Potential-density pairs for galaxies

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Abstract
A new class of triaxial potential-density pairs, which consists of an infinite number of families, is presented. The first family corresponds to density distributions that decrease not faster than r−2 at large radii r, and hence is relevant for galaxies with massive haloes. It includes as special cases Binney's logarithmic potential, and the scale-free models of Richstone and Toomre. The second family is the family of Stäckel potentials, studied elsewhere. The associated density distributions fall off as r−4 or slower. The mass models belonging to the higher order families may have steeper density profiles. The whole class is ‘generated’ by a set of exactly ellipsoidal density distributions, analogous to the Ferrers ellipsoids. Many properties of the models resemble closely those of the Stäckel models. In particular, specification of the density profile along the short axis is sufficient to determine not only the whole density distribution that has a potential of the assumed form, but also the potential itself. It is shown that each of the present models is related to a Stäckel model and vice versa. As an example a simple mass model with a logarithmic potential and a nearly ellipsoidal density distribution is introduced. The related Stäckel model is a triaxial generalization of Hénon's isochrone. An ellipsoidal mass model with a density profile similar to the Jaffe profile is presented also. The orbital structure in three potentials of the first family is compared. The main periodic orbits are nearly unaffected by an appreciable change in the isophotal shapes, but the extent of the stochastic zone is.

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