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AY202a Galaxies & Dynamics Lecture 18: Galaxy Clusters & Cosmology

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Note small range in T!

Temperature versus

X-ray

Luminosity

Mushotzky & Scharf ‘97

Compilation of Diego & Partridge ‘09

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

p = rvirial/rcore

X-ray Luminosity

vs Size

Diego & Partridge ‘09

Cluster gas element abundances from x-ray spectra

(Mushotzky)

Evolution, or lack thereof,

of [Fe/H]

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-3 108 K

Fabian

Perseus red= 0.5-1 kev

green = 1-2 kev

blue = 2-7 kev

2 L μm

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?

Thermal Conduction?

Thermal Mixing?

Cosmic ray heating?

Absorption?

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

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

Mass reconstruction

Distance Measurement

Einstein radius

θE = 28.8”( )2( )

O L S

v Dds 1000 km/s Ds

Dds

Ds

Lensing Mass

Profile for

A2218

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

CMB

Exaggerated

spectral distortion

due to the SZ effect.

Scattered through an atmosphere with Compton parameter

y = 0.1 and

τβ = 0.05

(Birkinshaw)

Distorted CMB

Narrower frequency range from Carlstrom (2002)

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))2Λ(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

8 e2

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

= -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

Δ Iυ

Iυ

Δ Iυ

Iυ

Which gives

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

A2163 again

SZ Maps from J. Carlstrom’s group

(BIMA/OVRO; Carlstrom, Holder & Reese 2002)

SZ in WMAP data (stacked clusters)

W band V band Q band

(90 GHz) (60 GHz) (40 GHz)

Diego & Partridge (2009)

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

Lets compare the Baryonic cluster mass = Gas Mass + Galaxy Mass to the Dynamical Total Mass of the cluster.

Mgas (<R) = 4 πo 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

0

-kTR R d R dT

Gmp dr T dr

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

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

~ 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)

The Bullet Cluster

Vikhlinin et al 2009

Chandra Cluster Cosmology project Vikhlinin et al. 2009