View source for Frequency maps angular power spectra

<span style="color:Red">

= HFI detset maps power spectra =
-----------------------------


<span style="color:red">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), 

It was there, but some bastard removed it.

==Product description==

<span style="color:Red">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. 

==Production process==

<span style="color:Red">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).</span>

==Inputs==
<span style="color:Red">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.</span>

==Related products==

<span style="color:Red">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.</span>

If none, please delete this section

==File names and structure==

Power spectra are provided for the auto and cross products built from the 13 detsets available at 100, 143 and 217 GHz, namely: 
* 100-ds1, 100-ds2,
* 143-ds1, 143-ds2, 143-5, 143-6, 143-7, 
* 217-ds1, 217-ds2, 217-1, 217-2, 217-3, 217-4
which makes 13*(13+1)/2 = 91 spectra.  Filenames for the auto spectra are ''HFI_PowerSPect_{detset}_Relnum.fits'' and ''HFI_PowerSPect_{detset1}x{detset2}_Relnum.fits'' for the auto- and cross-spectra, respectively.  The list of the 91 files is given below.  Each files contains 2 BINTABLE extensions:


{| border="1" cellpadding="3" cellspacing="0" align="center" style="text-align:left"
! Column Name || Data Type || Units || Description
|-
!colspan="4" style="background:#ffdead;"| 1. EXTNAME = 'POW-SPEC' : Data columns
|-
|TEMP_CL || Real*4 || microK<sub>cmb</sub><sup>2</sup> || the power spectrum
|-
|TEMP_CL_ERR || Real*4 || microK<sub>cmb</sub><sup>2</sup> || estimate of the uncertainty in the power spectrum
|-
!colspan="4"|  Keywords
|-
|LMIN  ||     Integer || 0 || First value of ''ell'' (origin 0)
|-
|LMAX ||     Integer || value || Last value of ''ell'' (origin 0)
|-
!colspan="4" style="background:#ffdead;"| 2. EXTNAME = 'PSCOVMAT' : Data columns
|-
|COVMAT || Real*4 || microK<sub>cmb</sub><sup>4</sup> || the covariance matrix
|-
!colspan="4"|  Keywords
|-
|TDIM1 || Integer || (dim1, dim2) || matrix dimensions
|}


=== Ext POW-SPEC ===

A ''BINTABLE'' extension with two columns, containing the spectrum and the estimated uncertainty on the spectrum, which is simply the diagonal of the covariance matrix.  The length of both vectors is LMAX+1, which is the number of table rows (this is also the NAXIS keyword).

===Extension PSCOVMAT ===

A BINTABLE extension for the covariance matrix.  It consists of a single column of LMAX+1 cells, each cell containing the LMAX+1 elements which make up one row of the matrix.  

