Type I planetary migration in a self-gravitating disk

TL;DR

This study uses hydrodynamic simulations to analyze how self-gravity affects planetary migration rates in protoplanetary disks, revealing that ignoring self-gravity leads to overestimations and that disk gravity influences Lindblad torques.

Contribution

It demonstrates the importance of including disk self-gravity in migration models and quantifies its effect on Lindblad torques and migration rates.

Findings

Ignoring self-gravity overestimates migration rate by up to a factor of two.

Disk self-gravity enhances differential Lindblad torque proportionally to the Toomre parameter.

Torque enhancement can be modeled by shifting Lindblad resonances or using anisotropic pressure tensors.

Abstract

We investigate the tidal interaction between a low-mass planet and a self-gravitating protoplanetary disk, by means of two-dimensional hydrodynamic simulations. We first show that considering a planet freely migrating in a disk without self-gravity leads to a significant overestimate of the migration rate. The overestimate can reach a factor of two for a disk having three times the surface density of the minimum mass solar nebula. Unbiased drift rates may be obtained only by considering a planet and a disk orbiting within the same gravitational potential. In a second part, the disk self-gravity is taken into account. We confirm that the disk gravity enhances the differential Lindblad torque with respect to the situation where neither the planet nor the disk feels the disk gravity. This enhancement only depends on the Toomre parameter at the planet location. It is typically one order of magnitude smaller than the spurious one induced by assuming a planet migrating in a disk without self-gravity. We confirm that the torque enhancement due to the disk gravity can be entirely accounted for by a shift of Lindblad resonances, and can be reproduced by the use of an anisotropic pressure tensor. We do not find any significant impact of the disk gravity on the corotation torque.