Type I Planet Migration in Nearly Laminar Disks

TL;DR

This paper uses 2D hydrodynamic simulations to study low-mass planet migration in nearly laminar disks, confirming a critical mass for halting migration and revealing vortex instabilities at very low viscosities.

Contribution

It provides the first detailed simulation validation of the analytic prediction that low-viscosity disks can halt Type I planet migration at a critical mass.

Findings

Migration halts at ~10 Earth masses in low-viscosity disks.

Density feedback effects are suppressed at higher viscosities.

Vortex instability occurs at very low viscosity, causing orbital eccentricity.

Abstract

We describe 2D hydrodynamic simulations of the migration of low-mass planets ($\leq 30 M_{\oplus}$) in nearly laminar disks (viscosity parameter $\alpha < 10^{-3}$) over timescales of several thousand orbit periods. We consider disk masses of 1, 2, and 5 times the minimum mass solar nebula, disk thickness parameters of $H/r = 0.035$ and 0.05, and a variety of $\alpha$ values and planet masses. Disk self-gravity is fully included. Previous analytic work has suggested that Type I planet migration can be halted in disks of sufficiently low turbulent viscosity, for $\alpha \sim 10^{-4}$. The halting is due to a feedback effect of breaking density waves that results in a slight mass redistribution and consequently an increased outward torque contribution. The simulations confirm the existence of a critical mass ($M_{cr} \sim 10 M_{\oplus}$) beyond which migration halts in nearly laminar disks. For $\alpha \ga 10^{-3}$, density feedback effects are washed out and Type I migration persists. The critical masses are in good agreement with the analytic model of Rafikov (2002). In addition, for $\alpha \la 10^{-4}$ steep density gradients produce a vortex instability, resulting in a small time-varying eccentricity in the planet's orbit and a slight outward migration. Migration in nearly laminar disks may be sufficiently slow to reconcile the timescales of migration theory with those of giant planet formation in the core accretion model.