SELF-GRAVITATING POLAR RINGS IN AXISYMMETRICAL AND TRIAXIAL GALAXY POTENTIALS

A number of early type galaxies show a polar ring Of gas, dust, and st ars lying roughly perpendicular to the apparent major axis of the cent ral galaxy. Here, we study the dynamics of a self-gravitating annulus of matter which is inclined to the principal planes of a triaxial gala ctic potential tumbling about its short axis. In a steadily precessing equilibrium state, the precession rate of the ring in the potential m ust be equal to the tumbling speed of the triaxial figure. As in an ob late galaxy, both stable and unstable equilibria exist: in the tumblin g triaxial potential, there are stable equilibria bending toward the e quator, if the ring is light, and toward the pole, at higher ring mass . The former are similar to the ''anomalous retrograde orbits,'' while the latter resemble the stable equilibria for a self-gravitating ring in an oblate potential. We follow the time evolution of unstable pola r rings. In an oblate galaxy potential, even if the ring is not suffic iently massive to be stabilized, self-gravity can still cause the char acteristic warp up toward the pole. In the triaxial potential, when th e inclination of the polar ring is not such that its precession rate m atches the galaxy tumbling speed, the ring can wobble gently in a quas iperiodic manner if it is massive enough, but is disrupted if its mass is too low.