CMB quadrupole induced polarisation from Clusters and Filaments

CMB quadrupoleinduced polarisation from Clusters and Filaments Guo Chin Liu

CMB Observations COBE 1992 WMAP 2002 Boomerang 2001 MAXIMA 2001 DASI 2001

Universe history Inflation, phase transition Generate fluctuations z=4 Big bang Dark age Secondary anisotropy Fluct. Evolution Acoustic oscillation z=0 Recombination z=1000 Primordial anisotropy

Observed Power spectrum ℓ/ HInshaw et al. 2003

Planck △U/I △I/I U △Q/I ℓ/

How Polarisation Generate? Thomson scattering 入射の polarisation 方向散乱温度揺らぎの × monopole × dipole ○ quadrupole 入射波 e- linearly polarized 入射波

? Where the secondary polarisation come from? Statistic properties? Bias the primordial polarisation? Open new window?

CMB-induced— Primordial CMB Quadrupole LSS of the cluster P  Qcmb : Optical depth Obs 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 K Sazonov & Sunyaev 1999

CMB primordial Quadrupole To know dark energy from the evolution of Quadrupole Q2(z)=∫dk/kk3△2T2(k,z) ISW

CMB-induced—kinetic quadrupole V P vt2 Vt : transverse velocity Obs ＬSS of Obs. Estimate transverse velocity of cluster Zal’dovich & Sunyaev 1980

CMB-induced—doublescattering P  2vt P  2Te Te :cluster temperature Obs

Modulated Quadrupole Quadrupole Density fluctuation Quadrupole Sm(k,): = ∫d3pe(k-p,)△mT2(p,) e(k,)∫d3p△mT2(p,) =e(k,)∫d3p△0T2(p,)Ym2(p) cluster filament k p

Formula g()  - e(0)-() d/d visibility function: possibility of last scattering at epoch  C(E,B)ℓℓ4m∫k2dk<|∫dg()Sm(k,)Tm(E,B)ℓ(k,r)|2>

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

T>105K Gas Evolution 5<<△c >△c= 178 m(z) -0.6

simulations =∫d l T ne(phase)

simulations

E=B For all ionised particles

SZ thermal ℓ(ℓ+1)CTl /2 da Silva et al 2001 1000 10000 Comparing with SZ temperature sz polarisation Temp. : Cluster Polar. : Filament Factor 2 in small scales 1 order different in large scales

Why Filament Dominate? Filament, small scale visibility Filament, large scale Cluster, small scale Cluster, large scale

8 Amplitude  84

Bias primordial polarisation? r = QT/QS

Discussion--week lensing Spherical source E T Lensed T Lensed E Lensed B

Primordial E Lensed B Primordial B Comparing with lensing Erasing lensing effect? Pin down lensing to 2 order Seljak & Hirata 2004

Discussion—Faraday rotation RM from Clarke et al. 2001 and RM profile of Takada et al. 2002 • model for estimating RM • Universal constant B0 • -model profile(r)=0[1+(r/rc)2]-3/2 • <RM2>=1/N∫dM dn/dM[△(r)/2]2

Discussion—Faraday rotation

Summary of secondary effects

Summary • 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. • The power spectrum l(l+1)Cl/2 for all the ionisingparticles ~ 10-15 ~10-16 K2 • Secondary polarisation for cluster and filament dominate at the small scales.

Summary 4. At the intermediate scales, the B-mode power is dominatedby the lensing generated power spectrum. 5. The amplitude of the secondary polarisatioin  84 6. The power contribute from filament is much larger than the ICMdifferent with the case of tSZ. 7. Others secondary polarisation?

Discussion—temperature • Reducing the threshold increases the ionization particles=>Enhance the total and IGM polarization power • The structures of ICM are smoothed =>Reduce the ICM polarization power

Ionized gas and visibility function Te > 105 K Ionized visibility △c= 178 m(z) -0.6 (Eke 1996)

CMB quadrupole induced polarisation from Clusters and Filaments