Morphology and dynamical stability of self-gravitating vortices: Numerical simulations

TL;DR

This study uses high-resolution 2D hydrodynamic simulations to explore how self-gravity influences the formation, stability, and evolution of vortices in protoplanetary disks, revealing conditions for their longevity and structural changes.

Contribution

It provides the first detailed numerical analysis of self-gravitating vortices, establishing stability criteria and characterizing their internal structure and dynamics.

Findings

Self-gravity destabilizes large vortices but small ones are more robust.

Vortex survival depends critically on the Toomre parameter and disk temperature.

Self-gravitating vortices can persist for hundreds of orbits and develop secondary vortices.

Abstract

Theoretical and numerical studies have shown that large-scale vortices in Protoplanetary discs can result from various hydrodynamical instabilities. Once produced, such vortices can survive nearly unchanged over a large number of rotation periods, slowly migrating towards the star. In the outer disc, self-gravity may affect the vortex evolution and must be included in models. We performed 2D hydrodynamic simulations using the RoSSBi3D code. The outline of our computations was limited to Euler's equations assuming a non-homentropic and non-adiabatic flow for an ideal gas. A series of 45 runs were carried out starting from a Gaussian vortex-model; the evolution of vortices was followed during 300 orbits for various values of the vortex parameters and the Toomre parameter. Two simulations, with the highest resolution (HR) thus far for studies of vortices, were also run to better characterise the internal structure of the vortices and for the purpose of comparison with an isothermal case. We find that SG tends to destabilise the injected vortices, but compact small-scale vortices seem to be more robust than large-scale oblong vortices. Vortex survival critically depends on the value of the disc's Toomre parameter, but may also depend on the disc temperature at equilibrium. Disc SG must be small enough to avoid destruction in successive splitting and an approximate `stability' criterion is deduced for vortices. The self-gravitating vortices that we found persist during hundreds of rotation periods and look like the quasi-steady vortices obtained in the non-self-gravitating case. A number of these self-gravitating vortices are eventually accompanied by a secondary vortex with a horseshoe motion. These vortices reach a new rotational equilibrium in their core, tend to contract in the radial direction, and spin faster.