The Stability of Thick, Self-Gravitating Disks in Protostellar Systems.

We perform a computational survey of the stability of protostellar systems which contain a self-gravitating disk. The systems are initially represented by a point mass $M\sb{c}$ at the center and a geometrically thick, axisymmetric disk of mass $M\sb{d}$ 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: $M\sb{d}/M\sb{c}$ and $T/\vert W\vert$ (the ratio of rotational kinetic energy of the disk to the gravitational potential energy of the system). The focus of this work is the identification of systems within this two-dimensional parameter space that are marginally unstable toward the development of nonaxisymmetric distortions. The geometric form of the disk\u27s distortion and the likelihood of disk fragmentation as a result of such instabilities is examined with particular attention given to the formation of binary systems. The principal conclusions of this work are: (a) A computer code which results in data that does not require the application of numerical corrections is essential for the identification of marginally unstable models. (b) Models in which the central object is constrained to remain at the center of mass of the system show two principal instabilities, one supplanting the other as the stability of cooler systems is explored. (c) Models in which the central object is allowed to move and interact dynamically with the disk indicate that two new instabilities emerge. These new instabilities arise in disks that appear to be stable when the central object is constrained not to move. The instability occurring in the marginally unstable systems promotes the development of a tightly wound, one-armed spiral perturbation in the disk. (d) Disk fragmentation via the one-armed spiral mode is consistent with observations indicating that binary formation is the principal branch of the stellar formation process