On the local stability of vortices in differentially rotating discs

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.

arXiv comment18 pages, 12 figures, 1 table, accepted MNRAS 30/09/2014

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• Compact dust concentration in the MWC 758 protoplanetary disk
• On the convective overstability in protoplanetary discs
• Impact of Local Pressure Enhancements on Dust Concentration inTurbulent Protoplanetary Discs
• Dynamics of Dusty Vortices I: Extensions and limitations of the terminal velocity approximation
• Axisymmetric simulations of the convective overstability in protoplanetary discs
• Vortex survival in 3D self-gravitating accretion discs
• Constraining the masses of planets in protoplanetary discs from the presence or absence of vortices -- Comparison with ALMA observations
• Dynamics of Dusty Vortices II: Stability of 2D dust laden vortices
• Global magnetohydrodynamic simulations of the inner regions of protoplanetary discs. I. Zero-net flux regime
• Stability of Dusty Rings in Protoplanetary Discs