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