Clusters Background Information: Cluster Masses Clusters Home

Now we have the characteristic speed, or velocity dispersion of the cluster as well as its effective radius (Re). How do we put these together to get the mass?

We used the virial theorem to show that, for a small object orbiting a more massive one, we could get the mass of the bigger object from

But the fact that a cluster of galaxies is an extended structure, and we are using slightly different measures of velocity and size than in the case of simple orbital motion, we need to modify this slightly. For our case, a better approximation is

Now, realize that this is a very simple approximation, and accurate only to within a factor a few. Nonetheless it gives some interesting numbers for cluster masses. What we find is that cluster masses range from 1013 solar masses for small groups to 1015 - 1016 solar masses for rich clusters of galaxies. Remember, for comparison, the Milky Way's mass is 5x1011 solar masses or so, so a rich cluster might be 10,000x more massive than the Milky Way!