EE and TTTEEE plik likelihood using the detset cross spectra instead of the half mission one, and including empirical correlated noise correction for the TT spectra. '''COM_Likelihood_Data-extra-plik-DS.R2.00.tar.gz'''
+* TT, TE, EE, and TTTEEE Plik likelihood using the detset cross-spectra instead of the half-mission one, and including empirical correlated noise correction for the TT spectra, ''COM_Likelihood_Data-extra-plik-DS_R2.00.tar.gz'';
-* extended <math>\ell</math> range lensing likelihood. '''COM_Likelihood_Data-extra-lensing-ext.R2.00.tar.gz'''
+* extended &#8467 range lensing likelihood, ''COM_Likelihood_Data-extra-lensing-ext_R2.00.tar.gz''.
-Note that if this products are discussed in the Planck papers, they are not used for the baseline results.
+Note that although these products are discussed in the Planck papers, they are not used for the baseline results.
 Each file contains a '''readme.md''' description of the content and the use of the different likelihood files.
@@ Line 654: / Line 1,215: @@
 <!--
-===Likelihood===
+'''Likelihood'''
 <span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span>
 The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model.
 Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the {{PlanckPapers|planck2013-p08|1|Power spectrum & Likelihood Paper}} (for the CMB based likelihood) and in the  {{PlanckPapers|planck2013-p12|1|Lensing Paper}} (for the lensing likelihood) .
+The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute
+* one low-<math>\ell</math> temperature only likelihood (commander),
+* one low-<math>\ell</math> temperature and polarisation likelihood (lowlike), and
+* one higl-<math>\ell</math> likelihood CAMspec.
+The Commander likelihood covers the multipoles 2 to 49. It uses a semi-analytic method to sample the low-<math>\ell</math> temperature likelihood on an intermediate product of one of the component separated maps. The samples are used along with an analytical approximation of the likelihood posterior to perform the likelihood computation in the code. See {{PlanckPapers|planck2013-p08}} section 8.1 for more details.
+The ''lowlike'' likelihood covers the multipoles 2 to 32 for temperature and polarization data.  Since Planck is not releasing polarisation data at this time, the polarization map from WMAP9 is used instead. A temperature map is needed to perform the computation nevertheless, and we use here the same commander map. The likelihood is computed using a map-based approximation at low resolution and a master one at intermediate resolution, as in WMAP. The likelihood code actually calls a very slightly modified version of the WMAP9 code. This piece of the likelihood essentially provides a prior on the optical depth and has almost no other impact on cosmological parameter estimation. As such it could be replaced by a simple prior, and a user can decide to do so, which is one of the motivation to leave the three pieces of the CMB likelihood as different data packages; see {{PlanckPapers|planck2013-p08}} section 8.3 for more details. Note that the version of the WMAP code used here (code version v1.0) does not perform any test on the positive definiteness of the TT, TE, EE covariance matrices, and will return a null log likelihood in the unphysical cases where the absolute value of TE is too large. This will be corrected in a later version.
+The ''CAMspec'' likelihood covers the multipoles 50 to 2500 for temperature only. The likelihood is computed using a quadratic approximation, including mode to mode correlations that have been precomputed on a fiducial model. The likelihood uses data from the 100, 143 and 217 GHz channels. To do so it models the foreground at each frequency using the model described in the likelihood paper. Uncertainties on the relative calibration and on the beam transfer functions are included either as parametric models, or marginalized and integrated in the covariance matrix. Detailed description of the different nuisance parameters is given below. Priors are included in the likelihood on the CIB spectral index, relative calibration factors and beam error eigenmodes. See {{PlanckPapers|planck2013-p08}} section 2.1 for more details.
+The ''act/spt'' likelihood covers the multipoles 1500 to 10000 for temperature. It is described in{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}. It uses the code and data that can be retrieved from the [http://lambda.gsfc.nasa.gov/ Lambda archive] for [http://lambda.gsfc.nasa.gov/product/act/act_prod_table.cfm ACT] and [http://lambda.gsfc.nasa.gov/product/spt/spt_prod_table.cfm SPT]. It has been slightly modified to use a thermal and kinetic SZ model that matches the one used in CAMspec. As stated in{{BibCite|dun2013}}, the dust parameters a_ge and a_gs must be explored with the following priors: a_ge = 0.8 &plusmn; 0.2 and a_gs = 0.4 &plusmn; 0.2. Those priors are not included in the log likelihood computed by the code.
