DOI: 10.1051/0004-6361/200912072
Planet migration in three-dimensional radiative discs
W. Kley1, B. Bitsch1, and H. Klahr21 Institut für Astronomie & Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: wilhelm.kley@uni-tuebingen.de
2 Max-Planck-Institut für Astronomie, Heidelberg, Germany
Received 15 March 2009 / Accepted 10 August 2009
Abstract
Context. The migration of growing protoplanets depends on the thermodynamics of the
ambient disc. Standard modelling, using locally isothermal discs, indicate
an inward (type-I) migration in the low planet mass regime.
Taking non-isothermal effects into account,
recent studies have shown that the direction of the type-I migration
can change from inward to outward.
Aims. In this paper we extend previous two-dimensional studies and investigate the
planet-disc interaction in viscous, radiative discs using fully three-dimensional radiation
hydrodynamical simulations of protoplanetary accretion discs with embedded planets,
for a range of planetary masses.
Methods. We use an explicit three-dimensional (3D) hydrodynamical code
NIRVANA that includes full tensor viscosity.
We have added implicit radiation transport in the flux-limited diffusion
approximation, and to speed up the simulations significantly we have newly adapted
and implemented the FARGO-algorithm in a 3D context.
Results. First, we present results of test simulations that demonstrate the accuracy of the
newly implemented FARGO-method in 3D. For a planet mass of 20
Mearth, we then
show that including radiative effects also yields a torque reversal in full 3D.
For the same opacity law, the effect is even stronger in 3D than in the corresponding 2D
simulations, due to a slightly thinner disc. Finally, we demonstrate the extent of the
torque reversal by calculating a sequence of planet masses.
Conclusions. Through full 3D simulations of embedded planets in viscous, radiative discs, we confirm
that the migration can be directed outwards up to planet masses of about 33
Mearth.
As a result, the effect may help to resolve the problem of inward migration of
planets that is too rapid during their type-I phase.
Key words: accretion, accretion disks -- hydrodynamics -- radiative transfer -- planets and satellites: formation
© ESO 2009