Ay202a galaxies dynamics lecture 18 galaxy clusters cosmology
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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.

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Ay202a galaxies dynamics lecture 18 galaxy clusters cosmology
AY202a Galaxies & DynamicsLecture 18:Galaxy Clusters& Cosmology


X ray scaling laws
X-ray Scaling Laws

Note small range in T!

Temperature versus

X-ray

Luminosity

Mushotzky & Scharf ‘97




p = r velocity dispersionvirial/rcore

X-ray Luminosity

vs Size

Diego & Partridge ‘09


Chemistry
Chemistry velocity dispersion

Cluster gas element abundances from x-ray spectra

(Mushotzky)


Evolution, or lack thereof, velocity dispersion

of [Fe/H]


Cooling flows
Cooling Flows velocity dispersion

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 velocity dispersionμm

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?


Clusters cosmology
Clusters & Cosmology velocity dispersion

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


2mass galaxy groups
2MASS Galaxy Groups velocity dispersion

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


Gravitational lensing
Gravitational Lensing velocity dispersion

Mass reconstruction

Distance Measurement

Einstein radius

θE = 28.8”( )2( )

O L S

v Dds 1000 km/s Ds

Dds

Ds


Lensing Mass velocity dispersion

Profile for

A2218


Sunyaev zeldovich effect
Sunyaev-Zeldovich Effect velocity dispersion

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


CMB velocity dispersion

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



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 electron distribution) from an electron gas with density distribution n 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

Δ Iυ


Which gives electron distribution) from an electron gas with density distribution n

dA = ~  ( )2

where χis the comoving distanceand k is the curvature density 1 - Total

R L ΔIυ 1

θθ Iυ IX


Kinematic sz effect
Kinematic SZ Effect electron distribution) from an electron gas with density distribution n

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 Infrared experiment on Mauna Kea)

SZ Maps from J. Carlstrom’s group

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


SZ in WMAP data (stacked clusters) (SZ Infrared experiment on Mauna Kea)

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


Cluster baryon problem
Cluster Baryon “Problem” 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 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

0

-kTR R d R dT

Gmp  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 model:

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)





Combined constraints from clusters plus bao cmb sn ia
Combined constraints from clusters plus BAO, CMB & SN Ia model:

Chandra Cluster Cosmology project Vikhlinin et al. 2009


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