+The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first-order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first-order renormalization procedure. This means that the code will need both the TT and &phi;&phi; power spectrum up to &#8467; = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between &#8467; = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.
+</span>
+<span style="color:red">OUTSTANDING: description of likelihood masks </span>
+'''Production process'''
+'''Likelihood'''
+<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span>
+The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950  cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm  WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}  for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.
+Each data set comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<sup>-6</sup> or less are expected depending of the architecture.
+'''Inputs'''
+'''Likelihood'''
+; ''commander''<nowiki>:</nowiki>
+* all Planck channel maps;
+* compact source catalogues;
+* common masks;
+* beam transfer functions for all channels.
+; ''lowlike''<nowiki>:</nowiki>
+* WMAP9 likelihood data;
+* Low-<math>\ell</math> Commander map.
+; ''CAMspec''<nowiki>:</nowiki>
+* 100-, 143- and 217-GHz detector and detsets maps;
+* 857GHz channel map;
+* compact source catalogue;
+* common masks (0,1 and 3);
+* beam transfer function and error eigenmodes and covariance for 100-, 143- and 217-GHz detectors and detsets;
+* theoretical templates for the tSZ and kSZ contributions;
+* color corrections for the CIB emission for the 143- and 217-GHz detectors and detsets;
+* fiducial CMB model (bootstrapped from WMAP7 best-fit spectrum) estimated noise contribution from the half-ring maps for 100, 143 and 217 GHz.
+; ''lensing''<nowiki>:</nowiki>
+* the lensing map;
+* beam error eigenmodes and covariance for the 143- and 217-GHz channel maps;
+* fiducial CMB model (from Planck cosmological parameter best fit)
+; ''act/spt''<nowiki>:</nowiki>
+* data and code from [http://lambda.gsfc.nasa.gov/product/act/act_fulllikelihood_get.cfm here];
+* the tSZ and kSZ template are changed to match those of CAMspec.
+''' File names and Meta-data '''
+'''Likelihood'''
+<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span>
+'''Likelihood source code'''
+The source code is in the file
+: {{PLASingleFile |fileType=cosmo|name=COM_Code_Likelihood-v1.0_R1.10.tar.gz|link=COM_Code_Likelihood-v1.0_R1.10.tar.gz}} (C, f90 and python likelihood library and tools)
+'''Likelihood data packages'''
+The {{PLALikelihood|type=Data|link=data packages}} are
+: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-commander_R1.10.tar.gz | link=COM_Data_Likelihood-commander_R1.10.tar.gz}}'' (low-ell TT likelihood)
+: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lowlike_R1.10.tar.gz | link=COM_Data_Likelihood-lowlike_R1.10.tar.gz}}'' (low-ell TE,EE,BB likelihood)
+: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-CAMspec_R1.10.tar.gz | link=COM_Data_Likelihood-CAMspec_R1.10.tar.gz}}'' (high-ell TT likelihood)
+: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-actspt_R1.10.tar | link=COM_Data_Likelihood-actspt_R1.10.tar.gz}}'' (high-ell TT likelihood)
+: ''{{PLASingleFile | fileType=cosmo | name=COM_Data_Likelihood-lensing_R1.10.tar.gz | link=COM_Data_Likelihood-lensing_R1.10.tar.gz}}'' (lensing likelihood)
+Untar and unzip all files to recover the code and likelihood data. Each package comes with a README file; follow the instructions inclosed to
+build the code and use it. To compute the CMB likelihood one has to sum the log likelihood of each of the commander_v4.1_lm49.clik, lowlike_v222.clik and CAMspec_v6.2TN_2013_02_26.clik, actspt_2013_01.clik. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 5 files.
