Clusters of Galaxies:• Clusters are systems a few Mpc across, typically

containing ~ 50-1000 luminous galaxies within the central 1 Mpc

• Clusters are gravitationally bound with M of ~ 1014-1015 M

• Clusters are filled with hot x-ray gas• Only ~20% of galaxies live in clusters, most live in

groups or in the “field”• But it is hard to draw the line between group and

cluster, ~50% of galaxies live in clusters or groups• Clusters have higher densities than groups, contain a

majority of E’s and S0’s while groups are dominated by spirals

Local Group:

• The Milky Way is part of the Local Group: a concentration of ~ 30 galaxies, most of which are smaller than our own.

Typical galaxy clusters

• Galaxy clusters usually contain of order 1000 galaxies, with total mass 1014 M , spread over tens of Mpc but with cores a few Mpc in size.

– Clusters contain very hot (107-108K ) diffuse gas generally concentrated toward the center and at the centers of groups, that adds up to about as much mass as lies in galaxies. (It is seen at X-ray wavelengths.)

– Clusters come in a variety of “richness” (degree of central concentration). Rich clusters are dominated at their centers by one or more cD galaxies.

– Spiral galaxies within clusters tend to have less diffuse interstellar matter than field galaxies, probably due to stripping by galaxy interactions and by the cluster’s hot intergalactic medium (IGM).

The Virgo cluster:

• Irregular cluster• Distance = 16Mpc, closest to us• Diameter = 10 on the sky, 3 Mpc • ~2000 galaxies, mostly dwarfs (dE’s)• Bright galaxies – 20% ellipticals, rest are

spirals (Virgo is “spiral-rich”)– Ellipticals near center, spirals in outskirts

• M87 (cD galaxy) in the center

– Virgo is very clumpy w/ lots of substructure• Some parts of cluster may still be falling in, not virialized

– Lots of hot, intracluster gas (x-ray)– Also many intracluster stars …

Virgo, ~2,000 galaxies

Virgo, w/ROSAT

The Coma cluster:

• Nearest, rich cluster of galaxies

• Distance =90Mpc

• Diameter = 4-5 on the sky, 6-8 Mpc

• >10,000 galaxies!!– Mostly dE’s– Of the bright galaxies, <10% spirals, rest

are ellipticals or lenticulars (E/S0s)

• Roughly spherical in shape, probably virialized, 2 cD galaxies in the center

Coma, central portions

Coma, entire cluster

Coma, X-ray Images

Chandra

cD galaxies

• They are giant ellipticals, with a few other differences from normal besides total mass:

– More extended, relative to their core radii and the normal elliptical-galaxy luminosity profile.

– Often exhibit multiple nuclei, either because they are assimilating other cluster members (“galactic cannibalism”), or because these nuclei are cluster galaxies on linear (highly eccentric) orbits.

– Often surrounded with shells of infalling cluster IGM that compress and cool as they fall (“cooling flows”).

– Often associated with bright gravitational lensing of more distant galaxies, clusters or quasars.

cD galaxy with multiple (6!) nuclei

Measuring the masses of clusters:

• One way is to measure the velocities of galaxies in cluster

• Assuming the cluster is “virialized”,– 2U + KE = 0– KE = ½ mivi

2 = ½ M<v2> = 3/2 M2

• M = mass of cluster = measured radial velocity dispersion

– U = -3/5 GM2/R, for a uniform spherical distribution (remember for elliptical galaxy mass determination)

– M = 5<R>2 / G

Measuring the masses of clusters:

• Zwicky was the first one to do this (in 1933!) for the Coma cluster, observing only 8 galaxies

• Found M> 5 × 1014 M

• Calculated mass-to-light ratio and determined that about 90% of the mass necessary to account for observed ratio was missing and therefore invisible, or "dark".

But nobody believed him …

Virial masses of clusters:

• Poor clusters ~ 500-800 km/s– D ~ 1-3 Mpc

– M ~ 1014 h-1 M

• Rich clusters > 800 km/s– D ~ a few Mpc

– M ~ 1015 h-1 M

– Mass to light ratio of the cluster ~ several hundred M/L

• Even more dark matter! It’s everywhere ….

