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Secondary Polarisation ASIAA 2005 CMB quadrupole induced polarisation from Clusters and Filaments Guo Chin Liu
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Secondary Polarisation ASIAA 2005 CMB Observations COBE 1992 WMAP 2002 Boomerang 2001MAXIMA 2001DASI 2001
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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
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Secondary Polarisation ASIAA 2005 Observed Power spectrum HInshaw et al. 2003 ℓ /
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Secondary Polarisation ASIAA 2005 Planck △ I/I △ Q/I U ℓ / △ U/I
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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
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Secondary Polarisation ASIAA 2005 ? Where the secondary polarisation come from? Statistic properties? Bias the primordial polarisation? Open new window?
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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
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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)
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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
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Secondary Polarisation ASIAA 2005 CMB-induced— double scattering Obs P 2 v t P 2 T e Te :cluster temperature
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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
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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 11 (-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 22 (-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
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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
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Secondary Polarisation ASIAA 2005 Gas Evolution T>10 5 K 5< < △ c > △ c = 178 m (z) -0.6
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Secondary Polarisation ASIAA 2005 simulations =∫d l T n e (phase)
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Secondary Polarisation ASIAA 2005 simulations
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Secondary Polarisation ASIAA 2005 simulations
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Secondary Polarisation ASIAA 2005 simulations
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Secondary Polarisation ASIAA 2005 simulations
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Secondary Polarisation ASIAA 2005 E=B E-modeB-mode m=060 m= 1 04 m= 2 10 For all ionised particles
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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
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Secondary Polarisation ASIAA 2005 Why Filament Dominate? visibility Cluster, small scale Cluster, large scale Filament, small scale Filament, large scale
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Secondary Polarisation ASIAA 2005 88 Amplitude 8 4
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Secondary Polarisation ASIAA 2005 Bias primordial polarisation? r = Q T /Q S
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Secondary Polarisation ASIAA 2005 Discussion--week lensing T E Spherical source Lensed TLensed E Lensed B
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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
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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
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Secondary Polarisation ASIAA 2005 Discussion—Faraday rotation
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Secondary Polarisation ASIAA 2005 Summary of secondary effects
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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.
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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
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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
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Secondary Polarisation ASIAA 2005 Ionized gas and visibility function T e > 10 5 K Ionized △ c= 178 m (z) -0.6 (Eke 1996) visibility
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