Blind Component Separation for Polarized Obseravations of the CMB Jonathan Aumont, Juan-Francisco...

Blind Component Separation for Polarized Obseravations of the CMB

Jonathan Aumont,Juan-Francisco Macias-Perez24-03-2006

Rencontres de Moriond 2006La Thuile, Italy

Jonathan Aumont, LPSC Grenoble Moriond 2006

Overview

• Model of the microwave sky• Spectral matching algorithm extended to polarization• Planck simulations• Performances of the algorithm• Results• Conclusions

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

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

[Delabrouille, Cardoso & Patanchon, 2003, MNRAS]

• In this work, 10000 EM iterations are generally performed

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

Priors and Planck Simulations

• Blind analysis: • { RS , RN , A } • no priors

• Blind with A(T) = A(E) = A(B): • = { RS , RN , A } • we suppose that emission laws are the same in temperature and polarization

• Semi-Blind analysis: • = { RS , RN , 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

Blind separation (CMB + Foregrounds + Noise)

• CMB + Synchrotron + Dust + Noise• nside = 128

TT EE BB

TE TB EB

• Separation is efficient for TT, EE, TE, TB and EB• No detection of BB modes• Small bias in TT for l < 30

TT EE BB

TE TB EB

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

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

TT EE BB

TE TB EB

• Separation is efficient for TT, EE, BB, TE, TB, and EB• Small bias in TT for l < 50

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

Dust Synchrotron CMB

Mixing matrix reconstruction (arbitrary units)

(GHz) (GHz) (GHz)

Assuming A(T) = A(E) = A(B) (CMB + Foregrounds + Noise)

TT EE BB

TE TB EB

• Detection of BB modes for l < 50• No bias at low l in TT

Semi-blind exploration of small angular scales (CMB + Fgds + Noise)

TT EE BB

TE TB 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• nside = 512

Error bars of the reconstruction

CMB only / A fixedCMB + fgds / A(CMB) fixedCMB + fgds / Blind

• Presence of foregrounds increases the error bars by at least a factor of 2

TT EE BB

TE TB EB

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, RN and RS, 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]

Model of the microwave sky (2)

• Density matrix expressions:

• Example: 2 frequencies, 2 components data

Formalism (2)

• Density matrices:

• Then data reads:

Likelihood maximization

• Bayes Theorem:

• Wiener solution:

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

CMB power spectra

• CMB:Spectra generated with CAMB [Lewis et al. 2000] for: •

mb• • Gravitationnal lensing• r [10-4, 0.7]

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 KCMB (T) and 12,3 KCMB (E,B)per square pixels of side 7 arcmin and for a 14-months Planck survey

Blind reconstruction of the noise at 100 GHz

• Efficient reconstruction of the noise power spectra for T, E and B for nside = 512

TT EE BB

TE TB EB

• No bias at low l in TT

Synchrotron

Assuming A(T) = A(E) = A(B) (CMB + Foregrounds + Noise)

TT EE BB

TE TB EB

• Reconstruction of TT, EE, BB, TE, TB, EB up to l ~ 1500

Dust• nside = 512

TT EE BB

TE TB EB

Synchrotron• nside = 512

• Reconstruction of TT, EE, BB, TE, TB, EB up to l ~ 1500

Reconstruction of the CMB BB modes (CMB + Fgds + Noise)

A(CMB) fixedA fixed

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

Blind Component Separation for Polarized Obseravations of the CMB Jonathan Aumont, Juan-Francisco...

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