The Mass Contained in Clusters

Clusters of galaxies contain contain 1014 to 1015 solar masses. They must have masses of this size to explain how they are held together by gravity (see the right panel). However, only about 1/10 of this mass can be identified with matter that is emitting visible light. This is yet another manifestation of the dark matter problem. The Universe seems to contain much more mass than we can see.

Measuring the Mass of Clusters
How can we measure masses in clusters of galaxies? There are several methods at our disposal. Although none of them are completely direct, taken together they give a reliable estimate of the masses contained in clusters of galaxies.

  • We may measure rotation curves for spiral galaxies and determine the masses of individual spiral members of a cluster as we discussed earlier for our own galaxy. The rotation curves depend on measuring Doppler effects for rotating galaxies. For nearby galaxies one can resolve opposite sides of the galaxy and measure the Doppler shift separately to estimate the rotation speed. For galaxies further away the two sides cannot be resolved, but the rotation leads to broadening of spectral lines. Thus, a careful study of line broadening for distant spiral galaxies can be used to estimate rotational speeds. Such studies indicate rotation curves very similar to those found for the Milky Way, giving estimates for the mass that are factors of 10 or so larger than the luminous matter.
  • In principle, we can treat two galaxies in a cluster like we do binary stars and use Kepler's laws to determine the mass of the "binary". In practice, the motion of galaxies in clusters is too slow for us to follow the orbital motion, so this method cannot be used directly. However, it can be used in an approximate way by measuring radial velocity using Doppler methods and the present separation of the galaxies to estimate the orbit. This is not very reliable for a single pair of galaxies, but we may expect it to be more reliable when averaged over a whole set of pairs in a cluster, so it can give a reasonable estimate of the total mass of the cluster.
  • We can view the set of galaxies in the cluster as a gravitationally bound system. By studying the average motion of the members of the cluster, we can ask how large a gravitational field must be present to keep the system bound for long periods. The required gravitational field can then be related to the total mass that generates it by Newton's gravitational law.

    • All of these methods indicate large amounts non-luminous matter in clusters of galaxies. Further, they indicate that the discrepancy between "unseen" and "seen" matter is as large as a factor of 10-100.

    Hot X-Ray Gases in Clusters
    Earlier, we saw evidence that galaxies like our own have dark matter halos containing as much as 10 times the luminous matter of the galaxy. The even larger discrepancy between luminous and non-luminous matter for clusters of galaxies suggests that the dark matter is not just contained in halos associated with individual galaxies. It must also be found in the regions between the galaxies in clusters. One source of this additional mass is gas lying between the galaxies in a cluster. Superposed on an optical picture of a group of galaxies in the adjacent figure is an X-ray image taken by ROSAT. The image shows confined hot gas (which produces X-rays) highlighted in false red color.