+The CMB and lensing likelihood format are different. The CMB files have the termination .clik, the lensing one .clik_lensing.  The lensing data being simpler (due to the less detailled modeling permitted by the lower signal-noise), the file is a simple ascii file containing all the data along with comments describing it, and linking the different quantities to the lensing paper. The CMB file format is more complex and must accommodate different forms of data (maps, power spectrum, distribution samples, covariance matrices...). It consists of a tree structure containing the data. At each level of the tree structure a given directory can contain array data (in the form of FITS files or ascii files for strings) and scalar data (joined in a single ascii file "_mdb").  Those files are not user modifiable and do not contain interesting meta-data for the user. Tools to manipulate those files are included in the code package as optional python tools. They are documented in the code package.
+'''Likelihood masks'''
+The masks used in the Likelihood paper {{PlanckPapers|planck2013-p08}} are found in
+{{PLASingleFile|fileType=map|name=COM_Mask_Likelihood_2048_R1.10.fits|link=COM_Mask_Likelihood_2048_R1.10.fits}}
+which contains ten masks which are written into a single ''BINTABLE'' extension of 10 columns by 50331648 rows (the number of Healpix pixels in an Nside = 2048 map).  The structure is as follows, where the column names are the names of the masks:
+{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left" width=800px
+|+ '''Likelihodd masks file data structure'''
+|- bgcolor="ffdead"
+!colspan="4" | 1. EXTNAME = 'MSK-LIKE' : Data columns
+|- bgcolor="ffdead"
+! Column Name || Data Type || Units || Description
+|-
+|CL31 || Real*4 || none || mask
+|-
+|CL39 || Real*4 || none || mask
+|-
+|CL49 || Real*4 || none || mask
+|-
+|G22 || Real*4 || none || mask
+|-
+|G35 || Real*4 || none || mask
+|-
+|G45 || Real*4 || none || mask
+|-
+|G56 || Real*4 || none || mask
+|-
+|G65 || Real*4 || none || mask
+|-
+|PS96 || Real*4 || none || mask
+|-
+|PSA82 || Real*4 || none || mask
+|-
+|- bgcolor="ffdead"
+! Keyword || Data Type || Value || Description
+|-
+|PIXTYPE ||  string || HEALPIX ||
+|-
+|COORDSYS ||  string || GALACTIC ||Coordinate system
+|-
+|ORDERING || string || NESTED  || Healpix ordering
+|-
+|NSIDE  ||   Int || 2048 || Healpix Nside
+|-
+|FIRSTPIX ||   Int*4 ||                  0 || First pixel number
+|-
+|LASTPIX ||   Int*4 || 50331647 || Last pixel number, for LFI and HFI, respectively
+|}
+-->
+'''Likelihood Masks'''
+'''General description'''
+We provide the masks for Temperature and Polarisation used to exclude the regions of strongest foreground emission in the CMB maps when computing the empirical spectra that we use to form the high-&#8467 likelihood.  The masks are provided for each frequency between 100 and 217 GHz, masking the appropriate part of the Galactic Plane and, for temperature only, the relevant population of point sources.  Note that to compute the empirical power spectrum of the maps, one should also take into account missing pixels in a particular map. This is not included in the masks we distribute.
+'''Production Process'''
+Complete production process for those masks is described in {{PlanckPapers|planck2014-a13}}.
+The temperature masks are the combination of a Galactic mask, a point source mask and (for 100Ghz and 217GHz) a CO mask. Extended objects, planets, etc are included in the point source mask.
+The polarization masks are simply the Galactic masks.
+The Galactic masks are obtained by thresholding a CMB corrected and <math>10^o</math> smoothed 353GHz map. The threshold is tuned so as to retain a given fraction of the sky, between 50% and 80%. Each mask is apodized by a <math>4^o.71</math> FWHM gaussian window function using the distance map. Special care is taken to smooth this distance map, in order to avoid strong caustics. The apodization down-weights  an effective 10% of the sky. Following {{PlanckPapers|planck2014-a13}}, the Galactic masks are named by the effective unmasked sky area G70, G60, G50 and G41.
