Frequency maps angular power spectra
HFI detset maps power spectra[edit]
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),
Angular power spectra of cut sky CMB dominated maps are provided to allow independant cosmological analysis.
Product description[edit]
For HFI, these are the auto and cross-spectra of the 13 detector (set) maps at 100, 143 and 217GHz, all analyzed on the same xx% of the sky for ease of comparison (see input section). 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[edit]
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).
The spectra computed up to ell=3508 using PolSpice (PolSpice reference)
are corrected from the effect of the cut sky, and from the nominal beam window function and average pixel function.
The covariance matrix only describes the statistical correlation induced by the
sample variance and cut sky,
using the formalism described in Efstathiou 2004, also sketched in the appendix
of P08 paper (likelihood), assuming the instrumental noise to be white and uniform.
Inputs[edit]
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.
The pixel mask is the so-called Galactic mask2 apodized to 2degrees, and point sources mask apodized at 30arcmin combining the sources detected by HFI at any frequency between 100 and 353GHz with the SZ and ERCSC sources catalog. Is it provided?
Related products[edit]
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.
If none, please delete this section
File names and structure[edit]
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:
Column Name | Data Type | Units | Description |
---|---|---|---|
1. EXTNAME = 'POW-SPEC' : Data columns | |||
TEMP_CL | Real*4 | microKcmb2 | the power spectrum |
TEMP_CL_ERR | Real*4 | microKcmb2 | estimate of the uncertainty in the power spectrum |
Keywords | |||
LMIN | Integer | 0 | First value of ell (origin 0) |
LMAX | Integer | value | Last value of ell (origin 0) |
2. EXTNAME = 'PSCOVMAT' : Data columns | |||
COVMAT | Real*4 | microKcmb4 | the covariance matrix |
Keywords | |||
TDIM1 | Integer | (dim1, dim2) | matrix dimensions |
Ext POW-SPEC[edit]
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[edit]
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[edit]
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[edit]
Product description[edit]
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
.Production process[edit]
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[edit]
The inputs are the following:
- 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):
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 | |||
Galactic plane masks | |||
COM_MASK_gal-06_2048_R1.00.fits | |||
COM_MASK_gal-07_2048_R1.00.fits |
- Beam window functions
- Monte Carlo simulations
- binning scheme (3 columns: central l parameter, first l, last l):
