cmb quadrupole induced polarisation from clusters and filaments
DESCRIPTION
CMB quadrupole induced 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. - PowerPoint PPT PresentationTRANSCRIPT
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 2001 MAXIMA 2001 DASI 2001
Secondary Polarisation ASIAA 2005
Big bang
Inflation, phase transitionGenerate fluctuations
Recombination z=1000Primordial anisotropy
Fluct. EvolutionAcoustic oscillation
Dark ageSecondary anisotropy
z=4
z=0
Universe history
Secondary Polarisation ASIAA 2005
Observed Power spectrum
HInshaw et al. 2003
ℓ/
Secondary Polarisation ASIAA 2005
Planck△I/I
△Q/I
U
ℓ/
△U/I
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How Polarisation Generate?
温度揺らぎの× monopole
× dipole
○ quadrupole
2
T 'd
d
' 入射
散乱の polarisation 方向
Thomson scattering
e-
'
'
入射波
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 Qcmb : 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 KSazonov & Sunyaev 1999
Secondary Polarisation ASIAA 2005
To know dark energy from the evolution of Quadrupole
CMB primordial Quadrupole
ISWQ2(z)=∫dk/k k3△2
T2(k,z)
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CMB-induced—kinetic quadrupole
V
Obs
P vt2
Vt : transverse velocity
L SS of Obs.
Estimate transverse velocity of clusterZal’dovich & Sunyaev 1980
Secondary Polarisation ASIAA 2005
CMB-induced—double scattering
Obs
P 2vt
P 2Te Te :cluster temperature
Secondary Polarisation ASIAA 2005
Modulated Quadrupole
Sm(k,):
= ∫d3p e(k-p,)△mT2(p,)
e(k,) ∫d3p △mT2(p,)
=e(k,) ∫d3p△0T2(p,)Ym
2(p)
kp
Quadrupole
cluster
filament
Density fluctuation Quadrupole
Secondary Polarisation ASIAA 2005
Formula
C(E,B)ℓℓ4m∫k2dk<|∫dg()Sm(k,)Tm(E,B)ℓ(k,r)|2>
m TmEl Tm
Bl
0 (-i)l jl(kr)/(kr)2 0
1 (-i)l [(l+1)jl-1(kr) - ljl(kr)] /
[(2l+1)kr-6l(l+1)]
(-i)l[3/2l(l+1)]*
jl(kr)/(kr)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)] jl(kr)
-(l+2)(l+1) jl-1(kr)/kr-l(l-1) jl+1(kr)/kr}
((l-2)!/6(l+2)!)/(2l+1)
(-i)l{(l+2) jl-1(kr)-(l-1) jl+1(kr)
((l-2)!/6(l+2)!)/(2l+1)
g() - e(0)-() d/dvisibility function: possibility of last scattering at epoch
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
Lbox=100h-1Mpc
Normalization 8=0.8,0.9, 1.0
Mdark: 2.1x1010 Mo/h Mgas:2.6x109 Mo/h
Secondary Polarisation ASIAA 2005
Gas Evolution
T>105K
5<<△c
>△c= 178 m(z) -0.6
Secondary Polarisation ASIAA 2005
simulations
=∫d l T ne(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=BE-mode B-mode
m=0 6 0
m=1 0 4
m=2 1 0
For all ionised particles
Secondary Polarisation ASIAA 2005
Comparing with SZ temperature
Temp. : ClusterPolar. : Filament
sz polarisation
Factor 2 in small scales1 order different in large scales
1000 10000
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
Amplitude 84
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Bias primordial polarisation?
r = QT/QS
Secondary Polarisation ASIAA 2005
Discussion--week lensing
T E Spherical source
Lensed T Lensed 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
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Discussion—Faraday rotationRM from Clarke et al. 2001 and RM profile of Takada et al. 2002
model for estimating RM
1.Universal constant B0
2. -model profile
(r)=0[1+(r/rc)2]-3/2
3.<RM2>
=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 ~ 10-15 ~10-16 K2
3. Secondary polarisation for cluster and filament dominate
at the small scales.
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 84
6. 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
Te > 105 K Ionized
△c= 178 m(z) -0.6
(Eke 1996)
visibility