Gap formation and stability in non-isothermal protoplanetary discs

TL;DR

This study investigates how non-isothermal conditions affect vortex formation and stability at planetary gap edges in protoplanetary discs, revealing that cooling times influence vortex lifetime and characteristics.

Contribution

It extends the theory of vortex formation to non-isothermal discs by incorporating a simple cooling function, analyzing its impact on vortex stability and lifetime through numerical simulations.

Findings

Increasing cooling times decrease perturbation growth rates.

Vortex lifetimes peak at an optimal cooling timescale.

Vortex characteristics depend on the cooling parameter eta.

Abstract

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 thus far employed locally isothermal discs, but the theory of this vortex-forming or `Rossby wave' instability was originally developed for adiabatic discs. We generalise the study of planetary gap stability to non-isothermal discs using customised 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 timescale $t_c=\beta\Omega_k^{-1}$, 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, over-dense vortex circulating the outer gap edge, typically lasting $O(10^3)$ orbits. Vortex lifetimes were found to generally increase with cooling times up to an optimal value, 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.