1. AY202a Galaxies & Dynamics Lecture 18: Galaxy Clusters & Cosmology

2. X-ray Scaling Laws Temperature versus X-ray Luminosity
Note small range in T!
Temperature versus
X-ray
Luminosity
Mushotzky & Scharf ‘97

3. Compilation of Diego & Partridge ‘09

4. Strong correlation between x-ray gas temperature and galaxy velocity dispersion

5. p = rvirial/rcore
X-ray Luminosity
vs Size
Diego & Partridge ‘09

6. Chemistry Cluster gas element abundances from x-ray spectra
(Mushotzky)

7. Evolution, or lack thereof,
of [Fe/H]

8. Cooling Flows Long except at cluster centers Gas cooling time
tcool = u/εff
 8.5x1010 yr x
( )-1 ( ) ½
Long except at cluster centers
where densities are high
ne T
10-3cm K
Fabian
Perseus red= kev
green = 1-2 kev
blue = 2-7 kev

9. 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?
Thermal Conduction?
Thermal Mixing?
Cosmic ray heating?
Absorption?
2 L μm
5 k T

10. Clusters & Cosmology
Ωmatter (Zwicky  ) from <M/L> and total luminosity density.
Hubble Constant from Sunyaev-Zeldovich effect (more on that later)
The Baryon Problem
Tracing Dark Matter
Cluster Abundances vs Redshift & Cosmological Parameters

11. 2MASS Galaxy Groups δρ/ρ = 12 δρ/ρ = 80
δρ/ρ = δρ/ρ = 80
σP (km/s)
RPV (Mpc)
log MV/LK
Log MP/LK
ΩM,V / /-0.02
ΩM,P / /-0.02
V=Virial Estimator P = Projected Mass

16. Gravitational Lensing
Mass reconstruction
Distance Measurement
Einstein radius
θE = 28.8” ( )2 ( )
O L S
v Dds 1000 km/s Ds
Dds Ds

17. Lensing Mass
Profile for
A2218

18. Sunyaev-Zeldovich Effect
In 1970 Sunyaev & Zeldovich realized that the CMB spectrum would be affected by passage through a hot gas via Inverse Compton scattering.

19. Scattered through an atmosphere with Compton parameter
Exaggerated
spectral distortion
due to the SZ effect.
Scattered through an atmosphere with Compton parameter
y = 0.1 and
τβ = 0.05
(Birkinshaw)
CMB
Distorted CMB

20. Narrower frequency range from Carlstrom (2002)

21. Scattering optical depth τe =  ne(r) T dl (dl along l.o.s.)
We calculate the Thermal SZ effect (SZ from thermalized electron distribution) from an electron gas with density distribution ne(r):
Scattering optical depth
τe =  ne(r) T dl (dl along l.o.s.)
Comptonization parameter
y =  ne(r) T dl
X-ray spectral surface brightness along l.o.s.
BX(E) =  (ne(r))2 Λ(E,Te) dl
k Te(r)
me c 2 1
4  (1+z)3
Where Λ is the spectral emissivity of the gas at energy E

22. and the x-ray angular diameter θ = L/dA
and again the Thomson cross-section is
T = ( )2
In the Rayleigh-Jeans region, we generally have for the change in brightness
= -2y
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
8  e2
me c2
Δ Iυ Iυ
Δ Iυ Iυ

23. Which gives
dA = ~  ( )2
where χ is the comoving distance and k is the curvature density 1 - Total
R L ΔIυ
θ θ Iυ IX

24. Kinematic SZ Effect 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

25. SZ measurements of A2163 from Holzapfel (1997) with SuZie (SZ Infrared experiment on Mauna Kea)

26. SZ Maps from J. Carlstrom’s group
A2163 again
SZ Maps from J. Carlstrom’s group
(BIMA/OVRO; Carlstrom, Holder & Reese 2002)

27. SZ in WMAP data (stacked clusters)
W band V band Q band
(90 GHz) (60 GHz) (40 GHz)
Diego & Partridge (2009)

28. Planck (launched May 14, 2009) will do an all-sky SZ survey for galaxy clusters. Two instruments (LFI and HFI) will survey in nine frequency bands between 30 and 857 GHz

29. Cluster Baryon “Problem”
Lets compare the Baryonic cluster mass = Gas Mass + Galaxy Mass to the Dynamical Total Mass of the cluster.
Mgas (<R) = 4 πo ro3  x2 (1+x2)-3/2 dx
where X = R/ro, and
MTot (<R) = ( )
where both are derived from x-ray data.
c.f. White & Frenk 1991, White et al. 1993 X
-kTR R d R dT
Gmp  dr T dr

30. by some simple trick substitutions, and remembering the Beta model:
z = x2/(1 + x2)
T(r) = To (r/ro)-
 R/ d/dr = -3Zβ
And
MTot (<R) = (3Zβ + )
with  0 β  1
k T R
G  mp

31. MGal,baryonic < Mgas or even << MGas
we also find that for the typical cluster
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
~ for h = 0.7
 Total ~  1 (!)
(in 1993 this was big, bad news for SCDM, but do go a long way towards solving the baryon problem)

32. The Bullet Cluster

34. Cosmological Parameters from Cluster Mass Functions

35. Constraints from the evolution of the mass function.
Vikhlinin et al 2009

36. Combined constraints from clusters plus BAO, CMB & SN Ia
Chandra Cluster Cosmology project Vikhlinin et al. 2009