2.0 2 2 3.0 3 3 4.0 4 4 5.0 5 5 6.0 6 6 7.0 7 7 8.0 8 8 9.0 9 9 10.0 10 10 11.0 11 11 12.0 12 12 13.0 13 13 14.0 14 14 15.0 15 15 16.0 16 16 17.0 17 17 18.0 18 18 19.0 19 19 20.0 20 20 21.0 21 21 22.0 22 22 23.0 23 23 24.0 24 24 25.0 25 25 26.0 26 26 27.0 27 27 28.0 28 28 29.0 29 29 30.0 30 30 31.0 31 31 32.0 32 32 33.0 33 33 34.0 34 34 35.0 35 35 36.0 36 36 37.0 37 37 38.0 38 38 39.5 39 40 41.5 41 42 43.5 43 44 45.5 45 46 47.5 47 48 49.5 49 50 51.5 51 52 53.5 53 54 55.5 55 56 57.5 57 58 59.5 59 60 61.5 61 62 63.5 63 64 65.5 65 66 67.5 67 68 69.5 69 70 71.5 71 72 73.5 73 74 75.5 75 76 77.5 77 78 80.0 79 81 83.0 82 84 86.0 85 87 89.0 88 90 92.0 91 93 95.0 94 96 98.0 97 99 101.0 100 102 104.0 103 105 107.0 106 108 110.0 109 111 113.0 112 114 116.0 115 117 119.0 118 120 122.5 121 124 126.5 125 128 130.5 129 132 134.5 133 136 138.5 137 140 142.5 141 144 146.5 145 148 150.5 149 152 154.5 153 156 158.5 157 160 163.0 161 165 168.0 166 170 173.0 171 175 178.0 176 180 183.0 181 185 188.0 186 190 193.0 191 195 198.0 196 200 203.5 201 206 209.5 207 212 215.5 213 218 221.5 219 224 227.5 225 230 233.5 231 236 239.5 237 242 246.0 243 249 253.0 250 256 260.0 257 263 267.0 264 270 274.0 271 277 281.0 278 284 288.5 285 292 296.5 293 300 304.5 301 308 312.5 309 316 320.5 317 324 329.0 325 333 338.0 334 342 347.0 343 351 356.0 352 360 365.5 361 370 375.5 371 380 385.5 381 390 395.5 391 400 406.0 401 411 417.0 412 422 428.0 423 433 439.0 434 444 450.5 445 456 462.5 457 468 474.5 469 480 487.0 481 493 500.0 494 506 513.0 507 519 526.5 520 533 540.5 534 547 554.5 548 561 569.0 562 576 584.0 577 591 599.0 592 606 614.5 607 622 630.5 623 638 647.0 639 655 664.0 656 672 681.0 673 689 698.5 690 707 716.5 708 725 735.0 726 744 754.0 745 763 773.5 764 783 793.5 784 803 814.0 804 824 835.0 825 845 856.5 846 867 878.5 868 889 901.0 890 912 924.0 913 935 947.5 936 959 972.0 960 984 997.0 985 1009 1022.5 1010 1035 1048.5 1036 1061 1075.0 1062 1088 1102.5 1089 1116 1130.5 1117 1144 1159.0 1145 1173 1188.5 1174 1203 1219.0 1204 1234 1250.0 1235 1265 1281.5 1266 1297 1314.0 1298 1330 1347.5 1331 1364 1382.0 1365 1399 1417.5 1400 1435 1453.5 1436 1471 1490.0 1472 1508 1527.5 1509 1546 1566.0 1547 1585 1605.5 1586 1625 1646.0 1626 1666 1687.5 1667 1708 1730.0 1709 1751 1773.5 1752 1795 1818.0 1796 1840 1864.0 1841 1887 1911.5 1888 1935 1960.0 1936 1984 2009.5 1985 2034 2060.0 2035 2085 2112.0 2086 2138 2165.5 2139 2192 2220.0 2193 2247 2276.0 2248 2304 2333.5 2305 2362 2392.5 2363 2422 2453.0 2423 2483 2515.0 2484 2546 2578.5 2547 2610 2643.5 2611 2676 2710.0 2677 2743 2778.0 2744 2812 2848.0 2813 2883 2920.0 2884 2956 2993.5 2957 3030
Related products[edit]
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.
File Names[edit]
- LFI_PowerSpect_030_R1.00.fits
- LFI_PowerSpect_044_R1.00.fits
- LFI_PowerSpect_070_R1.00.fits
Meta Data[edit]
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:
Column Name | Data Type | Units | Description |
---|---|---|---|
L | Integer*4 | ell parameter | |
TEMP_CL | Real*8 | uK | (temperature) |
TEMP_CL_ERR | Real*8 | uK | 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.
