Collisionless analogs of riemann ellipsoids: Self-consistent model of an ellipsoid with “oblique” rotation

Abstract

A new model of an ellipsoidal stellar system in which there is no equatorial plane of symmetry perpendicular to the rotation axis is constructed. In its orientation with respect to the rotation axis, the model recalls some types of Riemann fluid ellipsoids. The motion of a particle is investigated and the condition found for it to touch the boundary surface of the ellipsoid. A feature of the model is the nonvanishing of some of the nondiagonal components of the velocity dispersion tensor. The model has two independent parameters - the semiaxis ratio a/sub 2//a/sub 1/ and the angle of the orientation of the figure of the ellipsoid relative to the rotation axis. Equivalent to the latter is the ratio /eta/ = ..cap omega../sup 2//sub 3//2A/sub 2/. In the (a/sub 2//a/sub 1/, /eta/) plane, the model occupies two isolated regions. In special cases, the model is transformed into four single-parameter figures of equilibrium. Two of them do not have velocity dispersion and are mutually adjoint (in the sense of Dedekind's theorem) analogs of the Riemann ellipsoids of the second kind without pressure. The two other figures have velocity dispersion. One is a Freeman ellipsoid of given shape, and the other ismore » a degenerate model with oblique rotation in which the component of the velocity dispersion is zero in the direction perpendicular to the principal plane (in which the rotation axis lies).« less