How strong are the Rossby vortices?

TL;DR

This study investigates the nonlinear saturation of Rossby wave instability in astrophysical discs through global 2D simulations, confirming the saturation mechanism and providing empirical formulas for growth rates.

Contribution

The paper demonstrates the nonlinear saturation mechanism of Rossby wave instability in discs and offers empirical formulas for maximum vorticity and growth rates based on simulations.

Findings

Confirmed the saturation mechanism analogous to wave-particle interactions.

Derived empirical fitting formulas for the instability's growth rate.

Explored effects of azimuthal mode number and energy leakage.

Abstract

The Rossby wave instability, associated with density bumps in differentially rotating discs, may arise in several different astrophysical contexts, such as galactic or protoplanetary discs. While the linear phase of the instability has been well studied, the nonlinear evolution and especially the saturation phase remain poorly understood. In this paper, we test the non-linear saturation mechanism analogous to that derived for wave-particle interaction in plasma physics. To this end we perform global numerical simulations of the evolution of the instability in a two-dimensional disc. We confirm the physical mechanism for the instability saturation and show that the maximum amplitude of vorticity can be estimated as twice the linear growth rate of the instability. We provide an empirical fitting formula for this growth rate for various parameters of the density bump. We also investigate the effects of the azimuthal mode number of the instability and the energy leakage in the spiral density waves. Finally, we show that our results can be extrapolated to 3D discs.