Component Separation of Polarized DataApplication to PLANCK

Jonathan Aumont

J-F. Macías-Pérez, M. Tristram, D. Santos

15-09-2005

Jonathan Aumont, LPSC Grenoble Polarisation 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

Jonathan Aumont, LPSC Grenoble Polarisation 2005

Data model (1)

• Data in the spherical harmonics space for X = { T,E,B }:

• Example: 2 frequencies, 2 components data:

Jonathan Aumont, LPSC Grenoble Polarisation 2005

Data model (2)

• Density matrices:

• Then data read:

• Matrix expressions:

Jonathan Aumont, LPSC Grenoble Polarisation 2005

Spectral matching

• Expectation-Maximization (EM) algorithm [Dempster et al. JRSS 1977]:

Set of parameters: iRS l ), RN ( 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]

Jonathan Aumont, LPSC Grenoble Polarisation 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

Jonathan Aumont, LPSC Grenoble Polarisation 2005

Planck separation (CMB + Noise)

• 200 Planck simulations (14 month survey, [30, 40, 70, 100, 143, 217, 353 GHz]), CMB + Noise, r = 0.7• nside = 128, 5000 EM iterations

TT EE BB

TETB EB

• Separation is efficient for TT, EE, TE, TB and EB• Separation of BB up to l ~ 100

Jonathan Aumont, LPSC Grenoble Polarisation 2005

Planck separation (CMB + Foregrounds + Noise) (1)

• 200 Planck simulations, CMB + Dust + Synchrotron + Noise• nside = 128, 5000 EM iterations

TT EE BB

TETB EB

• Separation is efficient for TT, EE, TE, TB and EB• Separation of BB up to l ~ 100

CMB

Jonathan Aumont, LPSC Grenoble Polarisation 2005

TT EE BB

TETB

EB

• Separation is efficient for TT, EE, BB, TE, TB, and EB

DustPlanck separation (CMB + Foregrounds + Noise) (2)

Jonathan Aumont, LPSC Grenoble Polarisation 2005

TT EE BB

TE TBEB

• Separation is efficient for TT, EE, BB, TE, TB, and EB

SynchrotronPlanck separation (CMB + Foregrounds + Noise) (3)

Jonathan Aumont, LPSC Grenoble Polarisation 2005

Planck separation (CMB + Foregrounds + Noise), nside = 512, r = 0.1

TT

EE

BB

TE

TT

TT

EEEE

BBBB

TE

TE

• Separation is efficient for TT, EE, TE• For CMB BB, separation up to l ~ 40

Jonathan Aumont, LPSC Grenoble Polarisation 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)

Jonathan Aumont, LPSC Grenoble Polarisation 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)

Jonathan Aumont, LPSC Grenoble Polarisation 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 = 138s/n = 7.5 . 10-3

l = 118s/n = 1.5 . 10-2

• CMB + noise

Jonathan Aumont, LPSC Grenoble Polarisation 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 -2r = 10 -1r = 0.7

Jonathan Aumont, LPSC Grenoble Polarisation 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)

CMBCMB + foregrounds

Jonathan Aumont, LPSC Grenoble Polarisation 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

Jonathan Aumont, LPSC Grenoble Polarisation 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]