Vertical Oscillations in Protostellar Disks. II. Free Modes and Resonances
Using the mathematical framework developed in the preceding paper, I analyze vertical oscillations in self-gravitating, protostellar disks. After calculating the equilibrium stratiÐcation, I Ðnd the set of normal modes and discuss their radiative damping. Global, spiral-type perturbations of the disks induce horizontal motions that drive these oscillations, giving rise to resonances at discrete radii. Disks with plausible distributions of surface density and temperature may contain one or more
... f these critical regions, which are always located between the corotation radius and the outer disk edge. A resonant vertical oscillation, whose amplitude saturates through radiative losses, creates a signiÐcant back-reaction on the spiral-type disturbance that drives it. I Ðnd the associated reaction force analytically and argue that its net e †ect is to stabilize the disk against the global perturbation. On the other hand, if such perturbations are to induce long-term accretion onto the central protostar, the disk must be marginally stable to their growth. Marginal stability can be maintained if the vertical resonance is always located close to the outer disk edge. This constraint is a practical boundary condition for the study of long-term disk evolution.