A SURVEY OF THE PRINCIPAL MODES OF NONAXISYMMETRIC INSTABILITY IN SELF-GRAVITATING ACCRETION DISK MODELS

We present a survey of the three principal nonaxisymmetric modes of in stability (the so-called P-, I-, and J-modes) that have been found in rotating, self-gravitating, accretion disk models. The relevant equati ons that describe the equilibrium structure and the linear stability p roperties are formulated quite simply for what has turned out to be th e ''standard'' idealized model of accretion tori orbiting a central st ar, the so-called slender incompressible torus with constant specific angular momentum. In this sense, our survey is a natural extension of the work done by Goodman & Narayan. We map out the three unstable nona xisymmetric modes in this model, and we illustrate the regions of inst ability in various parameter spaces, the most important of which is th e (M(D)M(C), T/\W\)-plane, where M(D)/M(C) is the torus/central star m ass ratio and T/\W\ is the ratio of the rotational kinetic energy of t he torus to the total gravitational potential energy of the system. We place particular emphasis on this parameter space because the physica l significance of the two ratios is easily understood and because of i ts potential importance for observers, having in mind protostellar sta r/disk systems for which the mass ratio of the two components can curr ently be determined and for which the ratio T/\W\ may eventually be es timated from observations. We compare our solutions of the linearized stability equations with the results previously obtained from linear a nalyses of (in)compressible two-dimensional annular models and from no nlinear hydrodynamical simulations of compressible three-dimensional t oroidal models. The I- and J-modes are primarily driven by self-gravit y, so they appear in all models with nonzero torus mass that are suffi ciently slender; the J-modes dominate over the I-modes only in the mos t slender of the unstable models; and the corresponding regions of ins tability are not expected to be strongly dependent on the assumption o f incompressibility or on the particular choice of the angular momentu m profile. The P-modes appear only at extremely low mass ratios (M(D)/ M(C) less than or equal to 1.15 x 10(-3)) and only in extremely slende r tori (aspect ratios epsilon less than or equal to 0.02733). Thus, th ey probably play no role in the dynamical evolution of realistic disk systems such as those around protostars and compact objects in active galactic nuclei-and the I-modes emerge as the most important and dange rous modes of instability for all self-gravitating accretion disks wit h small or moderate aspect ratios.