  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 Earth Masses) 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. 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. We perform
three-dimensional (3D) radiation hydrodynamical simulations of embedded planets
in protoplanteary discs. For planets on circular orbits at various locations we
measure the radial dependece of the torques. For all considered planet masses
(20-30 Earth masses) 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 intervall, migration is inward and given by the Lindblad value
for large radii. 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_Sol) convection ensues, which changes the structure of the disc and therefore
the torque on the planet as well. 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.
