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 submillimeter 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 subadiabatic radial stratification. We perform a series of two-dimensional shearing box simulations, varying the gas cooling (or relaxation) time, t cool, and initial vortex strength. We measure the vortex decay half-life, t half, and find that it can be roughly predicted by the timescale ratio t cool/t turn, where t turn is the vortex turnaround time. Decay is slow in both the isothermal (t cool ≪ t turn) and adiabatic (t cool ≫ t turn) limits; it is fastest when t cool ∼ 0.1 t turn, where t half is as short as ∼300 orbits. At tens of astronomical units where disk rings are typically found, t turn is likely much longer than t cool, potentially placing vortices in the fast decay regime.
