Diapositive 1

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
Overview

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

3
Model of the microwave sky

• In real space I,Q,U T,E,B in
  Fourier space

• Data in the spherical harmonics space for X
  T,E,B

• Density matrices

• Then data read

4
Spectral matching

• Expectation-Maximization (EM) algorithm
  Dempster et al. JRSS 1977
• Set of parameters q i RS ( l ), RN ( l ), A

• Iterations
• E-step expectation of the likelihood for q i
  (gaussian prior)
• M-step maximization of the likelihood to
  compute q i1

• In this work, 10000 EM iterations are generally
  performed

Delabrouille, Cardoso Patanchon, 2003, MNRAS
5
I, Q and U sky maps simulations

• 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

• Thermal dust emission
• Power-law model
• Normalized with respect to Archeops
• 353 GHz data Ponthieu et al. AA 2005

• Galactic synchrotron emission
• Template maps
• Giardino et al. AA 2002
• Isotropic spectral index ( a -2.7 )

• White noise maps normalized to the instrumental
  noise level for each frequency

6
Priors and Planck Simulations

• Blind analysis
• q RS , RN , A
• no priors
• Blind with A(T) A(E) A(B)
• q RS , RN , A
• we suppose that emission laws are the same in
  temperature and polarization
• Semi-Blind analysis
• q 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

7
Blind separation (CMB Foregrounds Noise)

• CMB Synchrotron Dust Noise
• nside 128

CMB
BB
EE
TT
EB
TE
TB

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

8
Blind separation (CMB Foregrounds Noise) (2)
Dust
TT
EE
BB
TE
TB
EB

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

9
Blind separation (CMB Foregrounds Noise) (3)
Synchrotron
TT
BB
EE
TE
TB
EB

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

10
Mixing matrix reconstruction (arbitrary units)
Blind
n (GHz)
n (GHz)
n (GHz)
Blind, assuming T E B
n (GHz)
n (GHz)
n (GHz)
Dust
Synchrotron
CMB
11
Assuming A(T) A(E) A(B) (CMB Foregrounds
Noise)
CMB
EE
TT
BB
TB
TE
EB

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

12
Semi-blind exploration of small angular scales
(CMB Fgds Noise)
CMB

• nside 512

EE
TT
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

13
Error bars of the reconstruction
CMB only / A fixed CMB fgds / A(CMB) fixed CMB
fgds / Blind
TT
EE
BB
TB
EB
TE

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

14
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 lt 50 at 5 s
• 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
Model of the microwave sky (2)

• Example 2 frequencies, 2 components data

• Density matrix expressions

16
Formalism (2)

• Density matrices
• Then data reads

Likelihood maximization
17
Sky maps simulations

• CMB
• Spectra generated with CAMB Lewis et al. 2000
  for concordance model with WMAP Bennet et al.
  2003 with gravitational lensing

• 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 ( a -2.7 )

• White noise maps for each frequency

18
CMB power spectra

• CMB
• Spectra generated with CAMB Lewis et al. 2000
  for
• W0 1, WL 0.7, Wm 0.3, Wb 0.046
• t 0.17
• Gravitationnal lensing
• r ? 10-4, 0.7

19
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 mKCMB
  (T) and 12,3 mKCMB (E,B)
• per square pixels of side 7 arcmin and for a
  14-months Planck survey

20
Blind reconstruction of the noise at 100 GHz

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

21
Assuming A(T) A(E) A(B) (CMB Foregrounds
Noise)
Synchrotron
EE
TT
BB
TE
TB
EB

• No bias at low l in TT

22
Semi-blind exploration of small angular scales
(CMB Fgds Noise)
Dust

• nside 512

EE
TT
BB
TE
TB
EB

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

23
Semi-blind exploration of small angular scales
(CMB Fgds Noise)
Synchrotron

• nside 512

EE
TT
BB
TE
TB
EB

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

24
Reconstruction of the CMB BB modes (CMB Fgds
Noise)
A(CMB) fixed A fixed
25
Reconstruction of the CMB BB modes with SAMPAN

• Satellite prototype experiment with polarized
  bolometers at 100, 143, 217, 353 GHz
• Sensitivity 10 times better than Planck
• Simulations with CMB Dust

r 10-2
r 10-3
r 10-1