Oblate Galaxy Models with Thin Tube Orbits
Abstract
The general theory for the construction of oblate Stackel models containing only infinitesimally thin shortaxis tube orbits is presented. These models connect the wellknown 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 phasespace distribution function for these thin orbit models is unique and can be found as the solution of a onedimensional 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 KuzminKutuzov mass models are considered. They connect Henon'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.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1990
 DOI:
 10.1086/168846
 Bibcode:
 1990ApJ...356..365D
 Keywords:

 Astronomical Models;
 Galactic Structure;
 Distribution Functions;
 Integral Equations;
 Kinematics;
 Orbital Mechanics;
 Stellar Motions;
 Velocity Distribution;
 Astrophysics;
 GALAXIES: INTERNAL MOTIONS;
 GALAXIES: STRUCTURE;
 STARS: STELLAR DYNAMICS