# 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.

## 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

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, with the error bars for the high-ell part only in order to avoid confusion.

### Likelihood[edit]

- source code:

* plc-1.0.tar.bz2 (C, f90 and python likelihood library and tools)

- data

* commander_v4.1_lm49.clik (low-ell TT likelihood) * lowlike_v222.clik (low-ell TE,EE,BB likelihood) * CAMspec_v6.2TN_2013_02_26.clik (high-ell TT likelihood) * lensing_likelihood_v4_ref.clik_lensing (lensing likelihood)

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.

Cosmic Microwave background

Flexible Image Transfer Specification