On the Evolution and Stability of a Protoplanetary Disk Dust Layer

Abstract

In this manuscript we perform detailed analytical and numerical studies of the physical processes that result from the interaction between the dust and gas components of a protostellar accretion disk. We consider the most favorable condition for dust sedimentation in a laminar gaseous background and look at the conditions that precede the onset of gravitational and shear instability. We adopt a two-fluid formalism to examine two issues of particular interest: (1) the slow sedimentation of a laminar dust layer, for which we are able to extract self-similar solutions, and (2) the rapid growth of perturbations to that slowly settling shear flow, for which we present a linear stability analysis. We also include two fundamental physical processes that have been ignored in previous work: the specificities of the two-fluid equations compared to the single-fluid approximation, and the potentially destabilizing effect of radiative cooling by the reduction of the buoyancy of fluid motions. From these results we are able to compare the conditions for onset of gravitational and shearing instabilities for various dust-to-gas surface density ratios and nebular structures. We confirm previous findings that during the dust sedimentation, the shearing instability occurs prior to the gravitational instability unless the disk is grossly enriched up to a level where the surface density of grains is comparable to that of the gas. Finally, we discuss the implications of these results with respect to theories of planetesimal formation and observations of protoplanetary disks.