Gap formation and stability in non-isothermal protoplanetary discs

Several observations of transition discs show lopsided dust distributions. A potential explanation is the formation of a large-scale vortex acting as a dust-trap at the edge of a gap opened by a giant planet. Numerical models of gap-edge vortices have so far employed locally isothermal discs in which the temperature profile is held fixed, but the theory of this vortex-forming or 'Rossby wave' instability was originally developed for adiabatic discs. We generalize the study of planetary gap stability to non-isothermal discs using customized numerical simulations of disc-planet systems where the planet opens an unstable gap. We include in the energy equation a simple cooling function with cooling time-scale t(c) = beta Omega(-1)(k), where Omega(k) is the Keplerian frequency, and examine the effect of beta on the stability of gap edges and vortex lifetimes. We find increasing beta lowers the growth rate of non-axisymmetric perturbations, and the dominant azimuthal wavenumber m decreases. We find a quasi-steady state consisting of one large-scale, overdense vortex circulating the outer gap edge, typically lasting O(10(3)) orbits. We find vortex lifetimes generally increase with the cooling time-scale t(c) up to an optimal value of t(c) similar to 10 orbits, beyond which vortex lifetimes decrease. This non-monotonic dependence is qualitatively consistent with recent studies using strictly isothermal discs that vary the disc aspect ratio. The lifetime and observability of gap-edge vortices in protoplanetary discs is therefore dependent on disc thermodynamics.