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Secondary Polarisation ASIAA 2005 CMB quadrupole induced polarisation from Clusters and Filaments Guo Chin Liu Slide 2 Secondary Polarisation ASIAA 2005 CMB Observations COBE 1992 WMAP 2002 Boomerang 2001MAXIMA 2001DASI 2001 Slide 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 Slide 4 Secondary Polarisation ASIAA 2005 Observed Power spectrum HInshaw et al. 2003 / Slide 5 Secondary Polarisation ASIAA 2005 Planck I/I Q/I U / U/I Slide 6 Secondary Polarisation ASIAA 2005 How Polarisation Generate? monopole dipole quadrupole polarisation Thomson scattering e-e- linearly polarized Slide 7 Secondary Polarisation ASIAA 2005 ? Where the secondary polarisation come from? Statistic properties? Bias the primordial polarisation? Open new window? Slide 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 Zaldovich & 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 Slide 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) Slide 10 Secondary Polarisation ASIAA 2005 CMB-induced kinetic quadrupole V Obs P v t 2 V t : transverse velocity SS of Obs. Estimate transverse velocity of cluster Zaldovich & Sunyaev 1980 Slide 11 Secondary Polarisation ASIAA 2005 CMB-induced double scattering Obs P 2 v t P 2 T e Te :cluster temperature Slide 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 Slide 13 Secondary Polarisation ASIAA 2005 Formula C (E,B) 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 Slide 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 Slide 15 Secondary Polarisation ASIAA 2005 Gas Evolution T>10 5 K 5< < c > c = 178 m (z) -0.6 Slide 16 Secondary Polarisation ASIAA 2005 simulations =d l T n e (phase) Slide 17 Secondary Polarisation ASIAA 2005 simulations Slide 18 Secondary Polarisation ASIAA 2005 simulations Slide 19 Secondary Polarisation ASIAA 2005 simulations Slide 20 Secondary Polarisation ASIAA 2005 simulations Slide 21 Secondary Polarisation ASIAA 2005 E=B E-modeB-mode m=060 m= 1 04 m= 2 10 For all ionised particles Slide 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 (+1)C Tl /2 da Silva et al 2001 SZ thermal Slide 23 Secondary Polarisation ASIAA 2005 Why Filament Dominate? visibility Cluster, small scale Cluster, large scale Filament, small scale Filament, large scale Slide 24 Secondary Polarisation ASIAA 2005 88 Amplitude 8 4 Slide 25 Secondary Polarisation ASIAA 2005 Bias primordial polarisation? r = Q T /Q S Slide 26 Secondary Polarisation ASIAA 2005 Discussion--week lensing T E Spherical source Lensed TLensed E Lensed B Slide 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 Slide 28 Secondary Polarisation ASIAA 2005 DiscussionFaraday 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 Slide 29 Secondary Polarisation ASIAA 2005 DiscussionFaraday rotation Slide 30 Secondary Polarisation ASIAA 2005 Summary of secondary effects Slide 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. Slide 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 Slide 33 Secondary Polarisation ASIAA 2005 Discussiontemperature 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 Slide 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