The Planck high-l temperature and polarization CMB power spectra and likelihood

Transcription

1 The Panck high- temperature and poarization CMB power spectra and ikeihood Franz Esner on behaf of the Panck coaboration 1/12/14

2 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

3 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

4 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

5 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

6 Masks: Poarization 1 GHz: Gaactic f SKY 7% 143 GHz: Gaactic f SKY 5% 217 GHz: Gaactic f SKY 41% 6

7 Foreground subtracted TT power spectrum D T T [µk 2 ] D T T [µk 2 ] Preiminary resuts TT ikeihood reduced χ 2 = 1.4, 2.45σ 7

8 Foreground subtracted TE power spectrum Discaimer: There are unmodeed residua systematics 14 7 D T E [µk 2 ] D T E [µk 2 ] Frequency averaged spectrum reduced χ 2 = 1.4 Preiminary resuts 8

9 Foreground subtracted EE power spectrum Discaimer: There are unmodeed residua systematics 1 1e-5 8 C EE [µk 2 ] C EE [µk 2 ] Frequency averaged spectrum reduced χ 2 = 1.1 Preiminary resuts 9

10 Consistency check: TT frequency power spectra 6 D TT [µk 2 ] D TT [µk 2 ] D TT [µk 2 ] D TT [µk 2 ] x1 143x x x Preiminary resuts 1

11 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 ] C EE [µk 2 ] Preiminary resuts 11

12 Data seection for the high- ikeihood Frequency beam [arcmin] noise [µk 2 ] -range 1 GHz GHz GHz D TT =18 b 2 =18 D TT =18 b 2 =18 D TT =18 b 2 = 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

13 The high- ikeihood We construct a fiducia Gaussian ikeihood, using a parametric foreground mode to marginaize over (12 parameters) D [µk 2 ] CIB tsz ksz Σ Foregrounds CIB tsz Point source Dust CMB

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 using the difference between auto and cross spectra 14

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 15

16 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 eements Condition number: O(1 11 ) 16

17 Likeihood verification on simuations We computed cosmoogica parameters from 1 simuated HFI data sets, marginaizing over 12 foreground parameters. 17

18 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

19 Acknowedgments CITA ICAT UNIVERSITÀ DEGLI STUDI DI MILANO ABabcdfghiejk 19

20 Appendix: TE frequency power spectra D TE [µk 2 ] D TE D TE D TE D TE D TE x1 1x143 1x x x x217 Preiminary resuts 2

21 Appendix: EE frequency power spectra C EE [µk 2 ] x1 C EE x143.1 C EE x217.1 C EE x143.1 C EE x217.1 C EE x217 Preiminary resuts 21

22 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

23 Appendix: Dust modeing vs. dust remova Pik (bue) - Mspec (red) comparison D D CMB [µk 2 ] x 1 Mspec Pik 143 x x x D [µk 2 ] Preiminary resuts 23

24 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 ] pikhmv17_tt_owteb CamSpecHM_TT_owTEB x x x217 Preiminary resuts 24