Secondary Polarisation ASIAA 2005

CMB quadrupole induced polarisation from

Clusters and Filaments

Guo Chin Liu

Secondary Polarisation ASIAA 2005

CMB Observations

COBE 1992 WMAP 2002

Boomerang 2001 MAXIMA 2001 DASI 2001

Secondary Polarisation ASIAA 2005

Big bang

Inflation, phase transitionGenerate fluctuations

Recombination z=1000Primordial anisotropy

Fluct. EvolutionAcoustic oscillation

Dark ageSecondary anisotropy

z=4

z=0

Universe history

Secondary Polarisation ASIAA 2005

Observed Power spectrum

HInshaw et al. 2003

ℓ/

Secondary Polarisation ASIAA 2005

Planck△I/I

△Q/I

U

ℓ/

△U/I

Secondary Polarisation ASIAA 2005

How Polarisation Generate?

温度揺らぎの× 　 monopole

× dipole

○ quadrupole

2

T 'd

d

' 入射

散乱の polarisation 方向

Thomson scattering

e-

'

'

入射波

入射波linearly polarized

Secondary Polarisation ASIAA 2005

?

Where the secondary polarisation come from?

Statistic properties?

Bias the primordial polarisation?

Open new window?

Secondary Polarisation ASIAA 2005

Obs

LSS of the cluster

P Qcmb　 : Optical depth

CMB-induced— Primordial CMB Quadrupole

LSS of the Obs.

First idea by Zal’dovich & Sunyaev (1980)Primordial CMB quadrupole 16 12 K

COBE Kogut et al. 1996

Average polarisation in the center of cluster : 3 KSazonov & Sunyaev 1999

Secondary Polarisation ASIAA 2005

To know dark energy from the evolution of Quadrupole

CMB primordial Quadrupole

ISWQ2(z)=∫dk/k k3△2

T2(k,z)

Secondary Polarisation ASIAA 2005

CMB-induced—kinetic quadrupole

V

Obs

P vt2

Vt : transverse velocity

Ｌ SS of Obs.

Estimate transverse velocity of clusterZal’dovich & Sunyaev 1980

Secondary Polarisation ASIAA 2005

CMB-induced—double scattering

Obs

P 2vt

P 2Te Te :cluster temperature

Secondary Polarisation ASIAA 2005

Modulated Quadrupole

Sm(k,):

= ∫d3p e(k-p,)△mT2(p,)

e(k,) ∫d3p △mT2(p,)

=e(k,) ∫d3p△0T2(p,)Ym

2(p)

kp

Quadrupole

cluster

filament

Density fluctuation Quadrupole

Secondary Polarisation ASIAA 2005

Formula

C(E,B)ℓℓ4m∫k2dk<|∫dg()Sm(k,)Tm(E,B)ℓ(k,r)|2>

m TmEl Tm

Bl

0 (-i)l jl(kr)/(kr)2 0

1 (-i)l [(l+1)jl-1(kr) - ljl(kr)] /

[(2l+1)kr-6l(l+1)]

(-i)l[3/2l(l+1)]*

jl(kr)/(kr)2

2 (-i)l {[(l+2)(l+1)/(2l-1)+l(l+1)/(2l+3)

-(2l+1)(l-1)(l+2)/(2l-1)(2l+3)] jl(kr)

-(l+2)(l+1) jl-1(kr)/kr-l(l-1) jl+1(kr)/kr}

((l-2)!/6(l+2)!)/(2l+1)

(-i)l{(l+2) jl-1(kr)-(l-1) jl+1(kr)

((l-2)!/6(l+2)!)/(2l+1)

g() - e(0)-() d/dvisibility function: possibility of last scattering at epoch

Secondary Polarisation ASIAA 2005

Simulation details

Public Hydra Code Couchnman et al. 1995

Pearce & Couchnman 1997

Non-radiative model

Cosmological parameters

m=0.3 b=0.044

=0.7 h=0.71

Lbox=100h-1Mpc

Normalization 8=0.8,0.9, 1.0

Mdark: 2.1x1010 Mo/h Mgas:2.6x109 Mo/h

Secondary Polarisation ASIAA 2005

Gas Evolution

T>105K

5<<△c

>△c= 178 m(z) -0.6

Secondary Polarisation ASIAA 2005

simulations

=∫d l T ne(phase)

Secondary Polarisation ASIAA 2005

simulations

Secondary Polarisation ASIAA 2005

simulations

Secondary Polarisation ASIAA 2005

simulations

Secondary Polarisation ASIAA 2005

simulations

Secondary Polarisation ASIAA 2005

E=BE-mode B-mode

m=0 6 0

m=1 0 4

m=2 1 0

For all ionised particles

Secondary Polarisation ASIAA 2005

Comparing with SZ temperature

Temp. : ClusterPolar. : Filament

sz polarisation

Factor 2 in small scales1 order different in large scales

1000 10000

ℓ(ℓ+

1)C

Tl /

2

da Silva et al 2001

SZ thermal

Secondary Polarisation ASIAA 2005

Why Filament Dominate?

visibility

Cluster, small scale

Cluster, large scale

Filament, small scale

Filament, large scale

Secondary Polarisation ASIAA 2005

8

Amplitude 84

Secondary Polarisation ASIAA 2005

Bias primordial polarisation?

r = QT/QS

Secondary Polarisation ASIAA 2005

Discussion--week lensing

T E Spherical source

Lensed T Lensed E Lensed B

Secondary Polarisation ASIAA 2005

Comparing with lensing

Primordial E

Primordial B

Lensed B

Erasing lensing effect?

Pin down lensing to 2 order

Seljak & Hirata 2004

Secondary Polarisation ASIAA 2005

Discussion—Faraday rotationRM from Clarke et al. 2001 and RM profile of Takada et al. 2002

model for estimating RM

1.Universal constant B0

2. -model profile

(r)=0[1+(r/rc)2]-3/2

3.<RM2>

=1/N∫dM dn/dM[△(r)/2]2

Secondary Polarisation ASIAA 2005

Discussion—Faraday rotation

Secondary Polarisation ASIAA 2005

Summary of secondary effects

Secondary Polarisation ASIAA 2005

Summary

1. The E-mode and B-mode have same power because the

symmetry of the quadrupole in its k-space is broken by

coupling with electron field.

2. The power spectrum l(l+1)Cl/2 for all the ionising

particles ~ 10-15 ~10-16 K2

3. Secondary polarisation for cluster and filament dominate

at the small scales.

Secondary Polarisation ASIAA 2005

4. At the intermediate scales, the B-mode power is dominated

by the lensing generated power spectrum.

5. The amplitude of the secondary polarisatioin 84

6. The power contribute from filament is much larger than the ICM

different with the case of tSZ.

7. Others secondary polarisation?

Summary

Secondary Polarisation ASIAA 2005

Discussion—temperature 1. Reducing the threshold increases the ionization particles

=>Enhance the total and IGM polarization power 2. The structures of ICM are smoothed

=>Reduce the ICM polarization power

Secondary Polarisation ASIAA 2005

Ionized gas and visibility function

Te > 105 K Ionized

△c= 178 m(z) -0.6

(Eke 1996)

visibility