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 2001MAXIMA 2001DASI 2001

Secondary Polarisation ASIAA 2005 Big bang Inflation, phase transition Generate fluctuations Recombination z=1000 Primordial anisotropy Fluct. Evolution Acoustic oscillation Dark age Secondary anisotropy z=4 z=0 Universe history

Secondary Polarisation ASIAA 2005 Observed Power spectrum HInshaw et al 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 入射 散乱 の polarisation 方向 Thomson scattering e-e- 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   Q cmb  : 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 Average polarisation in the center of cluster : 3   K Sazonov & Sunyaev 1999

Secondary Polarisation ASIAA 2005 To know dark energy from the evolution of Quadrupole CMB primordial Quadrupole ISW Q 2 (z)= ∫ dk/k k 3 △ 2 T2 (k,z)

Secondary Polarisation ASIAA 2005 CMB-induced— kinetic quadrupole V Obs P   v t 2 V t : transverse velocity Ｌ SS of Obs. Estimate transverse velocity of cluster Zal’dovich & Sunyaev 1980

Secondary Polarisation ASIAA 2005 CMB-induced— double scattering Obs P   2 v t P   2 T e Te :cluster temperature

Secondary Polarisation ASIAA 2005 Modulated Quadrupole S m (k,  ): = ∫ d 3 p  e (k-p,  ) △ m T2 (p,  )   e (k,  ) ∫ d 3 p △ m T2 (p,  ) =  e (k,  ) ∫d 3 p △ 0 T2 (p,  )Y m 2 (p) k p Quadrupole cluster filament Density fluctuationQuadrupole

Secondary Polarisation ASIAA 2005 Formula C (E,B)ℓ  ℓ 4  m ∫ k 2 dk mTmElTmEl TmBlTmBl 0(-i) l j l (kr)/(kr) 2 0 11  (-i) l [(l+1)j l-1 (kr) - lj l (kr)] / [(2l+1)kr-  6l(l+1)]  (-i) l [  3/2l(l+1)]* j l (kr)/(kr) 2 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)] j l (kr) -(l+2)(l+1) j l-1 (kr)/kr-l(l-1) j l+1 (kr)/kr}  ((l-2)!/6(l+2)!)/(2l+1)  (-i) l {(l+2) j l-1 (kr)-(l-1) j l+1 (kr)  ((l-2)!/6(l+2)!)/(2l+1) g(  )  - e  (  0)-  (  ) d  /d  visibility function: possibility of last scattering at epoch 

Secondary Polarisation ASIAA 2005 Simulation details Public Hydra Code Couchnman et al Pearce & Couchnman 1997 Non-radiative model Cosmological parameters  m =0.3  b =0.044   =0.7 h=0.71 L box =100h -1 Mpc Normalization  8 =0.8,0.9, 1.0 M dark : 2.1x10 10 M o /h M gas :2.6x10 9 M o /h

Secondary Polarisation ASIAA 2005 Gas Evolution T>10 5 K 5<  < △ c  > △ c = 178  m (z) -0.6

Secondary Polarisation ASIAA 2005 simulations  =∫d l  T n e (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=B E-modeB-mode m=060 m=  1 04 m=  2 10 For all ionised particles

Secondary Polarisation ASIAA 2005 Comparing with SZ temperature Temp. : Cluster Polar. : Filament sz polarisation Factor 2 in small scales 1 order different in large scales 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8 Amplitude   8 4

Secondary Polarisation ASIAA 2005 Bias primordial polarisation? r = Q T /Q S

Secondary Polarisation ASIAA 2005 Discussion--week lensing T E Spherical source Lensed TLensed 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 rotation RM from Clarke et al and RM profile of Takada et al model for estimating RM 1.Universal constant B 0 2.  -model profile  (r)=  0 [1+(r/r c ) 2 ] -3  /2 3. =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 ~ ~ K 2 3.Secondary polarisation for cluster and filament dominate at the small scales.

Secondary Polarisation ASIAA At the intermediate scales, the B-mode power is dominated by the lensing generated power spectrum. 5. The amplitude of the secondary polarisatioin   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 T e > 10 5 K Ionized △ c= 178  m (z) -0.6 (Eke 1996) visibility