"Halfway to Rayleigh" and other Insights to the Rossby Wave Instability

TL;DR

This paper analyzes the Rossby wave instability (RWI) in accretion disks, providing analytic criteria for its onset, growth rates, and effects of disk features, with implications for planetary gap formation and vortex development.

Contribution

It offers a comprehensive linear analysis of RWI in simplified disk models, deriving conditions and growth rates, including the influence of disk curvature and feature width.

Findings

Features wider than a scale-height become unstable near halfway to Rayleigh instability.

RWI growth rates scale as enthalpy amplitude to the 1/3 power.

Global curvature influences the susceptibility of planetary gap edges to RWI.

Abstract

The Rossby wave instability (RWI) is the fundamental non-axisymmetric radial shear instability in disks. The RWI can facilitate disk accretion, set the shape of planetary gaps and produce large vortices. It arises from density and/or temperature features, such as radial gaps, bumps or steps. A general, sufficient condition to trigger the RWI is lacking, which we address by studying the linear RWI in a suite of simplified models, including incompressible and compressible shearing sheets and global, cylindrical disks. We focus on enthalpy amplitude and width as the fundamental properties of disk features with various shapes. We find analytic results for the RWI boundary and growth rates across a wide parameter space, in some cases with exact derivations and in others as a description of numerical results. Features wider than a scale-height generally become unstable about halfway to Rayleigh instability, i.e.\ when the squared epicyclic frequency is about half the Keplerian value, reinforcing our previous finding. RWI growth rates approximately scale as enthalpy amplitude to the 1/3 power, with a weak dependence on width, across much of parameter space. Global disk curvature affects wide planetary gaps, making the outer gap edge more susceptible to the RWI. Our simplified models are barotropic and height-integrated, but the main results should carry over to more complex and realistic scenarios.