CMB spectrum & Likelihood Code

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 [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 Planck-2015-A10 . The asymmetric error bars associated to 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 Planck-2015-A11 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.

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.

TE and EE

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] = 30-1996. The data points relative to the multipole range [math] \ell [/math] = 2-29 will be released in a second moment. Analogously to the TT case, the [math] \ell\ge 30 [/math] spectrum is derived from the Plik likelihood Planck-2015-A11 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.

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.

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.

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 Planck-2015-A10. 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 Planck-2015-A10.

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 Planck-2013-XV and Planck-2015-A11. 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 and in Planck-2015-A11. 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 Planck-2015-A13). A thorough description of the models of unresolved foregrounds is given in Planck-2015-A11. 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:

1. Unbinned. TT: 2479 bandpowers ([math]\ell=30-2508[/math]); TE or EE: 1697 bandpowers ([math]\ell=30-1996[/math]).
2. 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-l spectrum ([math]\ell \lt 30[/math])

• 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 by Haslam et al. (1982)
• Commander [math]\chi^2[/math] based LM93 confidence mask Planck-2015-A10

High-l spectrum ([math]30 \le \ell \le 2508[/math])

• 100, 143, 143x217 and 217 GHz spectra and their covariance matrix (Sec. 3.3 Planck-2015-A13)
• best-fit foreground templates and inter-frequency calibration factors (Table 3 of Planck-2015-A13)
• Beam transfer function uncertainties Planck-2015-A07

File names and Meta data

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

• COM_PowerSpect_CMB_R2.nn.fits

which contains 7 BINTABLE extensions

1. TT low-ell, unbinned (TTLOLUNB)

with the low ell part of the spectrum, not binned, and for l=2-29. The table columns are

1. ELL (integer): multipole number
2. D_ELL (float): [math]D_ell[/math] as described above
3. ERRUP (float): the upward uncertainty
4. ERRDOWN (float): the downward uncertainty

2. TT high-ell, binned (TTHILBIN)

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:

1. ELL (float): mean multipole number of bin
2. L_MIN (integer): lowest multipole of bin
3. L_MAX (integer): highest multipole of bin
4. D_ELL (float): [math]D_\ell[/math] as described above
5. ERR (float): the uncertainty

3. TT high-ell unbinned (TTHILUNB)

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:

1. ELL (integer): multipole
2. D_ELL (float): [math]D_\ell[/math] as described above
3. ERR (float): the uncertainty

4. TE high-ell, binned (TEHILBIN)

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:

1. ELL (float): mean multipole number of bin
2. L_MIN (integer): lowest multipole of bin
3. L_MAX (integer): highest multipole of bin
4. D_ELL (float): [math]D_\ell[/math] as described above
5. ERR (float): the uncertainty

5. TE high-ell, unbinned (TEHILUNB)

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:

1. ELL (integer): multipole
2. D_ELL (float): [math]D_\ell[/math] as described above
3. ERR (float): the uncertainty

6. EE high-ell, binned (EEHILBIN)

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:

1. ELL (float): mean multipole number of bin
2. L_MIN (integer): lowest multipole of bin
3. L_MAX (integer): highest multipole of bin
4. D_ELL (float): [math]D_\ell[/math] as described above
5. ERR (float): the uncertainty

7. EE high-ell, unbinned (EEHILUNB)

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:

1. ELL (integer): multipole
2. D_ELL (float): [math]D_\ell[/math] as described above
3. 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.

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 CMB spectra are also given in seven simple text files, corresponding to each of the FITS file BINTABLE extensions described above.

Likelihood

PRELIMINARY TEXT VERSION. FILENAME ARE OBVIOUSLY NOT CORRECT.

As in 2013, the 2015 likelihood release consists in a code package and a few of data packages. The code compiles to a library allowing for the computation of log likelihoods for a given dataset. Each The data package contains the description (data and metadata) allowing for the computation of a single likelihood among the following

• 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 data package, one can compute the likelihood for different subsets of the planck data.

Library and tools

Description

The library consist in code written in C and f90. 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 to modify the multipole range of the TT likelihoods and reproduce the hybridization test performed in the paper is also available. 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.

