The migration of low-mass planets 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 as it may slow down, stal
l, or reverse 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 planets horseshoe region. This paper examines the properties of the corotation torque in discs where MHD turbulence develops as a result of the magnetorotational instability, considering a weak initial toroidal magnetic field. We present results of 3D MHD simulations carried out with two different codes. Non-ideal MHD effects and the discs vertical stratification are neglected, and locally isothermal disc models are considered. The running time-averaged torque exerted by the disc on a fixed planet is evaluated in three disc models. We first present 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 torque is found to be in decent agreement with its counterpart in laminar viscous disc models with similar viscosity 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.
The massive stars in the Galactic center inner arcsecond share analogous properties with the so-called Hot Jupiters. Most of these young stars have highly eccentric orbits, and were probably not formed in-situ. It has been proposed that these stars a
cquired their current orbits from the tidal disruption of compact massive binaries scattered toward the proximity of the central supermassive black hole. Assuming a binary star formed in a thin gaseous disk beyond 0.1 pc from the central object, we investigate the relevance of disk-satellite interactions to harden the binding energy of the binary, and to drive its inward migration. A massive, equal-mass binary star is found to become more tightly wound as it migrates inwards toward the central black hole. The migration timescale is very similar to that of a single-star satellite of the same mass. The binarys hardening is caused by the formation of spiral tails lagging the stars inside the binarys Hill radius. We show that the hardening timescale is mostly determined by the mass of gas inside the binarys Hill radius, and that it is much shorter than the migration timescale. We discuss some implications of the binarys hardening process. When the more massive (primary) components of close binaries eject most their mass through supernova explosion, their secondary stars may attain a range of eccentricities and inclinations. Such processes may provide an alternative unified scenario for the origin of the kinematic properties of the central cluster and S-stars in the Galactic center as well as the high velocity stars in the Galactic halo.
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 l
eads 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.
