Cooling-Induced Vortex Decay in Keplerian Disks

TL;DR

This paper investigates how radiative cooling influences vortex decay in protoplanetary disks, revealing that cooling timescales critically determine vortex longevity, with implications for observed disk asymmetries.

Contribution

It demonstrates that radiative cooling induces vortex decay in Keplerian disks and provides a predictive relation between cooling timescale and vortex lifetime.

Findings

Vortices decay faster when cooling time is comparable to vortex turnaround time.

Decay is slow in both isothermal and adiabatic limits, fastest at intermediate cooling times.

Vortices at tens of au may decay rapidly due to short cooling times relative to vortex timescales.

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.