Models for Anisotropic Spherical Stellar Systems with a Central Point Mass and Keplerian Falloff Velocity Dispersions

We add to the lore of spherical, stellar-system models a two-parameter familywith an anisotropic velocity dispersion, and a central point mass (``blackhole''). The ratio of the tangential to radial dispersions, is constant--andconstitutes the first parameter--while each decreases with radius as r^{-1/2}.The second parameter is the ratio of the central point mass to the total mass.The Jeans equation is solved to give the density law in closed form: rho\propto(r/r0)^{-c}/[1+(r/r0)^{3-c}]^2, where r0 is an arbitrary scale factor. The twoparameters enter the density law only through their combination c. At thesuggestion of Tremaine, we also explore models with only the root-sum-square ofthe velocities having a Keplerian run, but with a variable anisotropy ratio.This gives rise to a more versatile class of models, with analytic expressionsfor the density law and the dispersion runs, which contain more than oneradius-scale parameter.Comment: 10 pages. Final version to appear in ApJ; minor addition