The equilibrium of a galactic bar. II - Stellar-dynamical counterparts of the s-type Riemann ellipsoids

Abstract

The family of triaxial stellar systems described in Paper I of this series is generalized to include, in addition to the previous dependence on Jacobi's integral, a dependence of the distribution function on a second isolating integral of the motion of a star in the prevailing gravitational field. The second integral is approximated with the aid of a model of the stellar orbits which is valid in the absence of important resonances and which should be accurate in the systems of relatively small central concentration on which this investigation concentrates. The new stellar systems are stellar-dynamical counterparts of the classical S-type Riemann ellipsoids well known in the study of self-gravitating fluid systems, and, within the framework of stellar dynamics, they are also three-dimensional counterparts of the elliptical disks studied by Freeman and by Hunter. The Riemann-like stellar systems form an extensive family, and they exhibit a rich interplay of effects of the rotations of their triaxial figures and effects of the dependence of their distribution functions on the second integral of the motion. The family includes stellar-dynamical counterparts of the classical Maclaurin spheroids, Jacobi ellipsoids, and Dedekind ellipsoids. The study of triaxial, Riemann-like systems is related to the study ofmore » bar modes of oscillation in corresponding axisymmetric, Maclaurin-like systems. On the basis of this relationship, it is shown that an axisymmetric stellar system having the structure of a uniformly rotating polytrope of index n = 0.5 is dynamically unstable with respect to a bar mode if the ratio of the rotational kinetic energy to the magnitude of the gravitational potential energy exceeds 0.166.« less