SELF-GRAVITATING POLAR RINGS IN AXISYMMETRICAL AND TRIAXIAL GALAXY POTENTIALS

A number of early type galaxies show a polar ring Of gas, dust, and stars lying roughly perpendicular to the apparent major axis of the central galaxy. Here, we study the dynamics of a self-gravitating annulus of matter which is inclined to the principal planes of a triaxial galactic potential tumbling about its short axis. In a steadily precessing equilibrium state, the precession rate of the ring in the potential must be equal to the tumbling speed of the triaxial figure. As in an oblate galaxy, both stable and unstable equilibria exist: in the tumbling triaxial potential, there are stable equilibria bending toward the equator, 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 polar rings. In an oblate galaxy potential, even if the ring is not sufficiently massive to be stabilized, self-gravity can still cause the characteristic warp up toward the pole. In the triaxial potential, when the inclination of the polar ring is not such that its precession rate matches the galaxy tumbling speed, the ring can wobble gently in a quasiperiodic manner if it is massive enough, but is disrupted if its mass is too low.