Numerical experiments on the stability of preplanetary disks

Gravitational stability of gaseous protostellar disks is relevant to theories of planetary formation. Stable gas disks favor formation of planetesimals by the accumulation of solid material; unstable disks allow the possibility of direct condensation of gaseous protoplanets. We present the results of numerical experiments designed to test the stability of thin disks against large-scale, self-gravitational disruption. The disks are represented by a distribution of about 6 × 10⁴ point masses on a two-dimensional (r, φ) grid. The motions of the particles in the self-consistent gravity field are calculated, and the evolving density distributions are examined for instabilities. Two parameters that have major influences on stability are varied: the initial temperature of the disk (represented by an imposed velocity dispersion), and the mass of the protostar relative to that of the disk. It is found that a disk as massive as 1M_⊙, surrounding a 1M_⊙ protostar, can be stable against long-wavelength gravitational disruption if its temperature is about 300°K or greater. Stability of a cooler disk requires that it be less massive, but even at 100°K a stable disk can have an appreciable fraction ($\text{～}\text{1}\text{3}$) of a solar mass.