1. 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 ~ 10 14 - 10 15 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

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

3. Typical galaxy clusters Galaxy clusters usually contain of order 1000 galaxies, with total mass 10 14 M , spread over tens of Mpc but with cores a few Mpc in size. –Clusters contain very hot (10 7 -10 8 K ) 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).

4. 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 …

5. Virgo, ~2,000 galaxies

6. Virgo, w/ROSAT

7. 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

8. Coma, central portions

9. Coma, entire cluster

10. Coma, X-ray Images Chandra

11. 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.

12. cD galaxy with multiple (6!) nuclei

13. 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 m i v i 2 = ½ M = 3/2 M  2 M = mass of cluster  = measured radial velocity dispersion –U = -3/5 GM 2 /R, for a uniform spherical distribution (remember for elliptical galaxy mass determination) –M = 5  2 / G

14. 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 × 10 14 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 …

15. Virial masses of clusters: Poor clusters –  ~ 500-800 km/s –D ~ 1-3 Mpc –M ~ 10 14 h -1 M  Rich clusters –  > 800 km/s –D ~ a few Mpc –M ~ 10 15 h -1 M  –Mass to light ratio of the cluster ~ several hundred M  /L  Even more dark matter! It’s everywhere ….

16. Hot x-ray gas: As we have seen, clusters are full of hot x-ray gas –T ~ 10 7 – 10 8 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

17. X-ray spectrum of Coma, Henriksen & Mushotsky (1986) 9 x 10 7 K

18. Masses of clusters from x-ray gas: If we assume the cluster is in hydrostatic equilibrium, –dP/dr = -(GM(r)/r 2 ) ,  =density of the gas, P=pressure –From the ideal gas law: P= (  /  m H )kT,  = mean molecular weight (~0.6 for an ionized plasma), m H = mass of the hydrogen atom, k=Boltzman constant –So, dP/dr = (k/  m H )(T d  /dr +  dT/dr) = -(GM(r)/r 2 )  –(kT/  m H )(r/  d  /dr + r/T dT/dr) = -(GM(r)/r 2 )  –kT/  m H G (dln  /dlnr + dlnT/dlnr) = -M(r)/ r –And finally, M(r) = -kT/  m H G (dln  /dlnr + dlnT/dlnr) r –If the gas is isothermal, dlnT/dlnR = 0, so –M(r) = -kT/  m H G (dln  /dlnr) r

19. Masses of clusters from x-ray gas: We have: M(r) = -kT/  m H G (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 10 14 M  –But the gaseous mass (from x-ray luminosity) is only ~ 4 – 5.5 x 10 13 M  –Typical cluster masses: Total: 5 x 10 14 M  to 5 x 10 15 M  Luminous mass: ~5% Gaseous mass: 10-30% Dark matter: 60-85% !!!!!

20. Masses from Gravitational lensing:

21. Gravitational lensing When  = 0, or the source is directly behind the lens, we have an Einstein ring at an angle:  E = (4GM/c 2 ) 1/2 x (D ds /D s D d ) 1/2 We can also define a critical density,  crit = (c 2 /4  G) x (D s /D d D ds ), such that lensing occurs when the surface density, M(  crit The geometry of a non-point source lensing mass is much more complex, but can be modeled to determine the mass distribution of the cluster. In general arcs (due to the non-symmetry of the cluster mass distribution) are formed near the critical curve defined by  =  E, when  is small. The enclosed mass can be measured by the radius of the arcs.

22. Fort & Mellier 1994

25. z=5.58 or 12.6 billion light years

26. z~7 or 12.9 billion light years Kneib et al., Feb 15. 2004!

27. Probable z~7 galaxy or 12.9 billion light years Kneib et al., Feb 15. 2004!

28. Probable z~7 galaxy or 12.9 billion light years Kneib et al., Feb 15. 2004!

30. Cluster masses from gravitational lensing: Strong lensing constraints: –A370M~5x10 13 h -1 M/L ~270h –A2390M~8x10 13 h -1 M/L ~240h –MS2137M~3x10 13 h -1 M/L ~500h –A2218M~1.4x10 14 h -1 M/L ~360h Weak lensing constraints (a subset): –MS1224M/L ~800h –A1689M/L ~400h –CL1455M/L ~520h –A2218M/L ~310h –CL0016M/L ~180h –A851M/L ~200h –A2163M/L ~300h Yep, lots o’ dark matter!