Range of outward migration and influence of the disc’s mass on the migration of giant planet cores

Institut für Astronomie & Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: bertram.bitsch@uni-tuebingen.de

Received: 6 May 2011
Accepted: 11 October 2011

Abstract

Context. The migration of planets plays an important role in the early planet-formation process. An important problem has been that standard migration theories predict very rapid inward migration, which poses problems for population synthesis models. However, it has been shown recently that low-mass planets (20–30 M_Earth) that are still embedded in the protoplanetary disc can migrate outwards under certain conditions. Simulations have been performed mostly for planets at given radii for a particular disc model.

Aims. Here, we plan to extend previous work and consider different masses of the disc to quantify the influence of the physical disc conditions on planetary migration. The migration behaviour of the planets will be analysed for a variety of positions in the disc.

Methods. We perform three-dimensional (3D) radiation hydrodynamical simulations of embedded planets in protoplanetary discs. We use the explicit-implicit 3D hydrodynamical code NIRVANA that includes full tensor viscosity, and implicit radiation transport. For planets on circular orbits at various locations we measure the radial dependence of the torques for three different planetary masses.

Results. For all considered planet masses (20–30 M_Earth) in this study we find outward migration within a limited radial range of the disc, typically from about 0.5 up to 1.5–2.5 a_Jup. Inside and outside this interval, migration is inward and given by the Lindblad value for large radii. Interestingly, the fastest outward migration occurs at a radius of about a_Jup for different disc and planet masses. Because outward migration stops at a certain location in the disc, there exists a zero-torque distance for planetary embryos, where they can continue to grow without moving too fast. For higher disc masses (M_disc > 0.02 M_⊙) convection ensues, which changes the structure of the disc and therefore the torque on the planet as well.

Conclusions. Outward migration stops at different points in the disc for different planetary masses, resulting in a quite extended region where the formation of larger cores might be easier. In higher mass discs, convection changes the disc’s structure resulting in fluctuations in the surface density, which influence the torque acting on the planet, and therefore its migration rate. Because convection is a 3D effect, 2D simulations of massive discs with embedded planets should be handled with care.