The effects of an extended background on a cluster have more in common with those of a central point mass than might first seem to meet the eye. In both cases the stellar orbits are dominated by an external mass distribution, not by their own selfconsistent gravitational field. One result is that the basic physical processes discussed in Part I must be averaged over the particular distribution of orbits for each system.

Observational evidence for a distributed background comes from several sources. Rotation curves of galaxies, particularly of giant spirals measured with 21cm emission from neutral hydrogen clouds, sometimes appear to be flat far beyond the optical image of the galaxy. This non-Keplerian relation between distance and velocity may indicate a halo surrounding the galaxy. Its total mass is very uncertain. To produce a significant dynamical effect it would have to be at least comparable with the stellar mass of the galaxy, and it could be much larger. The nature of this halo is unknown. Within galaxies, the orbits of globular clusters are dominated by the distributed stellar background, and possibly by the halo as well.

On a larger scale, Sections 41 and 42 already described the ‘missing mass’ problem for clusters of galaxies. The resolution of the problem may involve an unseen mass distributed throughout the cluster. The mass of very hot intracluster gas found in X-ray emission is usually an order of magnitude too small.