The Effect of Gravitational Instabilities on Protostellar Disks

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Abstract
This paper considers the hydrodynamical evolution of thin self-gravitating protostellar disks. These disks are initially in equilibrium and are stable to axisymmetric perturbations, but are generally unstable to nonaxisymmetric perturbations. The course of the nonaxisymmetric evolution which arises from small seed perturbations is followed into the nonlinear regime for a total of 21 different initial configurations which cover a range of initial sound-speed profiles and disk masses. The growth rates, pattern speeds, and shapes of the observed spiral modes are verified in the linear regime by comparing the results of the finite-difference simulations with the solutions of an appropriate linear eigenvalue problem. Two-armed spirals tend to predominate in the disks 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 effective viscosity due to the gravitational torques which arise in the model disks is then formulated. We argue that although a fairly accurate parameterization can indeed be found, a description of the gravitational instability of protostellar accretion disks in terms of an effective viscosity appears to be inherently flawed, owing to the global, rather than local, nature of the instability.

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