Nonaxisymmetric Instabilities in Self-Gravitating Disks: Linear and Quasi-linear Regimes

We calculated the angular momentum transport that arises from global nonaxisymmetric hydrodynamic instabilities in inviscid, self-gravitating, polytropic disks surrounding point-mass stars in the quasi-linear regime. We first determined the properties of nonaxisymmetric disk modes with azimuthal dependence e(im phi) in the linear regime. We found that nearly all disks tested were unstable, even those with Toomre Q > 1, and that m = 1 modes were usually the dominant mode. Using our linear results, we calculated quasi-linear torques for insight into the angular momentum transport expected in nonlinear simulations. Jeans-like J modes dominate disks when self-gravity is important and gravitational stress drives angular momentum transport. Shear-driven P and edge modes dominate disks with weak self-gravity and the Reynolds stress drives angular momentum transport. Intermediate modes, I modes arise in disks with properties between those where J modes are dominant and those where P and edge modes are dominant and gravitational and Reynolds stresses both drive angular momentum transport.