Systematic effects Systematic effects in CMB data of in CMB data of

ESA’s satellite PlanckESA’s satellite Planck

Tarun Souradeep (IUCAA, Pune)

& Francois Bouchet (IAP, Paris)

CEFIPRA mid-term presentation (Mussoorie, Oct. 27, 2007)

Quantum fluctuations

super adiabatic amplified by

inflation (rapid expansio

n)

Galaxy & Large sc

ale

Structure fo

rmation

Via gravitational insta

bility

Early Universe

Present Universe

The Cosmic screen

Cosmic Microwave backgroundCosmic Microwave background

George SmootJohn Mather

COBE

Cosmic Background Explorer

First detection of CMB

anisotropy (1992)

2003 Second NASA CMB Satellite mission

First NASA CMB Satellite mission

-200 K < T < 200 KTrms ¼ 70 K

CMB temperature Tcmb = 2.725 K

Saha et al 2006

WMAP map of CMB anisotropy

Hence, a powerful tool for constraining cosmological parameters.

Fig. M. White 1997

The Angular power spectrum of CMB anisotropy dependssensitively on Cosmological parameters

lC

Multi-parameter Joint likelihood (MCMC)

NASA/WMAP science team

Total energy density

Baryonic matter density

Dawn of Precision cosmology !!

Dark energy density

Good old Cosmology, … New trend !

Underlying statistics: Gaussian

Power spectrum : ‘Nearly’ Scale invariant /scale free form

Spin characteristics: (Scalar) Density perturbations

Type of scalar perturbation: Adiabatic -- no entropy fluctuations

The nature of initial/primordial perturbations

The Background universe Homogeneous & isotropic space: Cosmological principle

Flat (Euclidean) Geometry … but global topology?

… but are there features ?

… cosmic (Tensor) Gravity waves ?

Early Universe in CMB

CMB Task force report 2005

Timeline of CMB researchWMAP-1yr

nowWMAP-3yr

WMAP-8yrPlanck (ESA)

Next Gen. spaceCMBPOL/Sampan

Angular power spectrum

estimation : Evading modeling

systematics in foreground removal

1. CMB anisotropy power spectrum using linear combinations of WMAP maps Authors: Rajib Saha, Simon Prunet, Pankaj Jain, Tarun Souradeep Submitted to Phys. Rev D. (under review) arXiv:0706.3567

2. Angular power spectrum of CMB anisotropy from WMAP Authors: Tarun Souradeep (IUCAA), Rajib Saha (IITK, IUCAA), Pankaj Jain (IITK) New Astron.Rev. 50 (2006) 854-860

3. A re-analysis of the 3-year WMAP temperature power spectrum & likelihood Authors: (IUCAA+IITK )+ 4 international groups (JPL, Oslo, UIUC,UCDavis)Astrophys.J. 656 (2007) 641-652

1 DA 2 DA

1 DA

2 DA4 DA

WMAP multi-frequency maps

Template Based foreground removal

Haslam 408GHz MapFDS Dust Map at 3000 Ghz

extrpolated to 94GHz

Subtract the best fit Galactic foreground templates from CMB maps

Frequency (in GHz)

IIT Kanpur + IUCAA

Independent, self contained analysis of WMAP multi-frequency maps Blind estimation - free of uncertainties in knowledge & model of foregrounds

Saha, Jain, Souradeep(WMAP1: Apj Lett 2006)

WMAP3 : Eriksen et al. ApJ. 2006 (5 international groups)

Estimate foreground cleanedWMAP

Polarization maps & powerSpectra (Indo-French Collab.)

WMAP power spectrum estimate

Study Biases in the Cl estimation:

Foreground induced at low multipoles

(ongoing: Rajib Saha, Simon Prunet, P. Jain,TS)

Bias: -( 1)2 1

Sl

c

Cn

l

Controlling other SystematicsNon-circular beam effect in CMB measurements

(S. Mitra, A. Sengupta, Souradeep, PRD 2004)WMAP Q beam Eccentricity =0.7

Close to the corrections in the WMAP 2nd data

release

(Hinshaw et al. 2006)

Bias Matrix

ll

ll lAC C

Status of ongoing projectsStatus of ongoing projects

• AAll’ll’ for NC beam + incomplete/weighted sky for NC beam + incomplete/weighted sky Mitra, Sengupta, Ray, Saha, & TS

(arXiv:astro-ph/0702100 Phys. Rev. D submitted)

• Fast implementation of Fast implementation of AAll’ll’ computation computation

Mitra, Sengupta, Ray, Prunet & TS : in progress

• NC beam deconvolution at map-makingNC beam deconvolution at map-making Basak, Prunet, Bouchet & TS : in progress

• NC beam effect in Weak lensing of CMBNC beam effect in Weak lensing of CMB Aich, Basak, Benabed & TS : in progress