Datasets

Each data set is stored in his own directory. The directory structure follows similar rules for each dataset, and stores data, template and metadata for each particular likelihood.

As in 2013, the CMB likelihood is cut into a low-ell and high-ell part. Moreover, for each of those, we distribute both a TT 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, that allow for estimate of the TT and T+P marginalized over the nuisance parameters. Combining both the low-ell and high-ell 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 and high-ell likelihood is available in Planck-2015-A11.

Similarly, in the case of lensing, we also distribute both the likelihood using either the reconstruction based on the temperature map only, or on T+P maps. Full description of the lensing likelihood is available in CITE.

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

=TT only - commander

This file allows for the computation of the CMB TT likelihood in the range [math]\ell=2-29[/math]. Using the optional tool in the code package it can be modified to cover any l range up to [math]\ell\lt 200[/math]

Production process

The likelihood is based on the result of the Commander approach which implements a Bayesian component separation in pixel space, sampling the posterior distribution of the parameter 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-ell 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 by Haslam et al. (1982)
• Commander [math]\chi^2[/math] based LM93 confidence mask Planck-2015-A10

File name and usage

The commander likelihood is distributed in commander_rc2_v1.1_l2_29_B.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) and an extra nuisance parameter consisting of the overall planck calibration.

=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.

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 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 dealt with by marginalizing over templates based on the 30GHz LFI and 353GHz HFI maps. The covariance matrix is based on 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 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 by Haslam et al. (1982)
• Commander [math]\chi^2[/math] based LM93 confidence mask Planck-2015-A10

File name and usage

The low ell TEB likelihood is distributed in 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.

High ell likelihoods

TT only - plik

This file allows for the computation of the CMB TT likelihood in the range [math]\ell=30-2508[/math]. Using the optional tool in the code package it can be modified to cover any l range in [math]29\lt \ell\lt 2509[/math].

Production process

The file contains the 100GHz, 143GHz, and 217GHz binned half mission TT cross spectra. Only the 100x100, 143x143, 143x217 and 217x217 are actually used. Masks and multipole ranges for each spectra are different and described in Planck-2015-A11. 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. The file also contains templates for the residual foreground contamination of each spectra. 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 for the effect of point sources. 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 217GHz half mission Temperature maps
• CMB cleaned (using the smica map) 353GHz map, CO emission maps, and planck catalogs for the masks.
• Planck 545GHz maps for the dust residual contamination template
• CIB, tSZ, kSZ, CIBxSZ templates

File name and usage

The high ell, plik TT likelihood is distributed in plik_dx11dr2_HM_v18_TT.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=2508[/math] (included), followed by a vector of 16 nuisance parameters. Those are, in that order

• A_cib_217, The CIB contamination at l=3000 in the 217GHz Planck map.
• cib_index, The effective slope of the CIB spectrum. This parameter should be set to -1.3
• xi_sz_cib, The szXcib cross correlation
• A_sz, the tSZ contamination at 143GHz
• ps_A_100_100, the point source contribution in 100x100
• ps_A_143_143, the point source contribution in 143x143
• ps_A_143_217, the point source contribution in 143x217
• ps_A_217_217, the point source contribution in 217x217
• ksz_norm, the ksz contamination
• gal545_A_100, the dust residual contamination at l=200 in 100x100
• gal545_A_143, the dust residual contamination at l=200 in 143x143
• gal545_A_143_217, the dust residual contamination at l=200 in 143x217
• gal545_A_217, the dust residual contamination at l=200 in 217x217
• 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

Note that when using this likelihood, the parameter cib_index must be set to -1.3, and we recommend using the following gaussian priors on the dust parameters :

• gal545_A_100, 7±2
• gal545_A_143, 9±2
• gal545_A_143_217, 21±8.5
• gal545_A_217, 80±20

and on the calibration parameters

• calib_100T, .999±0.001
• calib_217T, 0.995±0.002

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.

