Self-gravitating vortices in protoplanetary discs
PhD defense by Steven Rendon
Structures observed in protoplanetary discs could be due to large-scale vortices whose consequences on planetary formation are still uncertain. The main interest of the vortices is their ability to rapidly capture and trap the solid particles; indeed, the large clumps formed in the vortex core could gravitationally collapse into planetesimals or planetary cores. Self-gravity (SG) plays a key role in this scenario but also affects in a decisive way the morphology and evolution of the vortices.
In this work, I first study analytical models of vortices at equilibrium. Then, I propose a mathematical formalism for their study and obtain an analytical vortex solution of the 2D Euler and continuity equations. The difficulty of the hydrodynamic equations and the need to better characterise the problem led me to a 3D numerical approach. I developed RoSSBi3D, a compressible finite-volume code whose performances allow to reach the high-resolution required to address the problem.
In the two other sections, I focus on the impact of SG using high-resolution simulations for each of the two phases (gas and solid). Based on Toomre’s criterion, I find a stability condition that vortices should satisfy to resist the destabilising effects of SG and I confirm that massive discs cannot host large-scale vortices. In the case of bi-fluid simulations, I demonstrate that SG needs to be estimated four times, instead of one, in order to correctly account for dust contribution. I also find that high-resolution simulations are required to avoid artificial vortex decay and overestimate the dust feedback.