AY202a Galaxies & Dynamics

Lecture 17:Galaxy Groups & Clusters

continued

And V = |V1 - V2| < Vlim(V1,V2,m1,m2)

with two choices, either fix V or scale it as D.

Then select

Dlim and

Vlim as needed

for the sample

you have.

RSA Sample

2dF 2PIGS

2MRS Sample (raw)

2MRS Sample (filled)

2MRS Selection Function

2MRS Group Selection

Number of groups found f

2MRS Groups

3 largest 2MRS Groups Virgo, Fornax/Eridanus, Perseus-Pisces

/

=12

80

2MRS Group Mass Function

2MASS Galaxy Groups

δρ/ρ = 12 δρ/ρ = 80-------------------------------------------------------σP (km/s) 197 183RPV (Mpc) 1.71 0.97log MV/LK 1.70 1.53Log MP/LK 1.90 1.67ΩM,V 0.14+/-0.02 0.10+/-0.02ΩM,P 0.23+/-0.03 0.13+/-0.02-------------------------------------------------------- V=Virial Estimator P = Projected Mass

# Density versus redshift for various group surveys:

Cluster ClassificationJust like galaxies, clusters classified morphologically. Overall Compact Medium Compact Open LinearBautz Morgan classes I, I-II, II, II-III, III based on the

ratio between the brightness of 1st and rest I -- single central cD galaxy c.f. A2029 II -- intermediate III -- no dominant cluster galaxy c.f. Hercules

Rood-Sastry cD -- like BM I

types B -- Binary c.f. Coma

L -- Linear

C -- Core Compact

F -- Flat

I -- Irregular

Tuning Forks

Rood-Sastry cD -- B

Struble & Rood I -- F B -- cD

L -- F

C -- I

L

C

Sky Distribution of Abell Clusters 0.033 < z < 0.83

Optical

Substructure

(Geller & Beers ’82)

Cluster

MorphologyIrregular

A1367 A262

Regular

A2256 A85

(Jones & Forman ’84)

A2029

A2142

Hydra

Perrseus A. Fabian

Physics of Galaxy ClustersTo 0th order, assume spherical,

decreasing density from the center. If n(r) is the 3-D number density,

the projected density, N(R), is

N(R) = n[(R2+z2)½ ] dz

= 2

where z is the coordinate along the l.o.s. and R is the projected radius

∞

-∞

r n(r) dr

(r2 – R2) ½

∞

R

Hydrostatic Equilibrium

Good basic model for the hot gas is to assume Hydrostatic Equilibrium

dPg/dr = - g GM(r)/r2 P = where g means gas

= + differentiating the gas law

{ + } = - g GM(r)/r2

M(r) = { + }

kT

mp

dPg dg kT g k dT

dr dr mp mp dr k T dg g dT

mp dr dr

- rT d ln g d ln T

G mp d ln r d ln rdensity & temperature gradients

You can also treat the galaxies this way, just as a “gas” of much more massive particles

= gal P gal = 1/3 <v2> gal

= n k Tgal

=

and we can compare the gas and galaxy distributions

since they are living in the same potential.

dPgal GM

dr r2

<v2> dPgal kTgas 1 dgas

3gal dr mp gas dr

We can write for the relative density relations

( ) = ( ) β

where β = =

This is known as the Beta Model. If β = 1, gas and galaxies have the same distribution.

Generally β 1

IX (r) [ 1 + (b/rc)2 ]-3β + 1/2

gas gal

0,gas 0,gal mp <v2> mp 2los

3 k T kT

X-ray surface intensity and rc = optical galaxy core radius

Other Dynamical Quantities

Crossing Time

tcross ~ R/ ~ 2 x 109 yr for R=RA and H=70

Dynamical relaxation (Virialization) takes places on timescales of the crossing time, so (1) clusters are generally relaxed, and the centers of the clusters relax first

Two-Body Relaxation time is long in clusters

trelax ~ tcross (N / ln N)

so cluster galaxies are not in “thermal” equilibrium

X-ray Emission

Spectrum of x-ray gas is optically thin thermal bremhmmsstrahlung (free-free emission) plus emission lines

X-ray emission from Coma. ROSAT (left) and XMM (right). Note structure in the images.

Bremsstrahlung emissivity =

ευ = ( )½ e -hυ/kT gff(T,υ)

where ne and ni are the number density of electrons and ions, Z is the ion charge and gff is the Gaunt factor. Flat then exponentially decreasing. Typical x-ray temperatures are ~ 50 million degrees or kT = 5 kev

For a thermal pasma of solar abundance, bremsstrahlung alone gives

eff 3.0 x10-27 (T / 1K) ½ (ne / 1 cm-3)2 erg cm-3 s-1

32Z2e6neni 2

3 me c3 3kT me

When line emission is included:

εtotal 6.2 x10-27 (T / 1K) ½ (ne / 1 cm-3)2 erg cm-3 s-1

Use X-ray

features to study

Chemistry

(c.f. Mushotzsky)

A Case Study - The Virgo ClusterAssume D = 16 Mpc (HST Key Project)

Zw-B(0) magnitudes

6o Core v = 716 km/s

rH ~ 0.8 Mpc

MP ~ 8 x 1014 M

M/LB ~ 750 (M/L)But (1) substructure exists, (2) there is at least one

background group contaminating at 2200 km/s (Virgo W), and (3) Spirals avoid the center and appear to be infalling.

Virgo Cluster

Markarian’s Chain

Bohringer et al.

X-ray map

with contours

First problem is to find where the cluster really is:

JH85 from CfA survey, luminosity weighted center of all galaxies with v < 3000 km/s, m 14.5

error ~ 3’ --- iterate on sample

Isopleths in the Zwicky catalog

All known velocities in the 6 degree radius circle.

Virgo

Great Wall

Background Cl.

Spirals and Ellipticals are not in the same place in the cluster --- Spirals avoid the center.

Virgo Surface

Density

A hole around M87!

How much of this is just due to the Spirals?

Velocity

Histogram by Type

E’s look Gaussian

S’s are flat

Cluster Infall

JH ‘85