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(sub c) at the center and a geometrically thick, axisymmetric disk of mass M(sub 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(sub d)/M(sub c) and T/absolute value of W (the ratio of rotational kinetic energy if 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/absolute value of W at which thick disks first become dynamically unstable to nonaxisymmetric distortions is found to vary significantly with the mass ratio of the accertion disk system. Nonaxisymmetric eigenmodes with four distinctly different characters are identified in systems with mass ratios in the range 0.2 less than or equal to (M(sub d)/M(sub c)) less than or equal to 5.