Diskoseismology: Probing accretion disks. II. G-Modes, gravitational radiation reaction, and viscosity

General relativity requires the existence of a spectrum of oscillations which are trapped near the inner edge of accretion disks that are terminated at the innermost marginally stable orbit. In a previous paper we applied the Lagrangian formalism of Friedman and Schutz to the study of normal modes of such thin disk models, approximating the dominant relativistic effects via a modified Newtonian potential. In this work we describe the Lagrangian perturbation vectors in terms of the derivatives of a scalar potential as has been done by Ipser and Lindblom. Using this potential, we derive a single partial differential equation governing the oscillation of a disk. The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall into two main classes which are analogous to the p-modes and g-modes in the Sun. Specifically in this work we compute the eigenfunctions and eigenfrequencies of isothermal disks, and indicate how these results can be generalized to other disk models. We also compute the (assumed) relatively small rates of growth or damping of the modes due to various mechanisms, in particular gravitational radiation reaction and parameterized models of viscosity. We find that for certain parameters the p-modes are unstable to gravitational radiation reaction (CFS instability), while both the p-modes and g-modes are unstable to viscosity unless highly anisotropic viscosity models are considered.