Abstract
We investigate the gravitational interaction of a Jovian-mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the 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 protoplanet. Non-linear two-dimensional hydrodynamic simulations are employed using 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-circular orbit after a characteristic viscous time-scale of ∼104 initial orbital periods. This is found to be independent of whether the protoplanet is allowed to accrete mass or not. Inward migration is helped by the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion on to the central star. Maximally accreting protoplanets reach about 4 Jovian masses on reaching the neighbourhood of the central star. Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is ∼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 planets 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 for a number of close orbiting giant planets as well as their inward orbital migration can be accounted for by consideration of disc-protoplanet interactions during the late stages of giant planet formation.
Highlights
The recent discovery of a number of extrasolar giant planets orbiting around nearby solar–type stars has stimulated renewed interest in the theory of planet formation
The disc models used for all simulations using the codes NIRVANA and FARGO were of uniform surface density initially, had a value of ν = 10−5 throughout and a constant value of H/r = 0.04
An outflow boundary condition is used at the inner boundary for all calculations presented here since material in a viscous accretion disc will naturally flow onto the central star
Summary
The recent discovery of a number of extrasolar giant planets orbiting around nearby solar–type stars has stimulated renewed interest in the theory of planet formation. In the situation where the tidal torques are greater than the internal viscous torques in the disc, and the disc response becomes non linear, it is expected that an annular gap, or surface density depression, may be formed in the vicinity of the planet (Papaloizou & Lin 1984, Lin & Papaloizou 1993) This tidal truncation of the protostellar nebula was investigated using non linear numerical simulations by Bryden et al (1999), hereafter BCLNP, and Kley (1999a), in order to examine the effect of gap formation on the mass accretion rate by an embedded giant protoplanet.
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