Anisotropic Spherical Systems

Abstract

For the systems we have so far discussed f has been restricted to be a function of energy alone, even though we have already shown that for a general non-rotating spherical stellar system, we expect f = f(E, J ²). In this chapter we shall consider these more general cases, where the pressure inside the system is anisotropic. We shall prove the existence of a purely growing instability in all spherical stellar systems for which the distribution function strongly favours radial orbits over orbits with the same energy and higher angular momentum. Such systems are likely to be the most relevant to real galaxies as evidence of high central velocity dispersion in galaxies is indicative of strong radial anisotropy [147], and such steep rises in velocity dispersions have been observed in the nuclei of nearby galaxies [51].