Production process

The file contains the 100GHz, 143GHz, and 217GHz binned half mission T and E cross spectra. In temperature, only the 100x100, 143x143, 143x217 and 217x217 are actually used, while in TE and EE all of them are. Masks and multipole ranges for each spectra are different and described in Planck-2015-A11. 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. The file also contains templates for the residual foreground contamination of each spectra. 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 for the effect of point sources. 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 217GHz half mission T+P maps
• CMB cleaned (using the smica map) 353GHz map, CO emission maps, and planck catalogs for the masks.
• Planck 545GHz and 353GHz maps for the dust residual contamination template
• CIB, tSZ, kSZ, CIBxSZ templates
• best fit CMB+fg model for the beam leakage template

File name and usage

The high ell, plik TTTEEE likelihood is distributed in plik_dx11dr2_HM_v18_TTTEEE.clik

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

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=2508[/math] (included), followed the EE and TE spectra (same range) and by a vector of 94 nuisance parameters. Those are, in that order

• A_cib_217, The CIB contamination at l=3000 in the 217GHz Planck map.
• cib_index, The effective slope of the CIB spectrum. This parameter should be set to -1.3
• xi_sz_cib, The szXcib cross correlation
• A_sz, the tSZ contamination at 143GHz
• ps_A_100_100, the point source contribution in 100x100
• ps_A_143_143, the point source contribution in 143x143
• ps_A_143_217, the point source contribution in 143x217
• ps_A_217_217, the point source contribution in 217x217
• ksz_norm, the ksz contamination
• gal545_A_100, the dust residual contamination at l=200 in 100x100TT
• gal545_A_143, the dust residual contamination at l=200 in 143x143TT
• gal545_A_143_217, the dust residual contamination at l=200 in 143x217TT
• gal545_A_217, the dust residual contamination at l=200 in 217x217TT
• galf_EE_A_100, The dust residual contamination at l=500 in 100x100EE
• galf_EE_A_100_143, The dust residual contamination at l=500 in 100x143EE
• galf_EE_A_100_217, The dust residual contamination at l=500 in 100x217EE
• galf_EE_A_143, The dust residual contamination at l=500 in 143x143EE
• galf_EE_A_143_217, The dust residual contamination at l=500 in 143x217EE
• galf_EE_A_217, The dust residual contamination at l=500 in 217x217EE
• galf_EE_index, the dust EE template slope, should be set to -2.4
• galf_TE_A_100, The dust residual contamination at l=500 in 100x100TE
• galf_TE_A_100_143, The dust residual contamination at l=500 in 100x143TE
• galf_TE_A_100_217, The dust residual contamination at l=500 in 100x217TE
• 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 143x217TE
• galf_TE_A_217, The dust residual contamination at l=500 in 217x217TE
• galf_TE_index, the dust EE template slope, should be set to -2.4
• bleak_epsilon_0_0T_0E, Beam leakage parameters, espilon_0, 100x100 TE
• bleak_epsilon_1_0T_0E, Beam leakage parameters, espilon_1, 100x100 TE
• bleak_epsilon_2_0T_0E, Beam leakage parameters, espilon_2, 100x100 TE
• bleak_epsilon_3_0T_0E, Beam leakage parameters, espilon_3, 100x100 TE
• bleak_epsilon_4_0T_0E, Beam leakage parameters, espilon_4, 100x100 TE
• bleak_epsilon_0_0T_1E, Beam leakage parameters, espilon_0, 100x143 TE
• bleak_epsilon_1_0T_1E, Beam leakage parameters, espilon_1, 100x143 TE
• bleak_epsilon_2_0T_1E, Beam leakage parameters, espilon_2, 100x143 TE
• bleak_epsilon_3_0T_1E, Beam leakage parameters, espilon_3, 100x143 TE
• bleak_epsilon_4_0T_1E, Beam leakage parameters, espilon_4, 100x143 TE
• bleak_epsilon_0_0T_2E, Beam leakage parameters, espilon_0, 100x217 TE
• bleak_epsilon_1_0T_2E, Beam leakage parameters, espilon_1, 100x217 TE
• bleak_epsilon_2_0T_2E, Beam leakage parameters, espilon_2, 100x217 TE