+The point source masks are different for each frequency. They are based on the 2015 Planck catalog and cut out all the sources detected at S/N = 5 or higher in each channel. Each source is masked with a circular aperture of size 3xFWHM of that channel (i.e. 3x9.′66 at 100GHz, 3x7.′22 at 143GHz, and 3x4.′90 at 217GHz). Note that we include in the point source masks all sources above our threshold, including possible galactic ones. The mask is further apodized with a gaussian window function with FWHM=30'.
+The CO masks is used only at 100GHz and 217GHz, since there is no (strong) CO line in the 147 GHz channel. They are based on the Type 3 CO map from the Planck2013 delivery. The CO map is smoothed to 120' and a threshold is applied to mask all regions above <math>1 K_{RJ} km s^{−1}</math>. The mask is further apodized to 30'.
+Mask combinations are performed by multiplying a galactic, a point source, and possibly a CO mask together.
+The Temperature masks are named in  {{PlanckPapers|planck2014-a13}} using the capital letter T and the effective sky fraction that is left unmasked. They are produced using the following
+* 100Ghz: T66 = G70+Point source mask 100Ghz+CO mask
+* 143Ghz: T57 = G60+Point source mask 143Ghz
+* 217Ghz: T47 = G50+Point source mask 217Ghz+CO mask
+The Polarization masks are named in  {{PlanckPapers|planck2014-a13}} using the capital letter P and the effective sky fraction that is left unmasked. They are produced using the following
+* 100Ghz: P70 = G70
+* 143Ghz: P50 = G50
+* 217Ghz: P41 = G41
+'''Inputs'''
+* Galactic masks: The SMICA CMB temperature map, the 353GHz temperature map.
+* Point source masks: The Planck 2015 catalog, the FWHM of each of the frequencies.
+* CO mask: the Type 3 CO map from the Planck 2013 delivery.
+''' File names and meta-data '''
+The masks are distributed in a single tar file ''COM_Likelihood_Masks_R2.00.tar.gz''.
+The files extract to 6 files
+* temperature_100.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 100Ghz, i.e. T66
+* temperature_143.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 143Ghz, i.e. T57
+* temperature_217.fits: an nside=2048 healpix map of double precision, containing the Temperature mask used at 217Ghz, i.e. T47
+* polarization_100.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 100Ghz, i.e. P70
+* polarization_143.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 143Ghz, i.e. P50
+* polarization_217.fits: an nside=2048 healpix map of double precision, containing the Polarization mask used at 217Ghz, i.e. P41
+</div>
+</div>
+<div class="toccolours mw-collapsible mw-collapsed" style="background-color: #EEE8AA;width:80%">
+'''2013 CMB spectrum and Likelihood'''
+<div class="mw-collapsible-content">
+'''General description'''
+'''CMB spectra'''
+The Planck best-fit CMB temperature power spectrum, shown in figure below, covers the wide range of multipoles <math> \ell </math> = 2-2479. Over the multipole range <math> \ell </math> = 2–49, the power spectrum is derived from a component-separation algorithm, ''Commander'', applied to maps in the frequency range 30–353 GHz over 91% of the sky {{PlanckPapers|planck2013-p06}}. The asymmetric error bars associated to this spectrum are the 68% confidence limits and include the uncertainties due to foreground subtraction. For multipoles greater than <math>\ell=50</math>, instead, the spectrum is derived from the ''CAMspec'' likelihood {{PlanckPapers|planck2013-p08}} by optimally combining the spectra in the frequency range 100-217 GHz, and correcting them for unresolved foregrounds. Associated 1-sigma errors include beam and foreground uncertainties. Both ''Commander'' and ''CAMspec'' are described in more details in the sections below.
+[[File: mission_spectrum.png|thumb|center|700px|'''CMB spectrum. Logarithmic x-scale up to <math>\ell=50</math>, linear at higher <math>\ell</math>; all points with error bars. The red line is the Planck best-fit primordial power spectrum (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}).''']]
+'''Likelihood'''
+The likelihood code (and the data that comes with it) used to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum, together with some foreground and some instrumental parameters. The data files are built primarily from the Planck mission results, but include also some results from the WMAP-9 data release. The data files are written in a specific format that can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code is used to read the data files, and given model power spectra and nuisance parameters it computes the log likelihood of that model.
