INTRINSIC NONAXISYMMETRIC INSTABILITIES IN GALAXY RINGS

We have investigated numerically the stability and temporal evolution of two-dimensional self-gravitating galaxy rings with flat rotation cu rves. The initial equilibrium models are composed of a polytropic flui d characterized by various polytropic indices (n = 0.5, 1, 1.5, 3, and 5) and embedded in a rigid scale-free logarithmic potential, but the fluid is evolved as an ideal gas with specific heat ratio gamma = 5/3. Massless and very low-mass rings are unconditionally stable against b oth self-gravity driven modes and convective modes. As the self-gravit y is increased, one of three nonaxisymmetric modes of instability soon appears, depending on the polytropic index and the radial extent: Jea ns modes (J-modes) for n = 5 rings; Intermediate modes (I-modes) for 1 less than or equal to n less than or equal to 3 and for slender n = 0 .5 rings; and gravity modes (g-modes), along with nonlinear I-modes, f or extended n = 0.5 rings. The radial thickness of the orbiting fluid also influences the growth of these modes: more (less) extended rings require more (less) mass in order to develop an instability. If v(p) i s the characteristic speed dictated by the potential and v(o) is the t rue orbital speed in the rings, then these instabilities operate for v alues of v(p)/v(o) less than or equal to 0.95-0.99 (ring-to-galaxy mas s ratios approximately greater than or similar to 0.11-0.02). At sligh tly higher mass ratios, strong unstable modes commonly cause a tempora ry breakup of the rings and the formation of new, lumpy but long-lived , ring structures. The entire process is completed within typically 3 orbits (J-modes) to 6-10 orbits (I-modes). Thus, neither nuclear rings in barred galaxies or in active galactic nuclei, nor (co)counter-rota ting ''cores'' or polar rings in elliptical/S0 galaxies can safely acc umulate matter through accretion and survive in a smooth form. In part icular, some lumpy or distorted circumnuclear rings seen in barred gal axies may be due to the acting I-modes or J-modes that set in as soon as the accreted masses outgrow the relatively small critical value giv en above. Furthermore, the surprising absence of unstable g-modes from many models with n less than or equal to 1.5 which do not satisfy the Richardson stability criterion suggests that galaxy rings exhibit dyn amical properties that cannot be identified by studying infinite cylin drical/annular models. Counter to intuition, the g-modes are absent be cause the shear and rotation rates are high in mildly compressible pla nar rings with flat rotation curves. (C) 1997 Elsevier Science B.V.