• bleak_epsilon_3_0T_2E, Beam leakage parameters, espilon_3, 100x217 TE
• bleak_epsilon_4_0T_2E, Beam leakage parameters, espilon_4, 100x217 TE
• bleak_epsilon_0_1T_1E, Beam leakage parameters, espilon_0, 143x143 TE
• bleak_epsilon_1_1T_1E, Beam leakage parameters, espilon_1, 143x143 TE
• bleak_epsilon_2_1T_1E, Beam leakage parameters, espilon_2, 143x143 TE
• bleak_epsilon_3_1T_1E, Beam leakage parameters, espilon_3, 143x143 TE
• bleak_epsilon_4_1T_1E, Beam leakage parameters, espilon_4, 143x143 TE
• bleak_epsilon_0_1T_2E, Beam leakage parameters, espilon_0, 143x217 TE
• bleak_epsilon_1_1T_2E, Beam leakage parameters, espilon_1, 143x217 TE
• bleak_epsilon_2_1T_2E, Beam leakage parameters, espilon_2, 143x217 TE
• bleak_epsilon_3_1T_2E, Beam leakage parameters, espilon_3, 143x217 TE
• bleak_epsilon_4_1T_2E, Beam leakage parameters, espilon_4, 143x217 TE
• bleak_epsilon_0_2T_2E, Beam leakage parameters, espilon_0, 217x217 TE
• bleak_epsilon_1_2T_2E, Beam leakage parameters, espilon_1, 217x217 TE
• bleak_epsilon_2_2T_2E, Beam leakage parameters, espilon_2, 217x217 TE
• bleak_epsilon_3_2T_2E, Beam leakage parameters, espilon_3, 217x217 TE
• bleak_epsilon_4_2T_2E, Beam leakage parameters, espilon_4, 217x217 TE
• bleak_epsilon_0_0E_0E, Beam leakage parameters, espilon_0, 100x100 EE
• bleak_epsilon_1_0E_0E, Beam leakage parameters, espilon_1, 100x100 EE
• bleak_epsilon_2_0E_0E, Beam leakage parameters, espilon_2, 100x100 EE
• bleak_epsilon_3_0E_0E, Beam leakage parameters, espilon_3, 100x100 EE
• bleak_epsilon_4_0E_0E, Beam leakage parameters, espilon_4, 100x100 EE
• bleak_epsilon_0_0E_1E, Beam leakage parameters, espilon_0, 100x143 EE
• bleak_epsilon_1_0E_1E, Beam leakage parameters, espilon_1, 100x143 EE
• bleak_epsilon_2_0E_1E, Beam leakage parameters, espilon_2, 100x143 EE
• bleak_epsilon_3_0E_1E, Beam leakage parameters, espilon_3, 100x143 EE
• bleak_epsilon_4_0E_1E, Beam leakage parameters, espilon_4, 100x143 EE
• bleak_epsilon_0_0E_2E, Beam leakage parameters, espilon_0, 100x217 EE
• bleak_epsilon_1_0E_2E, Beam leakage parameters, espilon_1, 100x217 EE
• bleak_epsilon_2_0E_2E, Beam leakage parameters, espilon_2, 100x217 EE
• bleak_epsilon_3_0E_2E, Beam leakage parameters, espilon_3, 100x217 EE
• bleak_epsilon_4_0E_2E, Beam leakage parameters, espilon_4, 100x217 EE
• bleak_epsilon_0_1E_1E, Beam leakage parameters, espilon_0, 143x143 EE
• bleak_epsilon_1_1E_1E, Beam leakage parameters, espilon_1, 143x143 EE
• bleak_epsilon_2_1E_1E, Beam leakage parameters, espilon_2, 143x143 EE
• bleak_epsilon_3_1E_1E, Beam leakage parameters, espilon_3, 143x143 EE
• bleak_epsilon_4_1E_1E, Beam leakage parameters, espilon_4, 143x143 EE
• bleak_epsilon_0_1E_2E, Beam leakage parameters, espilon_0, 143x217 EE
• bleak_epsilon_1_1E_2E, Beam leakage parameters, espilon_1, 143x217 EE
• bleak_epsilon_2_1E_2E, Beam leakage parameters, espilon_2, 143x217 EE
• bleak_epsilon_3_1E_2E, Beam leakage parameters, espilon_3, 143x217 EE
• bleak_epsilon_4_1E_2E, Beam leakage parameters, espilon_4, 143x217 EE
• bleak_epsilon_0_2E_2E, Beam leakage parameters, espilon_0, 217x217 EE
• bleak_epsilon_1_2E_2E, Beam leakage parameters, espilon_1, 217x217 EE
• bleak_epsilon_2_2E_2E, Beam leakage parameters, espilon_2, 217x217 EE
• bleak_epsilon_3_2E_2E, Beam leakage parameters, espilon_3, 217x217 EE
• bleak_epsilon_4_2E_2E, Beam leakage parameters, espilon_4, 217x217 EE
• calib_100T, the relative calibration between the 100 and 143 TT spectra
• calib_217T, the relative calibration between the 217 and 143 TT spectra
• calib_100P, the calibration of the 100 EE spectra, This should be set to 1
• calib_143P, the calibration of the 143 EE spectra, This should be set to 1
• calib_217P, the calibration of the 217 EE spectra, This should be set to 1
• A_pol, the calibration of the polarization relative to the temperature, this should be set to 1
• A_planck, the planck absolute calibration

