On dust-gas gravitational instabilities in protoplanetary discs

Abstract: In protoplanetary disks the aerodynamical friction between particles and gas induces a variety of instabilities that facilitate planet formation. Of these we examine the so-called `secular gravitational instability' (SGI) in the two-fluid approximation, deriving analytical expressions for its stability criteria and growth rates. Concurrently, we present a physical explanation of the instability that shows how it manifests upon an intermediate range of lengthscales exhibiting geostrophic balance in the gas component. In contrast to a single-fluid treatment, the SGI is quenched within a critical disk radius, as large as 10 AU and 30 AU for cm and mm sized particles respectively, although establishing robust estimates is hampered by uncertainties in the parameters (especially the strength of turbulence) and deficiencies in the razor-thin disk model we employ. It is unlikely, however, that the SGI is relevant for well-coupled dust. We conclude by applying these results to the question of planetesimal formation and the provenance of large-scale dust rings.