THE STABILITY OF THICK, SELF-GRAVITATING DISKS IN PROTOSTELLAR SYSTEMS

Using numerical hydrodynamics techniques, we perform a nonlinear stability analysis of accretion disk systems that contain thick, self-gravitating disks. The systems are initially represented by a point mass M, at the center and a geometrically thick, axisymmetric disk of mass M(d) that supports uniform specific angular momentum and obeys an n = 3/2, polytropic equation of state. The equilibrium disk structure is uniquely defined upon the specification of two key dimensionless system parameters: M(d)/M(c) and T/\W\ (the ratio of rotational kinetic energy of the disk to the gravitational potential energy of the system). The focus of this work is on the identification of systems within this two-dimensional parameter space that are marginally unstable toward the development of nonaxisymmetric distortions. The geometric form and relative pattern speed of the disk's distortion as well as the likelihood of disk fragmentation as a result of such instabilities is examined, particularly in the context of protostellar systems. The value of T/\W\ at which thick disks first become dynamically unstable to nonaxisymmetric distortions is found to vary significantly with the mass ratio of the accretion disk system. For example, systems in which M(d)/M(c) = 0.2 become unstable to an m = 1 azimuthal mode when T/\W\ = 0.26 and unstable to an m = 2 azimuthal mode when T/\W\ = 0.43 whereas the anologous bifurcation points for systems with M(d)/M(c) = 5 occur at T/\W\ = 0.10 and 0.24, respectively. Nonaxisymmetric eigenmodes with four distinctly different characters are identified in systems with mass ratios in the range 0.2 les-than-or-equal-to M(d)/M(c) less-than-or-equal-to 5. One is related to the Papaloizou-Pringle instability; another appears to be related to the ''I-mode'' which has been identified in linear stability analyses of slim, self-gravitating, incompressible tori; and a third, whose amplitude does not grow exponentially without bound, exhibits a behavior that is well described as Landau supercritical stability. For all systems with mass ratios in this range, however, the mode to which thick disks first become unstable resembles the ''eccentric instability'' that has been identified earlier in thin, nearly Keplerian protostellar disks: it presents an open, one-armed spiral pattern that sweeps continuously in a trailing direction through more than 2pi radians, smoothly connecting the inner and outer edges of the disk and requires cooperative motion of the point mass for effective amplification. This particular instability promotes the development of a single, self-gravitating clump of material in orbit about the point mass, so its routine appearance at the initial bifurcation point along our examined sequences supports the conjecture that the eccentric instability provides a primary route to the formation of short-period binaries in protostellar systems.