Vortex generation in protoplanetary disks with an embedded giant planet

TL;DR

This study uses hydrodynamical simulations and modal analysis to investigate vortex formation in protoplanetary disks with embedded giant planets, revealing conditions under which vortices can form and their implications for planet formation.

Contribution

It demonstrates that giant planets can excite Rossby wave instability leading to vortex formation, with detailed analysis of the effects of numerical methods and viscosity.

Findings

Vortices form around Neptune- to Jupiter-mass planets in thin disks.

Viscosity stabilizes the disk and prevents vortex formation.

Finite-difference methods in polar coordinates effectively generate vortices.

Abstract

Vortices in protoplanetary disks can capture solid particles and form planetary cores within shorter timescales than those involved in the standard core-accretion model. We investigate vortex generation in thin unmagnetized protoplanetary disks with an embedded giant planet with planet to star mass ratio $10^{-4}$ and $10^{-3}$. Two-dimensional hydrodynamical simulations of a protoplanetary disk with a planet are performed using two different numerical methods. The results of the non-linear simulations are compared with a time-resolved modal analysis of the azimuthally averaged surface density profiles using linear perturbation theory. Finite-difference methods implemented in polar coordinates generate vortices moving along the gap created by Neptune-mass to Jupiter-mass planets. The modal analysis shows that unstable modes are generated with growth rate of order $0.3 \Omega_K$ for azimuthal numbers m=4,5,6, where $\Omega_K$ is the local Keplerian frequency. Shock-capturing Cartesian-grid codes do not generate very much vorticity around a giant planet in a standard protoplanetary disk. Modal calculations confirm that the obtained radial profiles of density are less susceptible to the growth of linear modes on timescales of several hundreds of orbital periods. Navier-Stokes viscosity of the order $\nu=10^{-5}$ (in units of $a^2 \Omega_p$) is found to have a stabilizing effect and prevents the formation of vortices. This result holds at high resolution runs and using different types of boundary conditions. Giant protoplanets of Neptune-mass to Jupiter-mass can excite the Rossby wave instability and generate vortices in thin disks. The presence of vortices in protoplanetary disks has implications for planet formation, orbital migration, and angular momentum transport in disks.