1. Secondary Polarisation ASIAA 2005 CMB quadrupole induced polarisation from Clusters and Filaments Guo Chin Liu

2. Secondary Polarisation ASIAA 2005 CMB Observations COBE 1992 WMAP 2002 Boomerang 2001MAXIMA 2001DASI 2001

3. 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

4. Secondary Polarisation ASIAA 2005 Observed Power spectrum HInshaw et al. 2003 ℓ  / 

5. Secondary Polarisation ASIAA 2005 Planck △ I/I △ Q/I U ℓ  /  △ U/I

6. 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

7. Secondary Polarisation ASIAA 2005 ? Where the secondary polarisation come from? Statistic properties? Bias the primordial polarisation? Open new window?

8. 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. 1996 Average polarisation in the center of cluster : 3   K Sazonov & Sunyaev 1999

9. 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)

10. 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

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

12. 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

13. 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 

14. 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 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

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

16. Secondary Polarisation ASIAA 2005 simulations  =∫d l  T n e (phase)

17. Secondary Polarisation ASIAA 2005 simulations

18. Secondary Polarisation ASIAA 2005 simulations

19. Secondary Polarisation ASIAA 2005 simulations

20. Secondary Polarisation ASIAA 2005 simulations

21. Secondary Polarisation ASIAA 2005 E=B E-modeB-mode m=060 m=  1 04 m=  2 10 For all ionised particles

22. 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 100010000 ℓ(ℓ+1)C Tl /2  da Silva et al 2001 SZ thermal

23. Secondary Polarisation ASIAA 2005 Why Filament Dominate? visibility Cluster, small scale Cluster, large scale Filament, small scale Filament, large scale

24. Secondary Polarisation ASIAA 2005 88 Amplitude   8 4

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

26. Secondary Polarisation ASIAA 2005 Discussion--week lensing T E Spherical source Lensed TLensed E Lensed B

27. 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

28. Secondary Polarisation ASIAA 2005 Discussion—Faraday rotation RM from Clarke et al. 2001 and RM profile of Takada et al. 2002 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

29. Secondary Polarisation ASIAA 2005 Discussion—Faraday rotation

30. Secondary Polarisation ASIAA 2005 Summary of secondary effects

31. 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 K 2 3.Secondary polarisation for cluster and filament dominate at the small scales.

32. 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   8 4 6. The power contribute from filament is much larger than the ICM different with the case of tSZ. 7. Others secondary polarisation? Summary

33. 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

34. Secondary Polarisation ASIAA 2005 Ionized gas and visibility function T e > 10 5 K Ionized △ c= 178  m (z) -0.6 (Eke 1996) visibility