# Galaxy Cluster Properties

Galaxies occur both in the field and in clusters. Most galaxies live in the field or in small groups; only ~ 20% live in big clusters.

Clusters vary greatly in properties:

 Group Rich Cluster Number of Galaxies 10s 100s - 1000s Size 1-2 Mpc 5-7 Mpc Velocity Dispersion ~ few 100s km/s 500 - 1000 km/s Masses 1013 Msun 1015 Msun

We live in the Local Group :

• 3 biggish spirals: Andromeda (M31), Milky Way, M33
• relatively bright companions: LMC, SMC (Milky Way); M32, NGC 205 (Andromeda)
• lots of small, low luminsosity dwarf ellipticals and and dwarf spheroidals
• no big ellipticals!

The M96 Group, aka The Leo Group (Watkins et al 2014):

The nearest galaxy cluster is the Virgo Cluster, at a distance of 16 Mpc. It is comprised of about classified 250 large galaxies (and 10x more smaller ones), and is classified as an irregular cluster , meaning that rather than being a "spherical" cluster, it has a lot of substructure.

The core of Virgo, Mihos et al 2005

Virgo is a spiral-rich cluster. ~ 20% of the bright galaxies are ellipticals, the rest are spirals. But the faint galaxies are mostly dwarf ellipticals...

Virgo is not only filled with galaxies, but also with hot gas:

Left: X-ray image; right: optical image

Further away is a very massive cluster: the Coma cluster, at a distance of about 100 Mpc. Coma is about 6 Mpc in size and contains perhaps 10,000 galaxies. Very few of the galaxies in Coma are spiral; most are elliptical and S0.

The Coma Cluster, courtesy Adam Block

## How can we get the mass of a cluster?

Method 1:
If we assume the cluster is in virial equilibrium, we can use the velocities of the galaxies. The virial equation relates the kinetic energy (K) and potential energy (U) of a system in equilibrium as:

So what is the kinetic energy of the cluster? If we look at the galaxies, they would have a total kinetic energy of

where v is their full space velocity and sigma is the line of sight velocity dispersion of the galaxies in the cluster.

What about the gravitational potential energy of the cluster? For a uniform density sphere:

So we can solve for the total mass of the cluster:

Method 2: Another way to get the mass of the cluster is to use assume the X-ray gas is in hydrostatic equilibrium (ASTR221 hydrostatic equilibrium notes). This means that the thermal pressure of the gas is in equilibrium with the gravitational potential:

Using the density and temperature of the hot gas you can then solve for the cluster mass.

Method 3: A third way of measuring the mass of the cluster is to count up all the galaxies, adopt a mass-to-light ratio for each one to determine their mass, and then tally up the mass directly.

The first two answers give reasonably consistent results. The third answer is an order of magnitude too small. What does this mean? Either:

• Virial equilibrium and hydrostatic equilibrium are bad assumptions. In this case the cluster is flying apart, because the velocities of the galaxies are greater than the binding mass. Probably not correct -- we see lots of clusters, they are not transient objects.

•
• Dark matter exists on large scales in clusters!
• Cluster content: 10% galaxies, 20% hot gas, 70% dark matter