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AY202a Galaxies & Dynamics Lecture 18: Galaxy Clusters & Cosmology. X-ray Scaling Laws. Note small range in T!. Temperature versus X-ray Luminosity. Mushotzky & Scharf ‘97. Compilation of Diego & Partridge ‘09.
Note small range in T!
Mushotzky & Scharf ‘97
Diego & Partridge ‘09
Cluster gas element abundances from x-ray spectra
Gas cooling time
tcool = u/εff
8.5x1010 yr x
( )-1 ( ) ½
Long except at cluster centers
where densities are high
10-3cm-3 108 K
Perseus red= 0.5-1 kev
green = 1-2 kev
blue = 2-7 kev
5 k T
Typical cooling timescale for cluster centers < 109 yr
where does the material go? Mass deposition rate calculated as
dM/dt = where L is bolometric L
Problem is that there is little evidence except in a very few cases (e.g. Perseus) for recent star formation.
Solutions? AGN Heating?
Cosmic ray heating?
Ωmatter (Zwicky ) from
Hubble Constant from Sunyaev-Zeldovich effect (more on that later)
The Baryon Problem
Tracing Dark Matter
Cluster Abundances vs Redshift & Cosmological Parameters
δρ/ρ = 12 δρ/ρ = 80
σP (km/s) 197 183
RPV (Mpc) 1.71 0.97
log MV/LK 1.70 1.53
Log MP/LK 1.90 1.67
ΩM,V 0.14+/-0.02 0.10+/-0.02
ΩM,P 0.23+/-0.03 0.13+/-0.02
V=Virial Estimator P = Projected Mass
θE = 28.8”( )2( )
O L S
v Dds 1000 km/s Ds
In 1970 Sunyaev & Zeldovich realized that the CMB spectrum would be affected by passage through a hot gas via Inverse Compton scattering.
due to the SZ effect.
Scattered through an atmosphere with Compton parameter
y = 0.1 and
τβ = 0.05
Scattering optical depth
τe = ne(r)T dl (dl along l.o.s.)
y = ne(r)T dl
X-ray spectral surface brightness along l.o.s.
BX(E) = (ne(r))2Λ(E,Te) dl
me c 2
Where Λ is the spectral emissivity of the gas at energy E
3 me c2
and again the Thomson cross-section is
T = ()2
In the Rayleigh-Jeans region, we generally have for the change in brightness
For distance determinations, assume a round cluster with effective diameter L then
ne L T
and the x-ray intensity IX L ne2
and the x-ray angular diameter θ = L/dA
dA = ~ ( )2
where χis the comoving distanceand k is the curvature density 1 - Total
R L ΔIυ 1
θθ Iυ IX
Cluster motions also can
affect the CMB viewed
through them. The size of
the effect depends on the peculiar velocity of the cluster w.r.t. the expansion
SZ Maps from J. Carlstrom’s group
(BIMA/OVRO; Carlstrom, Holder & Reese 2002)
W band V band Q band
(90 GHz) (60 GHz) (40 GHz)
Diego & Partridge (2009)
Lets compare the Baryonic cluster mass = Gas Mass + Galaxy Mass to the Dynamical Total Mass of the cluster.
Mgas ( where X = R/ro, and MTot ( where both are derived from x-ray data. c.f. White & Frenk 1991, White et al. 1993 X 0 -kTR R d R dT Gmp dr T dr
where X = R/ro, and
MTot ( where both are derived from x-ray data. c.f. White & Frenk 1991, White et al. 1993 X 0 -kTR R d R dT Gmp dr T dr
where both are derived from x-ray data.
c.f. White & Frenk 1991, White et al. 1993
-kTR R d R dT
Gmp dr T dr
z = x2/(1 + x2)
T(r) = To (r/ro)-
R/ d/dr = -3Zβ
MTot ( with 0 β 1 k T R G mp
with 0 β 1
k T R
MGal,baryonic < Mgas or even << MGas
In the average cluster
MGas ~ 0.1 h-1.5 MTotal
Simulations (White & Frenk, etc.) suggest that at least on 1 Mpc scales, Gas = CDM distributions
But we also have
baryon (nucleosynthesis) ~ 0.02 h-2
~ 0.044 for h = 0.7
Total ~ 0.25 1 (!)
(in 1993 this was big, bad news for SCDM, but do go a long way towards solving the baryon problem)
Vikhlinin et al 2009
Chandra Cluster Cosmology project Vikhlinin et al. 2009