Mass models with Stackel potentials

Triaxial mass models with a gravitational potential of Stäckel form in ellipsoidal coordinates are investigated. Models are constructed by specification of the z-axis density profile ψ(z) choice of an ellipsoidal coordinate system, and subsequent application of the generalized Kuzmin formula. For each profile ψ(z) there is a two-parameter family of triaxial separable models. The parameters are the positions of the two pairs of foci on the z-axis of the ellipsoidal coordinates in which the potential is of Stäckel form or, equivalently, the central axis ratios of the density distribution. Smooth mass models are generated by smooth profiles ψ(z). The density, ϱ, in these separable models cannot fall off more rapidly than r−4 as the radius |r→∞|⁠, except on the z-axis. All models in which ϱ falls off less rapidly than r−4 become round as |r→∞|⁠. Models with a singular density in the centre only do not exist. Specific examples are presented. Among these is a separable triaxial generalization of the modified Hubble model [|~(1+r²)-3/2|]. For a number of cases the potential is given explicitly.