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
Below an example of the header of two masks used as input: COM_MASK_gal-06_2048_R1.00.fits and LFI_MASK_030-ps_2048_R1.00.fits:
XTENSION= 'BINTABLE' / binary table extension BITPIX = 8 / 8-bit bytes NAXIS = 2 / 2-dimensional binary table NAXIS1 = 4 / width of table in bytes NAXIS2 = 50331648 / number of rows in table PCOUNT = 0 / size of special data area GCOUNT = 1 / one data group (required keyword) TFIELDS = 1 / number of fields in each row TTYPE1 = 'Mask ' / label for field 1 TFORM1 = 'E ' / data format of field: 4-byte REAL TUNIT1 = 'none ' / physical unit of field EXTNAME = '06-GalMask' DATE = '2013-02-16T11:07:42' / file creation date (YYYY-MM-DDThh:mm:ss UT) CHECKSUM= 'NaGVNZGUNaGUNYGU' / HDU checksum updated 2013-02-16T11:07:43 DATASUM = '2540860986' / data unit checksum updated 2013-02-16T11:07:43 COMMENT COMMENT *** Planck params *** COMMENT PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation ORDERING= 'NESTED ' / Pixel ordering scheme, either RING or NESTED NSIDE = 2048 / Resolution parameter for HEALPIX FIRSTPIX= 0 / First pixel # (0 based) LASTPIX = 50331647 / Last pixel # (0 based) INDXSCHM= 'IMPLICIT' / Indexing: IMPLICIT or EXPLICIT OBJECT = 'FULLSKY ' / Sky coverage, either FULLSKY or PARTIAL BAD_DATA= -1.6375E+30 COORDSYS= 'GALACTIC' FILENAME= 'COM_MASK_gal-06_2048_R1.00.fits' COMMENT --------------------------------------------------------------------- COMMENT Combined galactic mask 0.6 sky fraction COMMENT Objects used: COMMENT /sci_planck/lfi_dpc_test/ashdown/repository/masks/component_separation/d COMMENT x9/combined_mask_0.60_sky_fraction.fits COMMENT --------------------------------------------------------------------- END
XTENSION= 'BINTABLE' / binary table extension BITPIX = 8 / 8-bit bytes NAXIS = 2 / 2-dimensional binary table NAXIS1 = 4 / width of table in bytes NAXIS2 = 50331648 / number of rows in table PCOUNT = 0 / size of special data area GCOUNT = 1 / one data group (required keyword) TFIELDS = 1 / number of fields in each row TTYPE1 = 'Mask ' / label for field 1 TFORM1 = 'E ' / data format of field: 4-byte REAL TUNIT1 = 'none ' / physical unit of field EXTNAME = '030-PSMask' DATE = '2013-02-16T11:03:20' / file creation date (YYYY-MM-DDThh:mm:ss UT) CHECKSUM= 'fR7ThO7RfO7RfO7R' / HDU checksum updated 2013-02-16T11:03:21 DATASUM = '3828742620' / data unit checksum updated 2013-02-16T11:03:21 COMMENT COMMENT *** Planck params *** COMMENT PIXTYPE = 'HEALPIX ' / HEALPIX pixelisation ORDERING= 'NESTED ' / Pixel ordering scheme, either RING or NESTED NSIDE = 2048 / Resolution parameter for HEALPIX FIRSTPIX= 0 / First pixel # (0 based) LASTPIX = 50331647 / Last pixel # (0 based) INDXSCHM= 'IMPLICIT' / Indexing: IMPLICIT or EXPLICIT OBJECT = 'FULLSKY ' / Sky coverage, either FULLSKY or PARTIAL BAD_DATA= -1.6375E+30 COORDSYS= 'GALACTIC' FILENAME= 'LFI_MASK_030-ps_2048_R1.00.fits' COMMENT --------------------------------------------------------------------- COMMENT The radius of the holes is 3 times the sigma of the beam at the correspo COMMENT nding frequency and sigma is FWHM/(2*sqrt(2ln2)) COMMENT FWHM at 30GHz used = 33.158 arcmin COMMENT Objects used: COMMENT /planck/sci_ops1/LFI_MAPs/DX9_Delta/MASKs/mask_ps_30GHz_beam33amin_nside COMMENT 2048.00_DX9_nonblind_holesize3.fits COMMENT --------------------------------------------------------------------- END
(Planck) High Frequency Instrument
Cosmic Microwave background
Sunyaev-Zel'dovich
Early Release Compact Source Catalog
(Planck) Low Frequency Instrument
Flexible Image Transfer Specification
Full-Width-at-Half-Maximum