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=β Ω _k^{-1}, where Ω_k is the Keplerian frequency, and examine the effect of β on the stability of gap edges and vortex lifetimes. We find increasing β 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(10³) orbits. We find vortex lifetimes generally increase with the cooling time-scale t_c up to an optimal value of t_c ∼ 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.