+Detailed description of the installation and usage of the likelihood code and data is provided in the package. The package includes five data files: four for the CMB likelihoods and one for the lensing likelihood. All of the likelihoods delivered are described in detail in the Power spectrum & Likelihood Paper {{PlanckPapers|planck2013-p08}}  (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood) {{PlanckPapers|planck2013-p12}}.
 The CMB full likelihood has been divided into four parts to allow using selectively different ranges of multipoles. It also reflects the fact that the mathematical approximations used for those different parts are very different, as is the underlying data. In detail, we distribute
@@ Line 674: / Line 1,437: @@
 The ''lensing'' likelihood covers the multipoles 40 to 400 using the result of the [[Specially_processed_maps | lensing reconstruction]]. It uses a quadratic approximation for the likelihood, with a covariance matrix including the marginalized contribution of the beam transfer function uncertainties, the diffuse point source correction uncertainties and the cosmological model uncertainty affecting the first order non-gaussian bias (N1). The correlation between temperature and lensing is not taken into account. Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. This means that the code will need both the TT and $\phi\phi$ power spectrum up to <math>\ell</math> = 2048 to correctly perform the integrals needed for the renormalization. Nevertheless, the code will only produce an estimate based on the data between <math>\ell</math> = 40 to 400. See {{PlanckPapers|planck2013-p12}} section 6.1 for more details.
-</span>
-<span style="color:red">OUTSTANDING: description of likelihood masks </span>
-==Production process==
-===Likelihood===
+'''Production process'''
-<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span>
+'''CMB spectra'''
+The <math>\ell</math> < 50 part of the Planck power spectrum is derived from the Commander approach, which implements Bayesian component separation in pixel space, fitting a parametric model to the data by sampling the posterior distribution for the model parameters {{PlanckPapers|planck2013-p06}}. The power spectrum at any multipole <math>\ell</math> is given as the maximum probability point for the posterior <math>C_\ell</math> distribution, marginalized over the other multipoles, and the error bars are 68% confidence level {{PlanckPapers|planck2013-p08}}.
+The <math>\ell</math> > 50 part of the CMB temperature power spectrum has been derived by the CamSpec likelihood, a code that implements a pseudo-Cl based technique, extensively described in Sec. 2 and the Appendix of {{PlanckPapers|planck2013-p08}}. Frequency spectra are computed as noise weighted averages of the cross-spectra between single detector and sets of detector maps. Mask and multipole range choices for each frequency spectrum are summarized in Table 4 of {{PlanckPapers|planck2013-p08}}. The final power spectrum is an optimal combination of the 100, 143, 143x217 and 217 GHz spectra, corrected for the best-fit unresolved foregrounds and inter-frequency calibration factors, as derived from the full likelihood analysis (cf Planck+WP+highL in Table 5 of {{PlanckPapers|planck2013-p11}}). A thorough description of the models of unresolved foregrounds is given in Sec. 3 of {{PlanckPapers|planck2013-p08}} and Sec. 4 of {{PlanckPapers|planck2013-p11}}. The spectrum covariance matrix accounts for cosmic variance and noise contributions, together with unresolved foreground and beam uncertainties. Both spectrum and associated covariance matrix are given as uniformly weighted band averages in 74 bins.
+'''Likelihood'''
 The code is based on some basic routines from the libpmc library in the [http://arxiv.org/abs/1101.0950  cosmoPMC] code. It also uses some code from the [http://lambda.gsfc.nasa.gov/product/map/dr5/likelihood_get.cfm  WMAP9 likelihood] for the lowlike likelihood and{{BibCite|dun2013}}{{BibCite|Keis2011}}{{BibCite|Reic2012}}  for the act/spt one. The rest of the code has been specifically written for the Planck data. Each likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper {{PlanckPapers|planck2013-p08}} (section 2 and 8) and in the lensing paper {{PlanckPapers|planck2013-p12}} (section 6.1). We refer the reader to those papers for full details. The data are then encapsulated into the specific file format.
