THE EFFECT OF GRAVITATIONAL INSTABILITIES ON PROTOSTELLAR DISKS

This paper considers the hydrodynamical evolution of thin self-gravita ting protostellar disks. These disks are initially in equilibrium and are stable to axisymmetric perturbations, but are generally unstable t o nonaxisymmetric perturbations. The course of the nonaxisymmetric evo lution which arises from small seed perturbations is followed into the nonlinear regime for a total of 21 different initial configurations w hich cover a range of initial sound-speed profiles and disk masses. Th e growth rates, pattern speeds, and shapes of the observed spiral mode s are verified in the linear regime by comparing the results of the fi nite-difference simulations with the solutions of an appropriate linea r eigenvalue problem. Two-armed spirals tend to predominate in the dis ks studied here. Moreover, we find the interesting result that the m = 2 mode saturates at the same amplitude for a variety of initial disk parameters. The nonlinear evolution of the surface density profiles of the disks is compared with solutions of the one-dimensional diffusion equation for viscous accretion disks. A parameterization of the effec tive viscosity due to the gravitational torques which arise in the mod el disks is then formulated. We argue that although a fairly accurate parameterization can indeed be found, a description of the gravitation al instability of protostellar accretion disks in terms of an effectiv e viscosity appears to be inherently flawed, owing to the global, rath er than local, nature of the instability.