===List of filenames===




 HFI_PowerSpect_100-ds1_R1.00.fits
 HFI_PowerSpect_100-ds1x100-ds2_R1.00.fits
 HFI_PowerSpect_100-ds1x143-5_R1.00.fits
 HFI_PowerSpect_100-ds1x143-6_R1.00.fits
 HFI_PowerSpect_100-ds1x143-7_R1.00.fits
 HFI_PowerSpect_100-ds1x143-ds1_R1.00.fits
 HFI_PowerSpect_100-ds1x143-ds2_R1.00.fits
 HFI_PowerSpect_100-ds1x217-1_R1.00.fits
 HFI_PowerSpect_100-ds1x217-2_R1.00.fits
 HFI_PowerSpect_100-ds1x217-3_R1.00.fits
 HFI_PowerSpect_100-ds1x217-4_R1.00.fits
 HFI_PowerSpect_100-ds1x217-ds1_R1.00.fits
 HFI_PowerSpect_100-ds1x217-ds2_R1.00.fits
 HFI_PowerSpect_100-ds2_R1.00.fits
 HFI_PowerSpect_100-ds2x143-5_R1.00.fits
 HFI_PowerSpect_100-ds2x143-6_R1.00.fits
 HFI_PowerSpect_100-ds2x143-7_R1.00.fits
 HFI_PowerSpect_100-ds2x143-ds1_R1.00.fits
 HFI_PowerSpect_100-ds2x143-ds2_R1.00.fits
 HFI_PowerSpect_100-ds2x217-1_R1.00.fits
 HFI_PowerSpect_100-ds2x217-2_R1.00.fits
 HFI_PowerSpect_100-ds2x217-3_R1.00.fits
 HFI_PowerSpect_100-ds2x217-4_R1.00.fits
 HFI_PowerSpect_100-ds2x217-ds1_R1.00.fits
 HFI_PowerSpect_100-ds2x217-ds2_R1.00.fits
 HFI_PowerSpect_143-5_R1.00.fits
 HFI_PowerSpect_143-5x143-6_R1.00.fits
 HFI_PowerSpect_143-5x143-7_R1.00.fits
 HFI_PowerSpect_143-5x217-1_R1.00.fits
 HFI_PowerSpect_143-5x217-2_R1.00.fits
 HFI_PowerSpect_143-5x217-3_R1.00.fits
 HFI_PowerSpect_143-5x217-4_R1.00.fits
 HFI_PowerSpect_143-5x217-ds1_R1.00.fits
 HFI_PowerSpect_143-5x217-ds2_R1.00.fits
 HFI_PowerSpect_143-6_R1.00.fits
 HFI_PowerSpect_143-6x143-7_R1.00.fits
 HFI_PowerSpect_143-6x217-1_R1.00.fits
 HFI_PowerSpect_143-6x217-2_R1.00.fits
 HFI_PowerSpect_143-6x217-3_R1.00.fits
 HFI_PowerSpect_143-6x217-4_R1.00.fits
 HFI_PowerSpect_143-6x217-ds1_R1.00.fits
 HFI_PowerSpect_143-6x217-ds2_R1.00.fits
 HFI_PowerSpect_143-7_R1.00.fits
 HFI_PowerSpect_143-7x217-1_R1.00.fits
 HFI_PowerSpect_143-7x217-2_R1.00.fits
 HFI_PowerSpect_143-7x217-3_R1.00.fits
 HFI_PowerSpect_143-7x217-4_R1.00.fits
 HFI_PowerSpect_143-7x217-ds1_R1.00.fits
 HFI_PowerSpect_143-7x217-ds2_R1.00.fits
 HFI_PowerSpect_143-ds1_R1.00.fits
 HFI_PowerSpect_143-ds1x143-5_R1.00.fits
 HFI_PowerSpect_143-ds1x143-6_R1.00.fits
 HFI_PowerSpect_143-ds1x143-7_R1.00.fits
 HFI_PowerSpect_143-ds1x143-ds2_R1.00.fits
 HFI_PowerSpect_143-ds1x217-1_R1.00.fits
 HFI_PowerSpect_143-ds1x217-2_R1.00.fits
 HFI_PowerSpect_143-ds1x217-3_R1.00.fits
 HFI_PowerSpect_143-ds1x217-4_R1.00.fits
 HFI_PowerSpect_143-ds1x217-ds1_R1.00.fits
 HFI_PowerSpect_143-ds1x217-ds2_R1.00.fits
 HFI_PowerSpect_143-ds2_R1.00.fits
 HFI_PowerSpect_143-ds2x143-5_R1.00.fits
 HFI_PowerSpect_143-ds2x143-6_R1.00.fits
 HFI_PowerSpect_143-ds2x143-7_R1.00.fits
 HFI_PowerSpect_143-ds2x217-1_R1.00.fits
 HFI_PowerSpect_143-ds2x217-2_R1.00.fits
 HFI_PowerSpect_143-ds2x217-3_R1.00.fits
 HFI_PowerSpect_143-ds2x217-4_R1.00.fits
 HFI_PowerSpect_143-ds2x217-ds1_R1.00.fits
 HFI_PowerSpect_143-ds2x217-ds2_R1.00.fits
 HFI_PowerSpect_217-1_R1.00.fits
 HFI_PowerSpect_217-1x217-2_R1.00.fits
 HFI_PowerSpect_217-1x217-3_R1.00.fits
 HFI_PowerSpect_217-1x217-4_R1.00.fits
 HFI_PowerSpect_217-1x217-ds1_R1.00.fits
 HFI_PowerSpect_217-1x217-ds2_R1.00.fits
 HFI_PowerSpect_217-2_R1.00.fits
 HFI_PowerSpect_217-2x217-3_R1.00.fits
 HFI_PowerSpect_217-2x217-4_R1.00.fits
 HFI_PowerSpect_217-2x217-ds1_R1.00.fits
 HFI_PowerSpect_217-2x217-ds2_R1.00.fits
 HFI_PowerSpect_217-3_R1.00.fits
 HFI_PowerSpect_217-3x217-4_R1.00.fits
 HFI_PowerSpect_217-3x217-ds1_R1.00.fits
 HFI_PowerSpect_217-3x217-ds2_R1.00.fits
 HFI_PowerSpect_217-4_R1.00.fits
 HFI_PowerSpect_217-4x217-ds1_R1.00.fits
 HFI_PowerSpect_217-4x217-ds2_R1.00.fits
 HFI_PowerSpect_217-ds1_R1.00.fits
 HFI_PowerSpect_217-ds1x217-ds2_R1.00.fits
 HFI_PowerSpect_217-ds2_R1.00.fits

