LOCAL PARTICLE SIMULATIONS OF VISCOUS SELF-GRAVITATING DISKS

We present the results of a particle simulation studying the local how of a viscous, self-gravitating disk in Keplerian motion. Our method i s based on Wisdom and Tremaine's (Astron. J. 95.3, 925-940, 1988) loca l simulation of planetary rings, but includes self-gravity. We impleme nt a new numerical prescription of interparticle viscosity that formal ly 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 gro wth 1 time of the most unstable mode are derived for a ''softened'' po tential that is used in the simulation. The objectives of this paper a re twofold: predictions regarding wavelength and growth time of a secu lar ring instability can be confirmed numerically. Moreover the relati ve density enhancement in the perturbed regions can be determined in t he nonlinear particle simulation it reaches values twice the unperturb ed density. The possible relevance of this mechanism for structuring p rotoplanetary accretion disks and planetary rings is'-briefly discusse d.