Secular Instability and Planetesimal Formation in the Dust Layer

Late in the gaseous phase of a protostellar disk, centimeter-sized bodies probably settle into a thin dust layer at the midplane. A velocity difference between the dust layer and the gas gives rise to turbulence, which prevents further settling and direct gravitational instability of the layer. The associated drag on the surface of the layer causes orbital decay in a few thousand years - as opposed to a few hundred years for an isolated meter-sized body. Within this widely accepted theoretical framework, we show that the turbulent drag causes radial instabilities even if the self-gravity of the layer is negligible. We formulate axisymmetric, height-integrated dynamical equations for the layer that incorporate turbulent diffusion of mass and momentum in radius and height, vertical settling, self-gravity, and resistance to compression due to gas entrained within the dust layer. In steady state, the equations describe the inward radial drift of a uniform dust layer. In perturbation, overdense rings form on an orbital timescale with widths comparable to the dust-layer thickness. Self-gravity is almost irrelevant to the linear growth rate but will eventually fragment and collapse the rings into planetesimals larger than a kilometer. We estimate that the drag instability is most efficient at 1 AU when most of the dust mass lies in the size range 0.1-3 m.