CMB spectra and likelihood code
Contents
[hide]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 Dℓ = ℓ(ℓ+1)Cℓ / 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-ℓ 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-ℓ Plik likelihoods, COM_Likelihood_Data-extra-plik-ext_R3.00.tar.gz;
- TE and EE high-ℓ 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-ℓ Camspec likelihoods COM_Likelihood_Data-extra-camspec-ext_R3.00.tar.gz;
- extended ℓ 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
2013 CMB spectrum and Likelihood
References[edit]
- ↑ Jump up to: 1.01.11.2 Planck 2018 results. VI. Cosmological parameters, Planck Collaboration, 2020, A&A, 641, A6.
- ↑ Jump up to: 2.002.012.022.032.042.052.062.072.082.092.102.112.12 Planck 2018 results. V. CMB Power Spectra and Likelihoods, Planck Collaboration, 2020, A&A, 641, A5.
- ↑ Jump up to: 3.03.13.23.33.4 Planck 2018 results. IV. Diffuse component separation, Planck Collaboration, 2020, A&A, 641, A4.
- ↑ Jump up to: 4.04.14.24.3 Planck 2018 results. III. High Frequency Instrument data processing and frequency maps, Planck Collaboration, 2020, A&A, 641, A3.
- ↑ Jump up to: 5.05.15.25.3 Planck 2018 results. VIII. Lensing, Planck Collaboration, 2020, A&A, 641, A8.
- ↑ Jump up to: 6.06.16.26.36.46.5 Planck 2015 results. X. Diffuse component separation: Foreground maps, Planck Collaboration, 2016, A&A, 594, A10.
- ↑ Jump up to: 7.007.017.027.037.047.057.067.077.087.097.107.117.127.137.147.157.167.17 Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of cosmological parameters, Planck Collaboration, 2016, A&A, 594, A11.
- ↑ Jump up to: 8.08.18.28.38.48.5 Planck 2015 results. XIII. Cosmological parameters, Planck Collaboration, 2016, A&A, 594, A13.
- ↑ Jump up to: 9.009.019.029.039.049.059.069.079.089.099.109.119.12 Planck 2013 results. XV. CMB power spectra and likelihood, Planck Collaboration, 2014, A&A, 571, A15.
- Jump up ↑ Planck 2015 results. VII. High Frequency Instrument data processing: Time-ordered information and beam processing, Planck Collaboration, 2016, A&A, 594, A7.
- Jump up ↑ Planck 2015 results. XII. Full Focal Plane Simulations, Planck Collaboration, 2016, A&A, 594, A12.
- ↑ Jump up to: 12.012.1 Planck 2015 results. XV. Gravitational Lensing, Planck Collaboration, 2016, A&A, 594, A15.
- ↑ Jump up to: 13.013.113.2 Planck 2013 results. XI. Component separation, Planck Collaboration, 2014, A&A, 571, A11.
- ↑ Jump up to: 14.014.114.214.3 Planck 2013 results. XVI. Cosmological parameters, Planck Collaboration, 2014, A&A, 571, A16.
- ↑ Jump up to: 15.015.115.2 Planck 2013 results. XVII. Gravitational lensing by large-scale structure, Planck Collaboration, 2014, A&A, 571, A17.
- ↑ Jump up to: 16.016.116.2 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).
- ↑ Jump up to: 17.017.1 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).
- ↑ Jump up to: 18.018.1 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).
- Jump up ↑ Planck 2013 results. VII. HFI time response and beams, Planck Collaboration, 2014, A&A, 571, A7.
Cosmic Microwave background
(Planck) High Frequency Instrument
Planck Legacy Archive
(Planck) Low Frequency Instrument
Sunyaev-Zel'dovich
Flexible Image Transfer Specification
Full-Width-at-Half-Maximum