The Panck high- temperature and poarization CMB power spectra and ikeihood Franz Esner on behaf of the Panck coaboration 1/12/14
Overview Updates since 213 Part 1: Power spectra Anaysis masks The Panck HFI power spectra Consistency checks and residuas Part 2: Likeihood Foreground mode Likeihood construction Verification 2
What s new More data: fu 29 months of observations, enabing further checks Improved data processing: systematics remova, caibration, beam reconstruction Improved foreground mode Larger sky-fraction used for anaysis More robust to systematics: based on haf-mission cross power spectra The 214 anaysis incudes poarization 3
The Panck high- ikeihood Exact ikeihood evauations are expensive: L(θ) exp ( 1/2 d C 1 d T ) Evauating pixe space ikeihoods takes O( 6 max) operations. We instead foow the Panck 213 approach: We use a fiducia Gaussian approximation, now generaized to incude poarization We work with a pre-compressed data vector: the empirica power spectrum coefficients 4
Masks: Temperature 1 GHz: Gaactic + point source + CO f SKY 66% 143 GHz: Gaactic + point source f SKY 57% 217 GHz: Gaactic + point source + CO f SKY 47% 5
Masks: Poarization 1 GHz: Gaactic f SKY 7% 143 GHz: Gaactic f SKY 5% 217 GHz: Gaactic f SKY 41% 6
Foreground subtracted TT power spectrum 6 5 4 D T T [µk 2 ] 3 2 1 D T T [µk 2 ] 6 3-3 -6 3 5 1 15 2 25 Preiminary resuts TT ikeihood reduced χ 2 = 1.4, 2.45σ 7
Foreground subtracted TE power spectrum Discaimer: There are unmodeed residua systematics 14 7 D T E [µk 2 ] -7-14 D T E [µk 2 ] 1-1 3 5 1 15 2 Frequency averaged spectrum reduced χ 2 = 1.4 Preiminary resuts 8
Foreground subtracted EE power spectrum Discaimer: There are unmodeed residua systematics 1 1e-5 8 C EE [µk 2 ] 6 4 2 C EE [µk 2 ] 4-4 3 5 1 15 2 Frequency averaged spectrum reduced χ 2 = 1.1 Preiminary resuts 9
Consistency check: TT frequency power spectra 6 D TT [µk 2 ] D TT [µk 2 ] D TT [µk 2 ] D TT [µk 2 ] 3 3 6 3 3 6 3 3 6 3 3 5 1 15 2 25 5 1 15 2 25 5 1 15 2 25 1x1 143x143 143x217 217x217 6 5 1 15 2 25 Preiminary resuts 1
Consistency check: poarization given temperature spectra Conditiona spectra and covariances: C P P C T T C P P,P P C T T = C P P + C P P,T T C 1 T T,T T (CT T C T T ) = C P P,P P C P P,T T C 1 T T,T T C T T,P P 15 1e-5 1 D TE [µk 2 ] 1 5 5 1 C EE [µk 2 ] 5 5 15 5 1 15 2 1 5 1 15 2 Preiminary resuts 11
Data seection for the high- ikeihood Frequency beam [arcmin] noise [µk 2 ] -range 1 GHz 9 143 GHz 7 217 GHz 5 1 143 1 217 143 217 D TT =18 b 2 =18 D TT =18 b 2 =18 D TT =18 b 2 =18 2 7 4 T: 3 12 P: 3 1 T: 3 2 P: 3 2 T: 3 25 P: 5 2 T: P: 3 1 T: P: 5 1 T: 3 25 P: 5 2 D = ( + 1)/2π C, b : beam 12
The high- ikeihood We construct a fiducia Gaussian ikeihood, using a parametric foreground mode to marginaize over (12 parameters) 217 217 1 3 D [µk 2 ] 1 2 1 1 CIB tsz ksz Σ Foregrounds CIB tsz Point source Dust CMB 1 5 1 15 2 25 13
The high- ikeihood We construct a fiducia Gaussian ikeihood, using a parametric foreground mode to marginaize over noise estimates of the data, obtained from haf-ring difference maps, corrected for bias using the difference between auto and cross spectra 14
The high- ikeihood We construct a fiducia Gaussian ikeihood, using a parametric foreground mode to marginaize over noise estimates of the data, obtained from haf-ring difference maps, corrected for bias a set of best fit power spectra at each frequency 15
The high- ikeihood We construct a fiducia Gaussian ikeihood, using a parametric foreground mode to marginaize over noise estimates of the data, obtained from haf-ring difference maps, corrected for bias a set of best fit power spectra at each frequency anaytica approximations to compute C covariance matrices Binned matrix with 23 23 eements Condition number: O(1 11 ) 16
Likeihood verification on simuations We computed cosmoogica parameters from 1 simuated HFI data sets, marginaizing over 12 foreground parameters. 17
Likeihood verification on data We checked that resuts are robust with respect to different ikeihood code impementations: Pik, Camspec, Hiipop, Mspec, Xfaster the mutipoe range used for anaysis removing individua frequency power spectra the choice of anaysis masks different foreground treatments: parametric modeing vs. map based ceaning 18
Acknowedgments CITA ICAT UNIVERSITÀ DEGLI STUDI DI MILANO ABabcdfghiejk 19
Appendix: TE frequency power spectra D TE [µk 2 ] D TE D TE D TE D TE D TE 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 5 1 15 2 1x1 1x143 1x217 143x143 143x217 217x217 Preiminary resuts 2
Appendix: EE frequency power spectra C EE [µk 2 ].1.5..5.1 1x1 C EE.5..5 1x143.1 C EE.5..5 1x217.1 C EE.5..5 143x143.1 C EE.5..5 143x217.1 C EE.5..5.1 5 1 15 2 217x217 Preiminary resuts 21
Appendix: The CMB ony ikeihood Given the data mode C = C CMB + C FG (θ), we marginaize over C FG using Gibbs samping, CMB, i+1 C C FG, i+1 P (C CMB, d) P (C FG CMB, i+1 C, d) C FG, i Preiminary resuts 22
Appendix: Dust modeing vs. dust remova Pik (bue) - Mspec (red) comparison D D CMB [µk 2 ] 1 5 1 x 1 Mspec Pik 143 x 143 143 x 217 217 x 217 5 3 D [µk 2 ] 2 1 1 2 3 5 1 15 2 5 1 15 2 5 1 15 2 5 1 15 2 Preiminary resuts 23
Appendix: Pik vs. Camspec residuas 6 D TT [µk 2 ] 3 3 1x1 D TT [µk 2 ] D TT [µk 2 ] D TT [µk 2 ] 6 3 3 6 3 3 6 3 3 6 5 1 15 2 25 5 1 15 2 25 5 1 15 2 25 pikhmv17_tt_owteb CamSpecHM_TT_owTEB 5 1 15 2 25 143x143 143x217 217x217 Preiminary resuts 24