1. Blind Component Separation for Polarized Obseravations of the CMB Jonathan Aumont, Juan-Francisco Macias-Perez 24-03-2006 Rencontres de Moriond 2006 La Thuile, Italy

2. Jonathan Aumont, LPSC GrenobleMoriond 2006 Overview Model of the microwave sky Spectral matching algorithm extended to polarization Planck simulations Performances of the algorithm Results Conclusions

3. Jonathan Aumont, LPSC GrenobleMoriond 2006 Model of the microwave sky Data in the spherical harmonics space for X = { T,E,B }: Density matrices: Then data read: In real space: { I,Q,U } { T,E,B } in Fourier space

4. Jonathan Aumont, LPSC GrenobleMoriond 2006 Spectral matching Expectation-Maximization (EM) algorithm [Dempster et al. JRSS 1977]: Set of parameters:  i  R S  l ), R N ( l ), A } Iterations: E-step: expectation of the likelihood for  i (gaussian prior) M-step: maximization of the likelihood to compute  i+1 [Delabrouille, Cardoso & Patanchon, 2003, MNRAS] In this work, 10000 EM iterations are generally performed

5. Jonathan Aumont, LPSC GrenobleMoriond 2006 I, Q and U sky maps simulations White noise maps normalized to the instrumental noise level for each frequency Thermal dust emission: Power-law model Normalized with respect to Archeops 353 GHz data [Ponthieu et al. A&A 2005] Galactic synchrotron emission: Template maps [Giardino et al. A&A 2002]: Isotropic spectral index (  -2.7 ) CMB Spectra generated with CAMB [Lewis et al. ApJ 2000] for concordance model according to WMAP1 [Bennett et al. ApJS 2003], r = 0.7 and gravitational lensing I Q I Q I Q

6. Jonathan Aumont, LPSC GrenobleMoriond 2006 Priors and Planck Simulations Blind analysis:  { R S, R N, A } no priors Blind with A(T) = A(E) = A(B):  = { R S, R N, A } we suppose that emission laws are the same in temperature and polarization Semi-Blind analysis:  = { R S, R N, A(dust,sync) } we suppose that the CMB electromagnetic spectrum is known and we fix it Planck simulations: LFI and HFI polarized channels: [30,40,70,100,143,217,353] GHz 14 months nominal mission complete sky coverage infinite resolution no systematics

7. Jonathan Aumont, LPSC GrenobleMoriond 2006 Blind separation (CMB + Foregrounds + Noise) CMB + Synchrotron + Dust + Noise n side = 128 TT EE BB TETB EB Separation is efficient for TT, EE, TE, TB and EB No detection of BB modes Small bias in TT for l < 30 CMB

8. Jonathan Aumont, LPSC GrenobleMoriond 2006 TT EE BB TE TB EB Separation is efficient for TT, EE, BB, TE, TB, and EB Dust Blind separation (CMB + Foregrounds + Noise) (2)

9. Jonathan Aumont, LPSC GrenobleMoriond 2006 TT EE BB TE TB EB Separation is efficient for TT, EE, BB, TE, TB, and EB Small bias in TT for l < 50 Synchrotron Blind separation (CMB + Foregrounds + Noise) (3)

10. Jonathan Aumont, LPSC GrenobleMoriond 2006 Blind Blind, assuming T = E = B DustSynchrotron CMB Mixing matrix reconstruction (arbitrary units) (GHz)

11. Jonathan Aumont, LPSC GrenobleMoriond 2006 Assuming A(T) = A(E) = A(B) (CMB + Foregrounds + Noise) TT EE BB TE TB EB CMB Detection of BB modes for l < 50 No bias at low l in TT

12. Jonathan Aumont, LPSC GrenobleMoriond 2006 Semi-blind exploration of small angular scales (CMB + Fgds + Noise) TT EE BB TETB EB Reconstruction of TT, TE, TB, EB up to l ~ 1500 Reconstruction of EE up to l ~ 1200 Reconstruction of BB up to l ~ 50 CMB n side = 512

