Rossby Wave Instabilities of Protoplanetary Discs with Cooling

TL;DR

This paper investigates how different cooling mechanisms affect the growth of Rossby wave instabilities in protoplanetary discs, revealing complex dependencies and potential enhancement of instabilities under certain conditions.

Contribution

It introduces a detailed analysis of cooling effects on RWI growth rates using linear perturbation theory with two cooling models, highlighting non-monotonic behaviors and conditions for instability enhancement.

Findings

Growth rates decrease with shorter cooling times in barotropic discs.

Non-monotonic dependence of growth rate on cooling in non-barotropic discs.

Maximum growth rate can occur at specific thermal diffusivity values.

Abstract

Rossby wave instabilities (RWIs) usually lead to nonaxisymmetric vortices in protoplanetary discs and some observed sub-structures of these discs can be well explained by RWIs. We explore how the cooling influences the growth rate of unstable RWI modes in terms of the linear perturbation analysis. The cooling associated with the energy equation is treated in two different ways. The first one we adopt is a simple cooling law. The perturbed thermal state relaxes to the initial thermal state on a prescribed cooling timescale. In the second, we treat the cooling as a thermal diffusion process. The difference in the growth rate between the adiabatic and isothermal modes becomes more pronounced for discs with smaller sound speed. For the simple cooling law, the growth rates of unstable modes monotonically decrease with the shorter cooling timescale in barotropic discs. But the dependence of growth rate with the cooling timescale becomes non-monotonic in non-baratopic discs. The RWI might even be enhanced in non-barotropic discs during the transition from the adiabatic state to the isothermal state. When the cooling is treated as the thermal diffusion, even in barotropic disc, the variation of growth rate with thermal diffusivity becomes non-monotonic. Further more, a maximum growth rate may appear with an appropriate value of thermal diffusivity. The angular momentum flux (AMF) is investigated to understand the angular momentum transport by RWI with cooling.