The effect of dust on vortices II: Streaming instabilities

Abstract One of the main questions in planet formation theory is how to cross the metre-scale barrier. In this two-part series, we assess the merits of vortex-based theories by investigating the effect of backreacting dust on vortices. Specifically, this second paper focuses on the ‘turbulent’ vortex theory, according to which the streaming instability (SI) might be active in vortices. We re-purpose the dusty vortex models derived in paper I as background flows for a linear stability analysis. To simplify the perturbation equations, we build an analogue of the shearing box that follows vortex streamlines instead of Keplerian orbits. This allows us to study the evolution of small wavelength perturbations. We find that inertial waves and dust density waves can propagate in vortices, but that they are not sinusoidal in time. We then extend resonant drag instability theory to these non-modal waves. This allows us to demonstrate that a close cousin of the SI remains active in vortices, a result that greatly strengthens the case for vortex-induced planetesimal formation. Our results also complement past simulations – which showed that the dust’s backreaction makes vortices unstable – by providing insights into the nature of (some of) the unstable modes. The caveat is that our work is restricted to the limit of dilute well-coupled dust and to the linear phase of the instability. Finally, our ‘vortex SI’ extends to 2D. We explain the mechanism of this ‘zonal flow RDI’, but remain unsure whether it is the unknown instability seen in 2D vortex simulations.