Models of accreting gas giant protoplanets in protostellar disks

We present evolutionary models of gas giant planets forming in protoplanetary disks. We first consider protoplanet models that consist of solid cores surrounded by hydrostatically supported gaseous envelopes that are in contact with the boundaries of their Hill spheres, and accrete gas from the surrounding disk. We neglect planetesimal accretion, and suppose that the luminosity arises from gas accretion alone. This generally occurs on a long time scale which may be comparable to the protostellar disk lifetime. We classify these models as being of type A, and follow their quasi static evolution until the point of rapid gas accretion is reached. We consider a second class of protoplanet models that have not hitherto been considered. These models have a free surface, their energy supply is determined by gravitational contraction, and mass accretion from the protostellar disk that is assumed to pass through a circumplanetary disk. An evolutionary sequence is obtained by specifying the accretion rate that the protostellar disk is able to supply. We refer to these models as being of type B. An important result is that these protoplanet models contract quickly to a radius similar to 2 x 10 super(10) cm and are able to accrete gas from the disk at any reasonable rate that may be supplied without any consequent expansion (e.g. a Jupiter mass in similar to few x 10 super(3) years, or more slowly if so constrained by the disk model). We speculate that the early stages of gas giant planet formation proceed along evolutionary paths described by models of type A, but at the onset of rapid gas accretion the protoplanet contracts interior to its Hill sphere, making a transition to an evolutionary path described by models of type B, receiving gas through a circumplanetary disk that forms within its Hill sphere, which is in turn fed by the surrounding protostellar disk. We consider planet models with solid core masses of 5 and 15 M , and consider evolutionary sequences assuming different amounts of dust opacity in the gaseous envelope. The initial protoplanet mass doubling time scale is very approximately inversely proportional to the magnitude of this opacity. Protoplanets with 5 M cores, and standard dust opacity require similar to 3 x 10 super(8) years to grow to a Jupiter mass, longer than reasonable disk life-times. A model with 1% of standard dust opacity requires similar to 3 x 10 super(6) years. Rapid gas accretion in both these cases ensues once the planet mass exc