= 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 [[CMB spectrum & Likelihood Code | 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 [http://adsabs.harvard.edu/abs/2002ApJ...567....2H  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 [http://adsabs.harvard.edu/abs/2005JCAP...11..001P Polenta et al, 2005,] for details). The software package uses [http://healpix.sourceforge.net/ 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==

The inputs are the following:

* [[Frequency Maps| LFI Frequency Maps]]
* Point source and galactic plane masks (the name being specified in the comment keyword in the header, see Note in ''Meta Data'' section below): 
{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"! Mask Name || 
|-
!colspan="4" | Point source masks
|-
|LFI_MASK_030-ps_2048_R1.00.fits || 
|-
|LFI_MASK_044-ps_2048_R1.00.fits || 
|-
|LFI_MASK_070-ps_2048_R1.00.fits || 
|-
!colspan="4" | Galactic plane masks
|-
|COM_MASK_gal-06_2048_R1.00.fits ||
|-
|COM_MASK_gal-07_2048_R1.00.fits ||
|}
* [[The RIMO#Beam_Window_Functions| Beam window functions]]
* Monte Carlo simulations
* binning scheme

==Related products==
<span style="color:Red">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.</span>
==File Names==

: LFI_PowerSpect_030_R1.00.fits
: LFI_PowerSpect_044_R1.00.fits
: LFI_PowerSpect_070_R1.00.fits

==Meta Data ==

The angular power spectra source list in each frequency is structured as a FITS binary table. 
The Fits extension is composed by the columns described below:


{| border="1" cellpadding="5" cellspacing="0" align="center" style="text-align:center"
|+ FITS header
|-
! Column Name || Data Type || Units || Description
|-
|L || Integer*4 || || ell parameter
|-
|TEMP_CL || Real*8 || uK<math>_{CMB}^2</math> || <math>C_l</math> (temperature) 
|-
|TEMP_CL_ERR || Real*8 || uK<math>_{CMB}^2</math> || <math>C_l</math> error
|-
|}


'''Note.-''' in the comment keyword in the header, the galactic and point source maps used to generate the angular spectra are specified (LFI_MASK_030-ps_2048_R1.00.fits and COM_MASK_gal-06_2048_R1.00.fits in the example below). Note also that, due to an oversight, the mask description related to COM_MASK_gal-xxx is wrong and should refer to the galactic mask. 

Below an example of the header. 

<pre>
XTENSION= 'BINTABLE'           /Written by IDL:  Sat Feb 16 00:44:22 2013
BITPIX  =                    8 /
NAXIS   =                    2 /Binary table
NAXIS1  =                   20 /Number of bytes per row
NAXIS2  =                  130 /Number of rows
PCOUNT  =                    0 /Random parameter count
GCOUNT  =                    1 /Group count
TFIELDS =                    3 /Number of columns
TFORM1  = '1J      '           /Integer*4 (long integer)
TTYPE1  = 'L       '           /
TFORM2  = '1D      '           /Real*8 (double precision)
TTYPE2  = 'TEMP_CL '           /
TFORM3  = '1D      '           /Real*8 (double precision)
TTYPE3  = 'TEMP_CL_ERR'        /
EXTNAME = 'POW-SPEC'           / Extension name
EXTVER  =                    1 /Extension version
DATE    = '2013-02-15'         /Creation date
TUNIT2  = 'uK_CMB^2'           /
TUNIT3  = 'uK_CMB^2'           /
FILENAME= 'LFI_PowerSpect_030_R1.00.fits' /
PROCVER = 'Dx9_delta'          /
COMMENT ---------------------------------------------
COMMENT     Original Inputs
COMMENT ---------------------------------------------
COMMENT TT_30GHz_maskCS0.60_PS30GHzdet_febecopWls
COMMENT Used Point source Mask LFI_MASK_030-ps_2048_R1.00.fits
COMMENT Used Point source Mask COM_MASK_gal-06_2048_R1.00.fits
COMMENT Used FebeCoP 30 GHz wls
END
</pre>


[[Category:Mission science products|006]]