The Structure and Stability of Selected, 2-D Self-Gravitating Systems.

Models of radially and vertically extended self-gravitating disks orbiting around a central point mass are relevant to the dynamics of astrophysical systems and are thought to be common in many galaxies. The gravity driven instabilities in these accretion disks are now believed to be a possible mechanism for star formation via disk fragmentation (Shu, Adams, & Lizano 1987, Adams, Rudin & Shu 1989; Christodoulou 1995). We quantify these regions of instability using a simple toroidal model of an accretion disk. We choose the two-dimensional axisymmetric, incompressible slender disks to examine and map out these principal modes of gravity driven instabilities. Through stability analyses and numerical simulations we have found that only the gravity driven intermediate modes (see Goodman and Narayan 1988) are important in all self-gravitating accretion disks with small or moderate axis ratios. The P-mode instability found by Papalaizou and Pringle (1983) is unlikely to play a role in the dynamics of realistic disk systems. Next, we extend the existing numerical methods for constructing equilibrium structures to include nonaxisymmetric systems. We have developed a new computational technique to obtain two-dimensional, nonaxisymmetric, compressible systems with nontrivial internal motions. We have constructed two types of two-dimensional configurations: infinite cylinders and infinitesimally thin disks. The infinite cylinders have been primarily restricted to elliptic-like boundaries but the disks have exhibited much more flexibility in their geometries. At smaller axis ratios, they become dumbbells or loosely coupled binaries. The topology and dynamics of the flow is governed by the presence of vortices and stagnation points. In our simulation it is shown that there are equilibrium configurations that can only exist in the presence of internal differential motions and not in uniformly rotating models. This indicates that in general, the equilibrium structures of these nonaxisymmetric configurations are dependent not just on the constant frame rotation but perhaps even more importantly on the internal differential fluid motion. This is especially important when we construct nonaxisymmetric models with high T/$\vert$W$\vert,$ where T and W are the kinetic and the gravitational potential energy respectively. In these systems, most of the contribution to T/$\vert$W$\vert$ comes from internal rotation