Frequency maps angular power spectra

Here will be a number of power spectra.

• For HFI, these are the auto and cross-spectra of the 13 detector (set) maps at 100, 143 and 217GHz, all masked with mask2 for ease of comparison. These are the maps used in the High-ell likelihood, although in the likelihood the cross-spectra used are obtained with different masks according to specific cross-spectra.

• For LFI, these will be at 30, 40, and 70 GHz. To Be filled by Polenta

HFI frequency maps power spectra

Outstanding:

• EFH to add the purpose of these spectra and of the associated covariance matrices, and a description of how they are obtained, including the inputs used to build them (maps, beams, mask),
• AMo to add description of FITS file with sample header.
• NB. contrary to the R1.00 (pre-)delivery, in the R1.10 final delivery each spectrum and associated covar matrix will be packaged together in a single file.

Product description

A general description of the product, including e.g. figures related to the contents (e.g. maps, tables), and some explanation of its scientific meaning. If there are scientific warnings about the use of the product (User’s caveats), they should also be given here, or at least references to other explanatory documents (papers etc).

Production process

Description of the Pipeline used to generate the product. In particular any limitations and approximations used in the data processing should be listed. Avoiding detailed descriptions of methods and referring to other parts of the ES and/or the relevant Planck papers for the details. References however should be quite detailed (i.e. it is not enough to direct the user to a paper, but the relevant section in the paper should be provided).

Inputs

A list (and brief description to the extent possible) of the input data used to generate this product (down to file names), as well as any external ancillary data sets which were used.

Related products

A description of other products that are related and share some commonalities with the product being described here. E.g. if the description is of a generic product (e.g. frequency maps), all the products falling into that type should be listed and referenced.

Meta data

A detailed description of the data format of each file, including header keywords for fits files, extension names, column names, formats….

LFI frequency maps power spectra

Product description

The angular power spectrum provides information about the distribution of power on the sky map at the various angular scales. It is especially important for CMB, because it is characterized by a number of features, most notably the acoustic peaks, that encode the dependence from cosmological parameters. Therefore, angular power spectra are the basic inputs for the Planck Likelihood Code, and for estimation of cosmological parameters in general.

For this release we have computed only temperature power spectra. Polarization is not included.

Please note that these spectra come from frequency maps. No component separation has been applied, and we have only masked Galactic Plane and detected point sources. Units are [math] \mu K^2_{CMB} [/math].

Production process

Spectra are computed using cROMAster, a implementation of the pseudo-Cl method described in Hivon et al, 2002. In addition to the original approach, our implementation allows for estimation of cross-power spectra from two or more maps (see Polenta et al, 2005, for details). The software package uses HEALPix modules for spherical harmonic transform and Cl calculation. The schematic of the estimation process is as follows:

• computing the a_lm coefficients from the input temperature map after masking Galactic Plane and point sources.
• computing the pseudo power spectrum from the alms.
• estimating the bias due to the noise power spectrum of the map from noise-only Monte Carlo simulations based on detector noise properties
• correcting for the effect of the adopted mask by computing the mode-mode coupling kernel corresponding to that mask
• deconvolving the effect due to the finite angular resolution of the telescope by using the beam window function
• deconvolving the effect due to the finite size of the pixel in the map by using a pixel window function
• binning the power spectrum from individual multipoles into bandpowers
• estimating error bars on bandpowers from signal plus noise Monte Carlo simulations, where signal simulations include only CMB anisotropies.

Inputs

• LFI Frequency Maps
• Galactic Plane and point source masks
• Beam window functions
• Monte Carlo simulations
• binning scheme

Related products

A description of other products that are related and share some commonalities with the product being described here. E.g. if the description is of a generic product (e.g. frequency maps), all the products falling into that type should be listed and referenced.

Meta data

A detailed description of the data format of each file, including header keywords for fits files, extension names, column names, formats….