# CMB spectrum & Likelihood Code

## Contents

## General description[edit]

### CMB spectra[edit]

TBW

### Likelihood[edit]

The likelihood code and data allow to compute the likelihood of a model that predicts the CMB power spectra, lensing power spectrum and foreground and some instrumental parameters. The data file are built from the Planck mission results, as well as the some ancillary data from the wmap9 data release. The data file are in a specific internal format and can only be read by the code. The code consists in a c/f90 library, along with some optional tools in python. The code allows to read the data files, and provided model power spectra and nuisance parameters to compute the log likelihood of the model.

Detailled description of the installation and usage of the likelihood code and data is provided in the package.

The package includes 4 data packages. 3 for the CMB likelihoods and 1 for the lensing likelihood. All of the likelihood delivered are described full in the Power spectrum & Likelihood Paper (for the CMB based likelihood) and in the Lensing Paper (for the lensing likelihood).

The CMB full likelihood has been cut in 3 different part to allow using selectivelly different range of multipoles. It also reflects the fact that the mathematical approximation used for those different part are very different, as well as the underlying data. In details, we are distributing one low-l Temperature only likelihood (commander), one low-l Temperature and Polarisation likelihood (lowlike) and one higl-l likelihood CAMspec.

The commander likelihood is covering the multipoles 2 to 49. It uses a semi-analytic method to sample the low-l 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 do the likelihood computation in the code.

The lowlike likelihood is covering the multipole 2 to 32 for Temperature and Polarization data. Planck is not releasing any polarisation data in this release. We are using here the WMAP9 polarization map which are included in the data package. A temperature map is needed to perform the computation nevertheless, and we are using 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 teh WMAP9 code. This piece of the likelihood is essentially providing 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 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.

The CAMspec likelihood is covering the multipoles 50 to 2500 for Temperature. 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 217Ghz channels. Doing so it must model the foreground in each of those frequency using a 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. Detailled description of the different nuisance parameter names and meaning is given below.

The lensing likelihood is covering the multipoles 40 to 400. It uses the result of the Lensing_map. 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). Cosmological uncertainty effects on the normalization are dealt with using a first order renormalization procedure. The correlation between Temperature power spectra and lensing one is not taken into accountThis means that even though no

## Production process[edit]

### CMB spectra[edit]

TBW

### Likelihood[edit]

Each of the likelihood file has been processed using a different and dedicated pipeline as described in the likelihood paper (P08) and in the lensing paper (P12). We refer the reader to those papers for more details.

## File names[edit]

### CMB spectra[edit]

The CMB spectrum and its covariance matrix is 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 $\langle l \rangle = 47-2419$ in bins of width $l=31$. 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 $D_l = l(l+1)C_l / 2\pi$ 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-ell parts, respectively, and with the error bars for the high-ell part only in order to avoid confusion.

### Likelihood[edit]

- source code:

* COM_Code_Likelihood-v1.0_R1.10.ext.tar.gz (C, f90 and python likelihood library and tools)

- data

* 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-lensing_R1.10.tar.gz (lensing likelihood)

Untar and unzip all files to recover the code and likelihood data. Each of the package comes with a README file describing the full package. 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. To compute the CMB+lensing likelihood, one has to sum the log likelihood of all 4 files.

### Retrieval from the Planck Legacy Archive[edit]

The Planck Legacy Archive can be accessed here:

http://www.sciops.esa.int/index.php?project=planck&page=Planck_Legacy_Archive

In order to retrieve the CMB spectra and likelihood files, one should select "Cosmology products" and look at the "CMB angular power spectra" and "Likelihood" sections. The files can be downloaded directly or through the "Shopping Basket".

Cosmic Microwave background

Flexible Image Transfer Specification