OBLATE GALAXY MODELS WITH THIN TUBE ORBITS

The general theory for the construction of oblate Stäckel models containing only infinitesimally thin short-axis tube orbits is presented. These models connect the well-known spherical systems built exclusively with circular orbits with similar axisymmetric disks and are useful for the interpretation of the internal velocity fields of galaxies. It is shown that the phase-space distribution function for these thin orbit models is unique and can be found as the solution of a one-dimensional Abel integral equation. An explicit expression for the mean streaming velocity is derived for the case of maximum rotation, and the velocity dispersions are calculated by direct solution of the Jeans equations. As an example, the Kuzmin-Kutuzov mass models are considered. They connect Hénon's spherical isochrone with Kuzmin's circular disk. Most of the properties of their thin orbit equilibrium models, including the distribution function itself, can be given in terms of elementary functions.