Local particle simulations of viscous self-gravitating disks

We present the results of a particle simulation studying the local flow of a viscous, self-gravitating disk in Keplerian motion. Our method is based on Wisdom and Tremaineʹs (Astron. J. 95.3, 925–940, 1988) local simulation of planetary rings, but includes self-gravity. We implement a new numerical prescription of interparticle viscosity that formally reduces to Navier-Stokes stresses. Inclusion of hydrodynamic Navier-Stokes-type viscous friction is essential for the system to develop a secular instability for high values of the stability parameter (Q > 1). In the framework of a linear perturbation theory wavelength and growth time of the most unstable mode are derived for a “softened” potential that is used in the simulation. The objectives of this paper are twofold: predictions regarding wavelength and growth time of a secular ring instability can be confirmed numerically. Moreover the relative density enhancement in the perturbed regions can be determined in the nonlinear particle simulation; it reaches values twice the unperturbed density. The possible relevance of this mechanism for structuring protoplanetary accretion disks and planetary rings is briefly discussed.