On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration

TL;DR

This paper investigates the behavior of corotation torques and horseshoe drag on low mass protoplanets in protoplanetary discs, revealing conditions for sustained outward or stalled migration due to nonlinear effects.

Contribution

It demonstrates that horseshoe drag can be sustained under certain viscosity conditions, significantly affecting protoplanet migration beyond linear theory predictions.

Findings

Horseshoe drag is many times larger than linear torque.

Sustained outward migration occurs with high enough viscosity.

Torque sign can change even with positive surface density gradients.

Abstract

We study the torque on low mass protoplanets on fixed circular orbits, embedded in a protoplanetary disc in the isothermal limit. For low mass protoplanets and large viscosity the corotation torque behaves as expected from linear theory. However, when the viscosity becomes small enough to enable horseshoe turns to occur, the linear corotation torque exists only temporarily after insertion of a planet into the disc, being replaced by the horseshoe drag first discussed by Ward. This happens after a time that is equal to the horseshoe libration period reduced by a factor amounting to about twice the disc aspect ratio. This torque scales with the radial gradient of specific vorticity, as does the linear torque, but we find it to be many times larger. If the viscosity is large enough for viscous diffusion across the coorbital region to occur within a libration period, we find that the horseshoe drag may be sustained. If not, the corotation torque saturates leaving only the linear Lindblad torques. As the magnitude of the non linear coorbital torque (horseshoe drag) is always found to be larger than the linear torque, we find that the sign of the total torque may change even for for mildly positive surface density gradients. In combination with a kinematic viscosity large enough to keep the torque from saturating, strong sustained deviations from linear theory and outward or stalled migration may occur in such cases (abridged).