Elliptical galaxies with separable potentials
Abstract
The perfect ellipsoid is presented: an inhomogeneous triaxial mass model with a gravitational potential that is of Stäckel form. The equations of motion are separable in ellipsoidal coordinates and all stellar orbits have three isolating integrals that are known explicitly. The orbital structure in the perfect ellipsoid is generic for all centrally concentrated triaxial mass models with a finite central density and a Stäckel potential, and it is tractable by analytic means. The orbital shapes are classified in terms of the values of the integrals of motion. Individual orbit densities can be computed without integration of the equations of motion, and some examples are shown. The relevance of mass models with Stäckel potentials for the construction of selfconsistent models of elliptical galaxies is discussed.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 1985
 DOI:
 10.1093/mnras/216.2.273
 Bibcode:
 1985MNRAS.216..273D
 Keywords:

 Celestial Mechanics;
 Elliptical Galaxies;
 Equations Of Motion;
 Galactic Structure;
 Gravitational Fields;
 Stellar Orbits;
 Astronomical Models;
 Density Distribution;
 Many Body Problem;
 Mass Distribution;
 Astrophysics