Hot x-ray gas:

• As we have seen, clusters are full of hot x-ray gas– T ~ 107 – 108 K, emission is from free-free emission (as in groups,

but hotter)– In fact, many distant clusters are now being discovered via x-ray

surveys (such as the ROSAT survey)– Temperatures are not uniform, we see patches of “hot spots”

which are not obviously associated with galaxies. May have been heated as smaller galaxies (or clumps of galaxies) fell into the cluster

– In densest regions, gas may cool and sink toward the cluster center as a “cooling flow”

– Unlikely that all of it has escaped from galaxies, some must be around from cluster formation process. It is heated via shocks as the gas falls into the cluster potential

– But some metals, must be from stars in galaxies– X-ray luminosity correlates with cluster classification, regular

clusters have high x-ray luminosity, irregular clusters have low x-ray luminosity

X-ray spectrum of Coma, Henriksen & Mushotsky (1986)

9 x 107 K

Masses of clusters from x-ray gas:

• If we assume the cluster is in hydrostatic equilibrium,– dP/dr = -(GM(r)/r2), =density of the gas, P=pressure

– From the ideal gas law: P= (/mH)kT , = mean molecular weight (~0.6 for an ionized plasma), mH = mass of the hydrogen atom, k=Boltzman constant

– So, dP/dr = (k/mH)(T d/dr + dT/dr) = -(GM(r)/r2)

– (kT/mH)(r/ d/dr + r/T dT/dr) = -(GM(r)/r2)

– kT/mHG (dln/dlnr + dlnT/dlnr) = -M(r)/ r

– And finally, M(r) = -kT/mHG (dln/dlnr + dlnT/dlnr) r

– If the gas is isothermal, dlnT/dlnR = 0, so

– M(r) = -kT/mHG (dln/dlnr) r

Masses of clusters from x-ray gas:

• We have: M(r) = -kT/mHG (dln/dlnr) r• So if we know dln/dlnr, we can measure the mass

distribution of cluster• If the cluster is spherically symmetric this can be

derived from x-ray intensity and spectral observations• For Virgo,

– Find M(r<1.8Mpc)~1.5 – 5.5 x 1014M

– But the gaseous mass (from x-ray luminosity) is only ~ 4 – 5.5 x 1013M

– Typical cluster masses:• Total: 5 x 1014 M to 5 x 1015 M

• Luminous mass: ~5%• Gaseous mass: 10-30%• Dark matter: 60-85% !!!!!

Masses from Gravitational lensing:

Gravitational lensing

When = 0, or the source is directly behind the lens, we havean Einstein ring at an angle:

E = (4GM/c2)1/2 x (Dds/DsDd)1/2

We can also define a critical density, crit = (c2/4G) x (Ds/DdDds),such that lensing occurs when the surface density, M(< E)/ 2 > crit

The geometry of a non-point source lensing mass is muchmore complex, but can be modeled to determine the mass distributionof the cluster. In general arcs (due to the non-symmetry of thecluster mass distribution) are formed near the critical curve defined by = E , when is small. The enclosed mass can bemeasured by the radius of the arcs.

Fort & Mellier1994

z=5.58 or 12.6 billion light years

z~7or 12.9 billion light yearsKneib et al., Feb 15. 2004!

Probable z~7 galaxyor 12.9 billion light yearsKneib et al., Feb 15. 2004!

Probable z~7 galaxyor 12.9 billion light yearsKneib et al., Feb 15. 2004!

Cluster masses from gravitational lensing:

• Strong lensing constraints:– A370 M~5x1013h-1 M/L ~270h– A2390 M~8x1013h-1 M/L ~240h– MS2137 M~3x1013h-1 M/L ~500h– A2218 M~1.4x1014h-1 M/L ~360h

• Weak lensing constraints (a subset):– MS1224 M/L ~800h– A1689 M/L ~400h– CL1455 M/L ~520h– A2218 M/L ~310h– CL0016 M/L ~180h– A851 M/L ~200h– A2163 M/L ~300h

Yep, lots o’ dark matter!