Just as with clusters of stars, clusters of galaxies may be isolated collections of masses interacting gravitationally. As such, they are interesting systems to understand. In addition, by studying the gravitational interactions, we learn about the masses of the individual galaxies and the cluster as a whole. It has been found that the number of galaxies per unit area in a cluster falls off approximately as exp[—(r/r0)1/4]. This is the same as the surface brightness in elliptical galaxies. We know that ellipticals are dynamically relaxed systems. If clusters and ellipticals have similar density distributions, then this suggests that some of the clusters are dynamically relaxed also.
Example 18.1 Crossing time for a cluster of galaxies
The time for a galaxy to cross from one side of a cluster to the other is called the crossing time. Find the crossing time for a cluster of galaxies with an extent of 1 Mpc, and galaxies moving at 103 km/s.
The time for a galaxy to cross is the diameter divided by the speed, so tcross = (106 pc)(3 X 1018 cm/pc)/(108 cm/s)
We think that clusters of galaxies have been around for over 1010 years (the age of our galaxy as determined from globular cluster HR diagrams). If they were not gravitationally bound they would have had many crossing times to evaporate. We therefore think that clusters are gravitationally bound. They have also had sufficient time to become relaxed, so we can apply the virial theorem to analyze their internal motions (Fig. 18.3).
Distribution of galax-ies.This is a two-dimensional view as seen from the Earth. It is from the APM Galaxy Survey, which detected over two million galaxies, covering approximately one-tenth of the whole sky.This image covers a region of about 100° X 50° about the South Galactic Pole.The intensities of each pixel are scaled by the number of galaxies in that pixel. [Steven Maddox, Nottingham University]
In terms of the internal motions, the virial mass is given by equation (13.47):
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