1. Component Separation of Polarized Data Application to PLANCK Jonathan Aumont J-F. Macías-Pérez, M. Tristram, D. Santos 15-09-2005

2. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Summary Component separation with polarized data method Description of the simulations – CMB + Dust + Synchrotron + Noise Component separation on Planck simulations – CMB + Noise – CMB + Foregrounds + Noise Effect of the foregrounds on the CMB reconstruction Discrimination of the tensor to scalar ratio – With Planck – With a next generation CMB polarization experiment

3. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Data model (1) Data in the spherical harmonics space for X = { T,E,B }: Example: 2 frequencies, 2 components data:

4. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Data model (2) Density matrices: Then data read: Matrix expressions:

5. Jonathan Aumont, LPSC GrenoblePolarisation 2005 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 In this work: A is fixed – semi-blind separation 5000 EM iterations [Delabrouille, Cardoso & Patanchon MNRAS 2003]

6. Jonathan Aumont, LPSC GrenoblePolarisation 2005 I, Q and U sky maps simulations White noise maps for each frequency Thermal dust emission: Power-law model Normalized with respect to Archeops 353 GHz data [Ponthieu et al. A&A 2005] (cf. M. Tristram talk) 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 WMAP [Bennett et al. ApJS 2003] with gravitational lensing I Q I Q I Q

7. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Planck separation (CMB + Noise) 200 Planck simulations (14 month survey, [30, 40, 70, 100, 143, 217, 353 GHz]), CMB + Noise, r = 0.7 n side = 128, 5000 EM iterations TT EE BB TE TB EB Separation is efficient for TT, EE, TE, TB and EB Separation of BB up to l ~ 100

8. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Planck separation (CMB + Foregrounds + Noise) (1) 200 Planck simulations, CMB + Dust + Synchrotron + Noise n side = 128, 5000 EM iterations TT EE BB TE TB EB Separation is efficient for TT, EE, TE, TB and EB Separation of BB up to l ~ 100 CMB

9. Jonathan Aumont, LPSC GrenoblePolarisation 2005 TT EE BB TE TB EB Separation is efficient for TT, EE, BB, TE, TB, and EB Dust Planck separation (CMB + Foregrounds + Noise) (2)

10. Jonathan Aumont, LPSC GrenoblePolarisation 2005 TT EE BB TE TB EB Separation is efficient for TT, EE, BB, TE, TB, and EB Synchrotron Planck separation (CMB + Foregrounds + Noise) (3)

11. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Planck separation (CMB + Foregrounds + Noise), n side = 512, r = 0.1 TT EE BB TE TT EE BB TE Separation is efficient for TT, EE, TE For CMB BB, separation up to l ~ 40

12. Jonathan Aumont, LPSC GrenoblePolarisation 2005 TT EE BB TE TB EB Error bars nearly twice larger in the case with foregrounds Bias occurs at lower l for BB in the case with foregrounds Effect of foregrounds on the recontruction of the CMB (1)

13. Jonathan Aumont, LPSC GrenoblePolarisation 2005 TT EE BB TE TB EB Larger error bars with foregrounds Differences within the error bars Effect of foregrounds on the recontruction of the CMB (2)

14. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Bias angular scale and signal to noise ratio This method allows separation for signal to noise ratios of order 10 -2 for Planck Signal to noise ratio reachable in the case of presence of foregrounds is twice larger CMB + foregrounds +noise l = 138 s/n = 7.5. 10 -3 l = 118 s/n = 1.5. 10 -2 CMB + noise

15. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Tensor to scalar ratio reachable with the Planck satellite (1) Reconstruction is possible for r ≥ 0.1, for a Planck 14 months survey r = 10 -2 r = 10 -1 r = 0.7

16. Jonathan Aumont, LPSC GrenoblePolarisation 2005 r < 0.7 cannot be caracterized by TT, EE and TE r ≥ 0.1 are reachable with BB for Planck r ~ 10 -2 may be reach with improvement of the method TT BB TE EE Tensor to scalar ratio reachable with the Planck satellite (2) CMB CMB + foregrounds

17. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Separation with the SAMPAN prototype Satellite experiment with polarized bolometers at 100, 143, 217, 353 GHz Sensitivity 10 times better than Planck Simulations with CMB + Dust r = 10 -4 r = 10 -2 r = 10 -3 r = 10 -1 For SAMPAN, r is reachable up to 10 -3

18. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Conclusions Component separation method for temperature can be applied to polarization Separation is efficient for CMB, dust and synchrotron emissions in the Planck case Foregrounds contamination reduces the sensitivity of the determination of the CMB spectra Further work needed to improve the method and to add beam and incomplete sky coverage effects [Aumont et al. in preparation] Polarized dust templates needed Planck will be able to constrain r ≥ 0.1 SAMPAN would be able to constrain r ≥ 10 -3 Further applications like detection of the primordial magnetic field [Aumont et al. in preparation]

19. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Formalism (2) Density matrices: Then data reads: Likelihood maximization Bayes Theorem: Wiener solution:

20. Jonathan Aumont, LPSC GrenoblePolarisation 2005 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

21. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Simulations (1) CMB: Spectra generated with CAMB [Lewis et al. 2000] for:      m   b   Gravitationnal lensing r  [10 -4, 0.7]

22. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Simulations (3) A matrix:

23. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Blind separation (A not fixed) A is not fixed, initial value of A is the ‘true’ A EB TB TE BB EE TT CMB spectra reconstructed roughly with the same precision

24. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Primordial magnetic field effect on the CMB At decoupling, a primordial magnetic field would affect CMB polarization by Faraday rotation. rms rotation angle [Kosowsky & Loeb 1996]: Simulations for Planck 14, 28 and 56 months surveys No foregrounds No effect on TT Weak field so effect negligeable on EE Generation of BB from EE modes depending on B 0 and 1/ 0 2

25. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Separation of primordial magnetic field effect Under our simple assumptions, Planck could detect the effect of primordial magnetic field of today intensity of order 10 nG B 0 = 10 nG B 0 = 1 nG B 0 = 5 nG

26. Jonathan Aumont, LPSC GrenoblePolarisation 2005 Residual noise estimation