Spherical Systems with Rotation

Abstract

We have so far discussed the stability of non-rotating systems and suggested that the results may be applicable to some giant elliptical galaxies and to the discussion of the evidence for a central black hole in the cores of galaxies. In general, however, galaxies do have some rotation albeit small in many cases. The question is how dependent are the results we have so far derived on the fact that we have assumed zero rotation, and whether they can be applied to real galaxies. In this chapter we shall consider this question and show that the results are indeed still valid even if there is a small amount of rotation, although clearly strongly rotating systems will behave quite differently. We shall discuss how the evolution of the radial orbit instability is affected by adding a small amount of rotation to the system and give a physical interpretation of the analysis.