Note that when using this likelihood, the parameter cib_index must be set to -1.3, the TE and EE dust slope to -2.4, and all the polarization related calibration (calib_xxxP and A_pol) to 1.

We recommend using the following gaussian priors on the dust parameters :

• gal545_A_100 7±2
• gal545_A_143 9±2
• gal545_A_143_217 21±8.5
• gal545_A_217 80±20
• galf_EE_A_100, 0.06±0.012
• galf_EE_A_100_143, 0.05±0.015
• galf_EE_A_100_217, 0.11±0.033
• galf_EE_A_143, 0.1±0.02
• galf_EE_A_143_217, 0.24±0.048
• galf_EE_A_217, 0.72±0.14
• galf_TE_A_100, 0.14±0.042
• galf_TE_A_100_143, 0.12±0.036
• galf_TE_A_100_217, 0.3±0.09
• galf_TE_A_143, 0.24±0.072
• galf_TE_A_143_217, 0.6±0.018
• galf_TE_A_217, 1.8±0.54

and on the T calibration parameters

• calib_100T, .999±0.001
• calib_217T, 0.995±0.002

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

The plik likelihood file described above have been explored using a Bayesian algorithm described in Planck-2015-A11. 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, CIBxSZ templates

File name and usage

The high ell, plik TT, nuisance marginalized likelihood is distributed in plik_lite_v18_TT.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=2508[/math] (included), 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 [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.

Production process

The plik likelihood file described above have been explored using a Bayesian algorithm described in Planck-2015-A11. 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 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, CIBxSZ templates

File name and usage

The high ell, plik TTTEEE, nuisance marginalized likelihood is distributed in plik_lite_v18_TTTEEE.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=2508[/math] (included), 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 baseline lensing likelihood, using only the Temperature smica map based lensing reconstruction. Only the lensing multipole range [math]\ell=40-400[/math]. is used. Covariance matrix for the likelihood are based on Monte Carlo. 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.

Production process

The smica temperature 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 smica_g30_ftl_full_pttptt.clik_lensing

When used with the library, it expects a vector of parameters consisting in the phiphi lensing spectrum ([math]\ell=0[/math] to [math]\ell=2048[/math] included), 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.

The TT spectrum is needed to compute the normalization and N1 corrections.

T+P

This file allows for the computation of baseline lensing likelihood, using both the Temperature and polarization smica map based lensing reconstruction. Only the lensing multipole range[math]\ell=40-400[/math]. is used. Covariance matrix for the likelihood are based on Monte Carlo. 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.

Production process

The smica temperature and polarization 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 and E CMB map
• 60% galactic mask
• best fit Planck CMB model

File name and usage

The T+P only lensing likelihood is distributed in smica_g30_ftl_full_pp.clik_lensing

When used with the library, it expects a vector of parameters consisting in the phiphi lensing spectrum ([math]\ell=0[/math] to [math]\ell=2048[/math] included), 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.

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