Planck Surveyor SatelliteEuropean Space Agency: Launch Aug. 2008

Francois Bouchet : Deputy PI of Planck-HFI +Simon Prunet, Karim Benabed : members of core

team

30 GHz 44 GHz 70 GHz

100 GHz 143 GHz 217 GHz

353 GHz 545 GHz 857 GHz

CMB Maps at the NINE Planck Frequencies

30Ghz 44Ghz

77Ghz 100Ghz

143Ghz 217Ghz

Combination of

Planck Channel maps(work in progress)

(R. Saha, T. Ghosh, P. Jain , TS

S. Prunet, F. Bouchet )

Input Simulated CMB map(in k unit)

Recovered foreground cleaned map(in mk unit)

Expected performance for Planck

Expected performance for Planck

(R. Saha, T. Ghosh, P. Jain , TS

S. Prunet, F. Bouchet )

Thompson scattering at redshift z=1100 (surface of last scattering)

generates a linear polarization pattern in the CMB sky.

CMB Polarization

Two polarization modes E&B

Four CMB spectra : ClTT, Cl

EE,ClBB,Cl

TE

(ongoing: Rajib Saha, Simon Prunet, P. Jain,TS)

WMAP CMB Polarization challenge

(ongoing: Rajib Saha, Simon Prunet, P. Jain,TS)

WMAP CMB Polarization challenge

100% WMAP noise10% WMAP noise1% WMAP noise

Related Publications (2006-07)

1. CMB anisotropy power spectrum using linear combinations of WMAP maps Authors: Rajib Saha, Simon Prunet, Pankaj Jain, Tarun Souradeep Journal ref: Submitted to Phys. Rev D. (under review) arXiv:0706.3567

2. Angular power spectrum of CMB anisotropy from WMAP Authors: Tarun Souradeep (IUCAA), Rajib Saha (IITK, IUCAA), Pankaj Jain (IITK) Journal ref: New Astron.Rev. 50 (2006) 854-860

3. CMB power spectrum estimation with non-circular beam and incomplete sky coverage

Authors: Sanjit Mitra (IUCAA), Anand S. Sengupta (Cardiff), Subharthi Ray (IUCAA), Rajib Saha (IITK, IUCAA), Tarun Souradeep (IUCAA)

Journal ref: Submitted to Phys. Rev D. (under review) arXiv:astro-ph/0702100

4. Non-Circular beam correction to the CMB power spectrum Authors: Tarun Souradeep (IUCAA), Sanjit Mitra (IUCAA), Anand Sengupta (Cardiff),

Subharthi Ray (IUCAA), Rajib Saha (IITK, IUCAA) Journal ref: New Astron.Rev. 50 (2006) 1030-1035 5. A re-analysis of the three-year WMAP temperature power spectrum and likelihood Authors: H. K. Eriksen, Greg Huey, R. Saha, F. K. Hansen, J. Dick, A. J. Banday, K. M. Gorski, P. Jain, J. B. Jewell, L. Knox, D. L. Larson, I. J. O'Dwyer, T. Souradeep, B. D. Wandelt Journal ref: Astrophys.J. 656 (2007) 641-652

Researchers

Exchange visits

Equipment

DL 320s NAS server

• HP Proliant DL320s storage server 3TB SATA Model. Intel Dual core 3070 Xeon processor

• 2.67 Ghz / 1067 Mhz FSB standard - 4 MB L2 Cache / 1 GB / hardware RAID/ 12 x 250

• GB SATA Drives/ Windows Storage Server 2003 R2 standard edition (AG650A)

• The NAS should have at least 2 network cards and should support NFS.

Planck Satellite on display at Cannes, France (on Feb. 1, 2007 , launch Aug 15,2008)

Thank Thank you !!!you !!!

1992

20032006

Cosmic “Super–IMAX” theater

Transparent universe

Opaque universe

14 GPc

Here & Now(14 Gyr)

0.5 Myr

WMAP 5: Angular power spectra

Pramoda Samal, R. Saha, J. Delabrouille, S. Prunet, P. Jain, TSarXiv:0903.3634(ApJ , press)

IPSE can recover the WMAP Polarization spectra after a bias correction (based on PSMForeground model)

Bias in the IPSE method

Bias arises when foreground & noisedominate over common angular scales-- weights are influenced by noise(Analytic study: Saha et al. PRD 08)

DAPSE: redressing the bias in IPSE method

DAPSE: Redressing the bias in IPSE(Direct angular power spectrum estimation)

Solution for weights :

Consider the 24 pairs of linear combinations of maps c & c’ that have no common detectors (DA)

1

/i n

c i i ilm l lm l

i

a w a B

[ ][ ][ ]

cc c c i ij il lm lm l l lij

C Tl

Fl

C a a w C w

C W WC

1

1

[ ] [ ]

[ ][ ][ ]

T Tl

Tl

C eW

e C e

[ ] 1 1 .. .. 1e

Minimize power in the Cross correlation power spectra1

/i n

c i i ilm l lm l

i

a w a B

1

1

[ ] [ ]

[ ][ ][ ]

Tl

Tl

C eW

e C e

Planck Sky Model (PSM) Different Model Comparison

DAPSE will have advantage compare to IPSE to those angular scales where foreground and noise start dominating compare to the signal. As, in DAPSE, we take cross correlation, the weights get less bias due to noise term.

