1. Clusters & Super Clusters Large Scale Structure Chapter 22

2. ~Half of all galaxies are in: clusters (mostly Es and S0s; mass > few times 10 14 to 10 15 M sun ) or groups (less dense; more Sp and Irr; less than 10 14 M sun ) Clusters  contain 100s to 1000s of gravitationally bound galaxies  Typically ~few Mpc across  Central Mpc contains 50 to 100 luminous galaxies (L > 2 x 10 10 L sun )  Abell’s catalogs (1958; 1989) include 4073 rich clusters Coma Cluster  Nearest clusters are Virgo and Fornax (containing 1000’s of galaxies; d=15-20 Mpc)  Richer cluster, Coma, at d=100 Mpc and several Mpc across, contains ~10,000 galaxies  Clusters filled with hot gas (T=10 7 – 10 8 K making them X-ray bright) Galaxy Clusters & Groups

3.  smaller than clusters  Contain less than ~100 galaxies  Loosely (but still gravitationally) bound  Contain more spirals and irregular galaxies than clusters “The Local Group” Groups

4. Compare relative sizes of groups and clusters

5.  Projected density of galaxies in a cluster drops as r 1/4 (similar to surface brightness of elliptical galaxies)  Crossing time in a typical cluster (galaxy moving at 1000 km/s, cluster size 1 Mpc)  10 9 years  Thus, clusters must be gravitationally bound systems and have possibly had enough time to “relax” M = 2 x 10 15 M sun If clusters are relaxed systems, we can use the virial theorem to estimate their masses M = 7.5(σ 2 R h /G) eq. 20.20 & 22.5 Now galaxies, rather than stars, are the masses whose line-of-sight velocities we measure. For Coma cluster, σ= 880 km/s and R h = 1.5 Mpc, what is mass?

6. Luminous matter does not make up this mass L B ~ 8 x 10 12 L B,sun M/L B ~ 250 M sun /L B,sun Adding up mass in DM halos of spiral galaxies still not enough Look for mass in hot, intracluster gas – Temp =10 7 to 10 8 K Estimate gas mass from diffuse X-ray emission Significant mass in gas – can be up to 10 times stellar mass Dynamical (virial) measurements indicate this accounts for about 10% to 20% of the mass... Clusters have a Dark Matter problem too...

7. Mass appears to be contained in individual galaxy halos that extend further than we can measure Clusters have their own Dark Matter halos as well M/L ratios for clusters is ~200:1 Example of dark matter evidence in clusters (and the exotic nature of DM)  The Bullet Cluster

8. Galaxy Mergers How common is it for objects to run into each other in space? Derive the time between collisions for an object with size R, velocity v in an environment with number density n  t = 1/(nv4πR 2 ) For Coma: galaxy sizes are ~ 1.3 x 10 11 R , v ~ √3 x 880 km/s = 1500 km/s, n ~ 3.5 x 10 -16 pc -3 gives t = 17 Gyr or 1.2 H o -1 (galaxy has on average a 50/50 chance of colliding) *Note that when galaxies collide, individual stars do not normally collide due to their tiny cross-sections Depending on conditions, galaxies may interact but not merge. Even small interactions can cause an increase in the entropy of the stellar system (i.e. thickens spiral disk).

9. Many clusters have a central dominant or cD galaxy at their center (e.g. M87 in Virgo) contain multiple nuclei could come from merger of central galaxies galactic “cannibalism” Numerical n-body simulations reveal what happens to the stars and gas when two galaxies collide and merge.

10. Are there structures larger than clusters? YES Local Supercluster - 10 6 galaxies about 30 Mpc across Can’t get mass with virial theorem Crossing times are too large, systems are not relaxed – just now collapsing In addition to superclusters, large scale structure of galaxies reveals large voids

11. Redshift surveys of distant galaxies reveal the 3-d large-scale structure in the Universe Galaxies appear to sit on 3-d surfaces (e.g. bubbles, sponges); structures are flattened along these surfaces Voids are ~50 Mpc across and more spherical Survey magnitude limit appears as galaxy “thinning” beyond z=0.15, but we an assume this structure continues…

12. Other redshift surveys:

13. Where does the structure come from? Top-down: Large scale structures form first (superclusters, voids) followed by smaller structures forming out of the matter Bottom-up: Small scale structures (i.e. galaxies) form first and then come together to form larger scale structures. Which is it?

14. Millennium Simulation Compares large galaxy surveys with simulations designed to model the data Assumes cold dark matter dominates Universe N-body simulation with particles interacting gravitationally 10 10 particles mapped from early times in the Universe to the present in cubes 700 Mpc on a side

15. Galaxies Dark Matter

16. The simulation shows that structure forms more along the lines of the “bottom-up” model (i.e. galaxies form first), but that these form in the already over-dense regions of the dark matter distribution. Redshift z=0 (t = 13.6 Gyr) Redshift z=1.4 (t = 4.7 Gyr) Redshift z=5.7 (t = 1.0 Gyr) Redshift z=18.3 (t = 0.21 Gyr)

17. Galaxy Luminosity Function A census of galaxies over a large enough region of space gives the number density of galaxies as a function of luminosity Φ is the number density of galaxies with luminosity between L and dL The “knee” of the distribution (where the exponential drop off in the LF occurs) is at L * = 2 x 10 10 L sun ~ L MW LF is weighted towards dim galaxies with α = -1.2 If we integrate Φ(L) weighted by L we get the luminosity density of the observable universe ~ 40 watt light bulb inside sphere of 1 AU radius!