Rossby Wave Instability with Self-Gravity

Abstract

The Rossby wave instability (RWI) in non-self-gravitating discs can be triggered by a bump at a radius $r_0$ in the disc surface mass-density (which is proportional to the inverse potential vorticity). It gives rise to a growing non-axisymmetric perturbation [$\propto \exp (im\varphi )$, $m=1,\mathrm{2..}$] in the vicinity of $r_0$ consisting of anticyclonic vortices which may facilitate planetesimal growth in protoplanetary discs. Here, we analyze a continuum of thin disc models ranging from self-gravitating to non-selfgravitating. The key quantities determining the stability/instability are: (1) the parameters of the bump (or depression) in the disc surface density, (2) the Toomre $Q$ parameter of the disc (a non-self-gravitating disc has $Q\gg 1$), and (3) the dimensionless azimuthal wavenumber of the perturbation ${\bar{k}}_{\varphi }=mQh/r_0$, where $h$ is the half-thickness of the disc. For discs stable to axisymmetric perturbations ($Q>1$), the self-gravity has a significant role for ${\bar{k}}_{\varphi }<\pi /2$ or $m<(\pi /2)(r_0/h)Q^{-1}$; instability may occur for a depression or groove in the surface density if $Q\lesssim 2$. For ${\bar{k}}_{\varphi }>\pi /2$ the self-gravity is not important, and instability may occur at a bump in the surface density. Thus, for all mode numbers $m\ge 1$, the self-gravity is unimportant for $Q>(\pi /2)(r_0/h)$. We suggest that the self-gravity be included in simulations for cases where $Q<(r_0/h)$.

5 pages, 5 figures

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