A torque formula for non-isothermal Type I planetary migration - II. Effects of diffusion

TL;DR

This paper investigates how heat and momentum diffusion influence the non-linear corotation torque in low-mass planets within protoplanetary discs, providing models that closely match numerical simulations.

Contribution

It introduces simple models that accurately predict the impact of diffusive processes on the corotation torque, extending understanding of planetary migration.

Findings

Diffusion sustains the corotation torque against saturation.

Strong diffusion recovers the linear corotation torque.

Models match numerical simulations within 20% accuracy.

Abstract

We study the effects of diffusion on the non-linear corotation torque, or horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for which the width of the horseshoe region is much smaller than the scale height of the disc. In the absence of diffusion, the non-linear corotation torque saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can act to sustain the corotation torque. In the limit of very strong diffusion, the linear corotation torque is recovered. For the case of thermal diffusion, this limit corresponds to having a locally isothermal equation of state. We present some simple models that are able to capture the dependence of the torque on diffusive processes to within 20% of the numerical simulations.