Planet migration in three-dimensional radiative discs

The migration of growing protoplanets depends on the thermodynamics of the ambient disc. Standard modelling, using locally isothermal discs, indicate in the low planet mass regime an inward (type-I) migration. Taking into account non-isothermal effects, recent studies have shown that the direction of the type-I migration can change from inward to outward. 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. 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. 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 M_earth we then show that the inclusion of radiative effects yields a torque reversal also in full 3D. For the same opacity law used 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. 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 M_earth. Hence, the effect may help to resolve the problem of too rapid inward migration of planets during their type-I phase.