On the local stability of vortices in differentially rotating discs

TL;DR

This study investigates the stability of dust-laden vortices in protoplanetary discs, extending classical solutions and analyzing their susceptibility to local perturbations, which impacts planetesimal formation theories.

Contribution

It generalizes the Kida vortex solution to include dust and vorticity variations and performs a local stability analysis considering streamline perturbations.

Findings

Parametric instabilities with growth rates around 0.05Ω_P were identified.

Density excess vortices show multiple narrow instability bands.

Vorticity concentration influences internal shear and stability.

Abstract

In order to circumvent the loss of solid material through radial drift towards the central star, the trapping of dust inside persistent vortices in protoplanetary discs has often been suggested as a process that can eventually lead to planetesimal formation. Although a few special cases have been discussed, exhaustive studies of possible quasi-steady configurations available for dust-laden vortices and their stability have yet to be undertaken, thus their viability or otherwise as locations for the gravitational instability to take hold and seed planet formation is unclear. In this paper we generalise and extend the well known Kida solution to obtain a series of steady state solutions with varying vorticity and dust density distributions in their cores, in the limit of perfectly coupled dust and gas. We then present a local stability analysis of these configurations, considering perturbations localised on streamlines. Typical parametric instabilities found have growthrates of $~0.05\Omega_P$, where $\Omega_P$ is the angular velocity at the centre of the vortex. Models with density excess can exhibit many narrow parametric instability bands while those with a concentrated vorticity source display internal shear which significantly affects their stability. However, the existence of these parametric instabilities may not necessarily prevent the possibility of dust accumulation in vortices.