AY202a Galaxies & Dynamics Lecture 17: Galaxy Groups & Clusters continued

And  V = | V 1 - V 2 | < V lim (V 1,V 2,m 1,m 2 ) with two choices, either fix  V or scale it as  D. Then select D lim and V lim 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 = σ P (km/s) R PV (Mpc) log M V /L K Log M P /L K Ω M,V 0.14+/ /-0.02 Ω M,P 0.23+/ / V=Virial Estimator P = Projected Mass

# Density versus redshift for various group surveys:

Cluster Classification Just like galaxies, clusters classified morphologically. Overall Compact Medium Compact Open Linear Bautz 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 < z < 0.83

Optical Substructure (Geller & Beers ’82)

Cluster Morphology Irregular A1367 A262 Regular A2256 A85 (Jones & Forman ’84)

A2029 A2142 Hydra

Perrseus A. Fabian

Physics of Galaxy Clusters To 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[(R 2 +z 2 ) ½ ] dz = 2  where z is the coordinate along the l.o.s. and R is the projected radius ∞ -∞ r n(r) dr (r 2 – R 2 ) ½ ∞R∞R

Hydrostatic Equilibrium Good basic model for the hot gas is to assume Hydrostatic Equilibrium dP g /dr = -  g GM(r)/r 2 P =  where g means gas  = + differentiating the gas law  { + } = -  g GM(r)/r 2  M(r) = { + } kT  m p dP g d  g kT  g k dT dr dr  m p  m p dr k T d  g  g dT  m p dr dr - rT d ln  g d ln T G  m p d ln r d ln r density & temperature gradients

You can also treat the galaxies this way, just as a “gas” of much more massive particles =  gal P gal = 1/3  gal = n k Tgal  = and we can compare the gas and galaxy distributions since they are living in the same potential. dP gal GM dr r 2 dP gal kT gas 1 d  gas 3  gal dr  m p  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 I X (r)  [ 1 + (b/r c ) 2 ] -3β + 1/2  gas  gal  0,gas  0,gal  m p  m p  2 los 3 k T kT X-ray surface intensity and r c = optical galaxy core radius

Other Dynamical Quantities Crossing Time t cross ~ R/  ~ 2 x 10 9 yr for R=R A 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 t relax ~ t cross (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 = ε υ = ( ) ½ e -hυ/kT g ff (T,υ) where n e and n i are the number density of electrons and ions, Z is the ion charge and g ff 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 e ff  3.0 x (T / 1K) ½ (n e / 1 cm -3 ) 2 erg cm -3 s  Z 2 e 6 n e n i 2  3 m e c 3 3kT m e

When line emission is included: ε total  6.2 x (T / 1K) ½ (n e / 1 cm -3 ) 2 erg cm -3 s -1

Use X-ray features to study Chemistry (c.f. Mushotzsky)

A Case Study - The Virgo Cluster Assume D = 16 Mpc (HST Key Project) Zw-B(0) magnitudes 6 o Core  v = 716 km/s r H ~ 0.8 Mpc M P ~ 8 x M  M/L B ~ 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