Cooling-Induced Vortex Decay in Keplerian Disks

Abstract

Vortices are readily produced by hydrodynamical instabilities, such as the Rossby wave instability, in protoplanetary disks. However, large-scale asymmetries indicative of dust-trapping vortices are uncommon in sub-millimeter continuum observations. One possible explanation is that vortices have short lifetimes. In this paper, we explore how radiative cooling can lead to vortex decay. Elliptical vortices in Keplerian disks go through adiabatic heating and cooling cycles. Radiative cooling modifies these cycles and generates baroclinicity that changes the potential vorticity of the vortex. We show that the net effect is typically a spin down, or decay, of the vortex for a sub-adiabatic radial stratification. We perform a series of two-dimensional shearing box simulations, varying the gas cooling (or relaxation) time, $t_{\rm cool}$, and initial vortex strength. We measure the vortex decay half-life, $t_{\rm half}$, and find that it can be roughly predicted by the timescale ratio $t_{\rm cool}/t_{\rm turn}$, where $t_{\rm turn}$ is the vortex turnaround time. Decay is slow in both the isothermal ($t_{\rm cool}\ll t_{\rm turn}$) and adiabatic ($t_{\rm cool}\gg t_{\rm turn}$) limits; it is fastest when $t_{\rm cool}\sim0.1\,t_{\rm turn}$, where $t_{\rm half}$ is as short as $\sim300$ orbits. At tens of au where disk rings are typically found, $t_{\rm turn}$ is likely much longer than $t_{\rm cool}$, potentially placing vortices in the fast decay regime.