WMAP7 EE Power SpectrumT. Ghosh, S.Prunet and T.Souradeep (in progress)

EE Power Spectrum from Simulations

T. Ghosh, S.Prunet and T.Souradeep (in progress)

WMAP7 low l EE Power Spectrum

T. Ghosh, S.Prunet and T.Souradeep (in progress)

TT Power Spectrum from Simulations

T. Ghosh, S.Prunet and T.Souradeep (in progress)

TT Low Multipole Bias

( 1)

2 1clean cmb cmbcl l l

nC C C

l

2 1fcmb cmb

l l

nC C

l

Analytic expression of bias at low multipoles

Saha et. al. PRD,2008

nf=2

Min (nc,nf)

T. Ghosh, S.Prunet and T.Souradeep (in progress)

WMAP7 TT Power SpectrumT. Ghosh, S.Prunet and T.Souradeep (in progress)

WMAP 7 TE Power Spectrum

T. Ghosh, S.Prunet and T.Souradeep (in progress)

IPSE & DAPSE: Cl estimate sans foreground

modeling

• IPSE & DAPSE : Internal estimation of the CMB angular spectrum without recourse to foreground models. I.e., evade systematics due to modeling uncertainties/ inadequacies. Especially useful for CMB polarization where foreground uncertainties are larger.

• Implemented successfully on WMAP1 & 3 for TT • TT, TE & EE for WMAP 5 (IPSE with bias correction) [Samal et al, PRD 09]

• Residuals consistent with known foreground [Ghosh et al, PRD 09]

• Analytic understanding of biases and variances in IPSE [Saha et al PRD 08]

• IPSE: WMAP EE power spectrum is a challenge due to noise being important even at low multipole. Noise in autocorrelation affects weight determination.

• DAPSE: resolves the above problem (by minimizing power in cross-correlation spectra) [Tuhin Ghosh, SP, TS, in progress]

• Exploring appropriate schemes for Planck. [T. Ghosh, TS, SP in progress]

Model Independent Foreground Maps

We obtained the best possible foreground maps at WMAP frequencies using popular techniques like “Wiener filtering” and “Needlet Analysis”.

T. Ghosh, J. Delabrouille, M. Remazellies, J. F. Cardoso and T.Souradeep

Model Independent

Estimate of Foregrounds Maps

T. Ghosh, R. Saha, P. Jain and T. Souradeep, PRD 2009

)]ˆˆ(exp[)(),( 212

21 qqnikPqqCn

LR

n

Preferred Directions in the universeCorrelation function on a Torus (periodic box)

SI violation at low wave-number, k q¿ 1

])(1[),( 22 021 i

ii qCqqC

20 )()( 20 ii

(Hajian & Souradeep 2003)

ˆ( ) ( )[1 ( ) ( )]LM LMP k A k g k Y k

(Pullen & Kamionkowski 2008)

More generally,

*' '( ) ( , ) ( , )LM

ll LM o o

dkD A k g k k

k

2

ˆ ˆˆ ˆ( , , , ) ( , , )

Legendre Expansion

( , )

( ) ( , )

k k p k k p

k

dkC P k k

k

1 1

1 1

1 1 1 1

'

*' '' ' ' '

' '

' '' '

ˆ ˆˆ ˆ( , , , ) ( , , )

Bipolar SH Expansion

( , )

( ) ( , ) ( , )

LM

LM L Mm m o o

LML M m

LM L Mm m m m

k k p k k p

k

dka a P k k k

k

C C

Statistical Isotropy: CMB Photon Statistical Isotropy: CMB Photon distributiondistribution

FT ˆˆ ˆ ˆ( , , ) ( , , ) ( , , , )x p k p k k p

(Moumita Aich & TS, in progress)

Statistical Isotropy: CMB Photon Statistical Isotropy: CMB Photon distributiondistribution

Free stream0

200 '0

''

(( , )

( ,

, )

... ( )) ll

rec

ecl

r

k

j k C

k

k

1 2

1

3 4

3 4

1

3 4

Free stream0

4 30 00 0 0 0

1 2

( ( , )

... ( )

, )

( , )

LLMrec

LMre

M

Ll

c

L

k

Lk C

k

k

j Cl

Statistical isotropy

General:Non-Statistical isotropy

(Moumita Aich & TS, PRD, in press)

Statistical Isotropy: CMB Photon Statistical Isotropy: CMB Photon distributiondistribution

3 1

4 2 1 2

1

2 1

2

1 2

4 3 ( )Large ( ) ( )

1 2

,,

,0

...

( , ) ... ( ( , )) LMl l r

lsl L

l l l LLMel

lc

LC

s l s s

k j k k

Non-Statistical isotropic terms also free-stream to large multipole values

(Moumita Aich & TS, PRD, in press)