SIMBAD references

The migration of low-mass planets, or type I planetary migration, has been studied in hydrodynamical disc models for more than three decades. For a long time, it was thought to be very rapid and directed inwards due to Lindblad torques. More recently, it has been shown that the corotation torque, linked to the horseshoe motion of the gas near the planet, may slow down or even reverse migration. How is this picture modified by the expected presence of a magnetic field in the protoplanetary disc? When the magnetic field is strong enough to prevent horseshoe motion, the corotation torque is replaced by a torque arising from magnetic resonances which may significantly alter the migration rate. In the case of a weaker magnetic field, the magnetic field is not strong enough to prevent horseshoe motion and a corotation torque then exists. In this regime, recent turbulent magnetohydrodynamical (MHD) simulations have reported the existence of an additional component of the corotation torque due to the presence of the magnetic field. The aim of this paper is to investigate the physical origin and the properties of this additional corotation torque. We performed MHD simulations of a low-mass planet embedded in a 2D laminar disc threaded by a weak toroidal magnetic field, where the effects of turbulence are modelled by a viscosity and a resistivity. We confirm that the interaction between the magnetic field and the horseshoe motion of the gas results in an additional corotation torque on the planet, which we dub the MHD torque excess. We demonstrate that it is caused by the accumulation of the magnetic field along the downstream separatrices of the horseshoe region, which gives rise to an azimuthally asymmetric underdense region at that location. The properties of the MHD torque excess are characterized by varying the slope of the density, temperature and magnetic field profiles, as well as the diffusion coefficients and the strength of the magnetic field. The sign of the torque excess and its radial distribution are found to be in agreement with the earlier full magnetorotational instability simulations. This sign depends on the density and temperature gradients only and is positive for profiles expected in protoplanetary discs. The magnitude of the torque excess is in turn mainly determined by the strength of the magnetic field and the turbulent resistivity. It can be strong enough to reverse migration even when the magnetic pressure is less than 1 per cent of the thermal pressure. The MHD torque excess can therefore lead to outward planetary migration in the radiatively efficient outer parts of protoplanetary discs, where the hydrodynamical corotation torque is too weak to prevent fast inward migration.