On the corotation torque in a radiatively inefficient disk

TL;DR

This paper derives and verifies a new expression for the corotation torque in adiabatic, radiatively inefficient disks, highlighting the role of entropy gradients and their impact on planetary migration.

Contribution

It introduces a novel torque formula incorporating entropy effects and validates it through hydrodynamical simulations, advancing understanding of planet-disk interactions.

Findings

Corotation torque depends on entropy gradient in adiabatic disks.

Hydrodynamical simulations confirm the analytical torque expression.

Entropy perturbations significantly influence planetary migration in radiatively inefficient regions.

Abstract

We consider the angular momentum exchange at the corotation resonance between a two-dimensional gaseous disk and a uniformly rotating external potential, assuming that the disk flow is adiabatic. We first consider the linear case for an isolated resonance, for which we give an expression of the corotation torque that involves the pressure perturbation, and which reduces to the usual dependence on the vortensity gradient in the limit of a cold disk. Although this expression requires the solution of the hydrodynamic equations, it provides some insight into the dynamics of the corotation region. In the general case, we find an additional dependence on the entropy gradient at corotation. This dependence is associated to the advection of entropy perturbations. These are not associated to pressure perturbations. They remain confined to the corotation region, where they yield a singular contribution to the corotation torque. In a second part, we check our torque expression by means of customized two-dimensional hydrodynamical simulations. In a third part, we contemplate the case of a planet embedded in a Keplerian disk, assumed to be adiabatic. We find an excess of corotation torque that scales with the entropy gradient, and we check that the contribution of the entropy perturbation to the torque is in agreement with the expression obtained from the linear analysis. We finally discuss some implications of the corotation torque expression for the migration of low mass planets in the regions of protoplanetary disks where the flow is radiatively inefficient on the timescale of the horseshoe U-turns.