INSTABILITY OF ROTATING STELLAR-SYSTEMS WITH ELONGATED ORBITS

We discuss the influence of rotation on the instability of radial orbi ts in collisionless gravitating systems such as elliptical galaxies an d the bulges of disk galaxies. We derive and study the dispersion rela tion for an exactly soluble problem, that of small perturbations in th e simplest possible model of a rotating spherical cluster with highly elongated stellar orbits. Rotation affects the development of instabil ity in radial orbits in three ways: 1) by creating a preference for in itial perturbations corresponding to an oblate spheroid (m = 0 mode) o r a triaxial ellipsoid (m = 2 mode); 2) by determining the minimum pos sible dispersion of the precession rates of stellar orbits, given the angular momentum of the system; 3) by directly affecting the growth ra te of unstable perturbations. The latter also affects different modes in different ways. For the analytic model studied here, rotation has n o effect at all on the instability growth rate of the axisymmetric m = 0 mode, while reducing it for modes with m not-equal 0. There is obse rvational evidence [Kormendy, J. and Illingworth, G. D. (1982), Astrop hys. J. 256, 460] that the relatively rapidly rotating bulges of disk galaxies are more similar to oblate spheroids than to either prolate o r triaxial ones, and that there is a lack of appreciable correlation b etween the rotation and shape of elliptical galaxies. Our results can be considered to argue for a theory confirming the foregoing observati onal evidence.