13. Jonathan Aumont, LPSC GrenobleMoriond 2006 Error bars of the reconstruction CMB only / A fixed CMB + fgds / A(CMB) fixed CMB + fgds / Blind Presence of foregrounds increases the error bars by at least a factor of 2 TT EE BB TE TB EB

14. Jonathan Aumont, LPSC GrenobleMoriond 2006 Conclusions Spectral matching algorithm extended to polarization to jointly deal with TT, EE, BB modes and also with cross power spectra TE, TB and EB We are able to separate blindly A, R N and R S, except for the CMB BB modes When we suppose A(T) = A(E) = A(B) we are able to recover CMB BB modes for l < 50 at 5  Effect of the presence of foregrounds increases the error bars of the reconstruction. Decreases by addition of priors Improvements: - beam smoothing - filtering smoothing - incomplete sky coverage effect - components with anisotropic spectral index [Aumont & Macias-Perez, 2006, submitted to MNRAS, astro-ph/0603044 ]

15. Jonathan Aumont, LPSC GrenobleMoriond 2006 Model of the microwave sky (2) Density matrix expressions: Example: 2 frequencies, 2 components data

16. Jonathan Aumont, LPSC GrenobleMoriond 2006 Formalism (2) Density matrices: Then data reads: Likelihood maximization Bayes Theorem: Wiener solution:

17. Jonathan Aumont, LPSC GrenobleMoriond 2006 Sky maps simulations Thermal dust emission: Dust power-law model [Prunet et al. 1998] : Normalized with respect to Archeops 353 GHz data [Ponthieu, …, Aumont et al. 2005] Galactic synchrotron emission: Template maps for I, Q and U [Giardino et al. 2002]: Isotropic spectral index (  -2.7 ) CMB Spectra generated with CAMB [Lewis et al. 2000] for concordance model with WMAP [Bennet et al. 2003] with gravitational lensing White noise maps for each frequency

18. Jonathan Aumont, LPSC GrenobleMoriond 2006 CMB power spectra CMB: Spectra generated with CAMB [Lewis et al. 2000] for:      m   b   Gravitationnal lensing r  [10 -4, 0.7]

19. Jonathan Aumont, LPSC GrenobleMoriond 2006 The mixing matrix, A Noise levels are relative noise levels with respect to the 143 GHz channel At this frequency, noise levels are 6,3  K CMB (T) and 12,3  K CMB (E,B) per square pixels of side 7 arcmin and for a 14-months Planck survey

20. Jonathan Aumont, LPSC GrenobleMoriond 2006 Blind reconstruction of the noise at 100 GHz Efficient reconstruction of the noise power spectra for T, E and B for n side = 512

21. Jonathan Aumont, LPSC GrenobleMoriond 2006 TT EE BB TETB EB No bias at low l in TT Synchrotron Assuming A(T) = A(E) = A(B) (CMB + Foregrounds + Noise)

22. Jonathan Aumont, LPSC GrenobleMoriond 2006 Semi-blind exploration of small angular scales (CMB + Fgds + Noise) TT EE BB TETB EB Reconstruction of TT, EE, BB, TE, TB, EB up to l ~ 1500 Dust n side = 512

23. Jonathan Aumont, LPSC GrenobleMoriond 2006 Semi-blind exploration of small angular scales (CMB + Fgds + Noise) TT EE BB TETB EB Synchrotron n side = 512 Reconstruction of TT, EE, BB, TE, TB, EB up to l ~ 1500

24. Jonathan Aumont, LPSC GrenobleMoriond 2006 Reconstruction of the CMB BB modes (CMB + Fgds + Noise) A(CMB) fixed A fixed

25. Jonathan Aumont, LPSC GrenobleMoriond 2006 Reconstruction of the CMB BB modes with SAMPAN r = 10 -3 r = 10 -2 r = 10 -1 Satellite prototype experiment with polarized bolometers at 100, 143, 217, 353 GHz Sensitivity 10 times better than Planck Simulations with CMB + Dust