Corotation torques experienced by planets embedded in weakly magnetized turbulent discs

¹ DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB30, WA, UK
e-mail: c.baruteau@damtp.cam.ac.uk
² Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA
³ Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot, IRFU/SAp, CEA/Saclay, 91191 Gif-sur-Yvette, France
⁴ Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK
⁵ Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apdo. Postal 48-3, 62251 Cuernavaca, Morelos, México

Received: 10 May 2011
Accepted: 14 July 2011

Abstract

Context. The migration of low-mass planets, or type I migration, is driven by the differential Lindblad torque and the corotation torque in non-magnetic viscous models of protoplanetary discs. The corotation torque has recently received detailed attention, because of its ability to slow down, stall, or reverse type I migration. In laminar viscous disc models, the long-term evolution of the corotation torque is intimately related to viscous and thermal diffusion processes in the planet’s horseshoe region. It is unclear how the corotation torque behaves in turbulent discs, and whether its amplitude is correctly predicted by viscous disc models.

Aims. This paper is aimed at examining the properties of the corotation torque in discs where magnetohydrodynamic (MHD) turbulence develops as a result of the magnetorotational instability (MRI), considering a weak initial toroidal magnetic field.

Methods. We present results of 3D MHD simulations carried out with two different codes. Non-ideal MHD effects and the disc’s vertical stratification are neglected, and locally isothermal disc models are considered. The running time-averaged tidal torque exerted by the disc on a fixed planet is evaluated in three different disc models.

Results. We first present simulation results with an inner disc cavity (planet trap). As in viscous disc models, the planet is found to experience a positive running time-averaged torque over several hundred orbits, which highlights the existence of an unsaturated corotation torque maintained in the long term in MHD turbulent discs. Two disc models with initial power-law density and temperature profiles are also adopted, in which the time-averaged tidal torque is found to be in decent agreement with its counterpart in laminar viscous disc models with similar viscosity alpha parameter at the planet location. Detailed analysis of the averaged torque density distributions indicates that the differential Lindblad torque takes very similar values in MHD turbulent and laminar viscous discs, and there exists an unsaturated corotation torque in MHD turbulent discs. This analysis also reveals the existence of an additional corotation torque in weakly magnetized discs.

Conclusions. Our results of 3D MHD simulations demonstrate the existence of horseshoe dynamics and an unsaturated corotation torque in weakly magnetized discs with fully developed MHD turbulence.