The migration and growth of protoplanets in protostellar discs

We investigate the gravitational interaction of a Jovian-mass protoplanet w ith a gaseous disc with aspect ratio and kinematic viscosity expected for t he protoplanetary disc from which it formed. Different disc surface density distributions are investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protop lanet. Non-linear two-dimensional hydrodynamic simulations are employed usi ng three independent numerical codes. A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near-c ircular orbit after a characteristic viscous time-scale of similar to 10(4) initial orbital periods. This is found to be independent of whether the pr otoplanet is allowed to accrete mass or not. Inward migration is helped by the disappearance of the inner disc, and therefore the positive torque it w ould exert, because of accretion on to the central star. Maximally accretin g protoplanets reach about 4 Jovian masses on reaching the neighbourhood of the central star. Our results indicate that a realistic upper limit for th e masses of closely orbiting giant planets is similar to 5 Jupiter masses, if they originate in protoplanetary discs similar to the minimum-mass solar nebula. This is because of the reduced accretion rates obtained for planet s of increasing mass. Assuming that some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated fo r a number of close orbiting giant planets as well as their inward orbital migration can be accounted for by consideration of disc-protoplanet interac tions during the late stages of giant planet formation.