 Each dataset comes with its own self check. Whenever the code is used to read a data file, a computation will be done against an included test spectrum/nuisance parameter, and the log-likelihood will be displayed along with the expected result. Difference of the order of 10<math>^{-6}</math> or less are expected depending of the architecture.
-==Inputs==
+'''Inputs'''
+'''CMB spectra'''
+; Low-l spectrum (<math>\ell < 50</math>):
+* frequency maps from 30–353 GHz
+* common mask {{PlanckPapers|planck2013-p06}}
+* compact sources catalog
+; High-l spectrum (<math>50 < \ell < 2500</math>):
+* 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 2 in {{PlanckPapers|planck2013-p08}})
+* best-fit foreground templates and inter-frequency calibration factors (Table 5 of {{PlanckPapers|planck2013-p11}})
+* Beam transfer function uncertainties {{PlanckPapers|planck2013-p03c}}
-===Likelihood===
+'''Likelihood'''
 ; ''commander'' :
@@ Line 717: / Line 1,499: @@
 * the tSZ andkSZ template are changed to match those of CAMspec
-== File names and Meta data ==
+''' File names and Meta data '''
+'''CMB spectra'''
+The CMB spectrum and its covariance matrix are distributed in a single FITS file named
+* ''{{PLASingleFile | fileType=cosmo | name=COM_PowerSpect_CMB_R1.10.fits | link=COM_PowerSpect_CMB_R1.10.fits}}''
+which contains 3 extensions
+; LOW-ELL (BINTABLE)
+: with the low ell part of the spectrum, not binned, and for l=2-49.  The table columns are
+# ''ELL'' (integer): multipole number
+# ''D_ELL'' (float): $D_l$ as described below
+# ''ERRUP'' (float): the upward uncertainty
+# ''ERRDOWN'' (float): the downward uncertainty
+; HIGH-ELL (BINTABLE)
+: with the high-ell part of the spectrum, binned into 74 bins covering <math>\langle l \rangle = 47-2419\ </math> in bins of width <math>l=31</math> (with the exception of the last 4 bins that are wider). The table columns are as follows:
+# ''ELL'' (integer): mean multipole number of bin
+# ''L_MIN'' (integer): lowest multipole of bin
+# ''L_MAX'' (integer): highest multipole of bin
+# ''D_ELL'' (float): $D_l$ as described below
+# ''ERR'' (float): the uncertainty
+; COV-MAT (IMAGE)
+: with the covariance matrix of the high-ell part of the spectrum in a 74x74 pixel image, i.e., covering the same bins as the ''HIGH-ELL'' table.
+The spectra give $D_\ell = \ell(\ell+1)C_\ell / 2\pi$ in units of $\mu\, K^2$, and the covariance matrix is in units of $\mu\, K^4$.  The spectra are shown in the figure below, in blue and red for the low- and high-<math>\ell</math> parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.
-===Likelihood===
+[[File: CMBspect.jpg|thumb|center|700px|'''CMB spectrum. Linear x-scale; error bars only at high <math>\ell</math>.''']]
-<span style="color:red"> ALL OF THE FOLLOWING IN THE LIKELIHOOD SECTION IS OLD. </span>
+'''Likelihood'''
 '''Likelihood source code'''
@@ Line 791: / Line 1,602: @@
 |}
--->
+</div>
+</div>
 == References ==

1. EXTNAME = 'MSK-LIKE' : Data columns
Column Name	Data Type	Units	Description
CL31	Real*4	none	mask
CL39	Real*4	none	mask
CL49	Real*4	none	mask
G22	Real*4	none	mask
G35	Real*4	none	mask
G45	Real*4	none	mask
G56	Real*4	none	mask
G65	Real*4	none	mask
PS96	Real*4	none	mask
PSA82	Real*4	none	mask
Keyword	Data Type	Value	Description
PIXTYPE	string	HEALPIX
COORDSYS	string	GALACTIC	Coordinate system
ORDERING	string	NESTED	Healpix ordering
NSIDE	Int	2048	Healpix Nside
FIRSTPIX	Int*4	0	First pixel number
LASTPIX	Int*4	50331647	Last pixel number, for LFI and HFI, respectively