Toward a Deterministic Model of Planetary Formation. II. The Formation and Retention of Gas Giant Planets around Stars with a Range of Metallicities

In an attempt to develop a deterministic theory for planet formation, we examine the accretion of cores of giant planets from planetesimals, gas accretion onto the cores, and their orbital migration. We adopt a working model for nascent protostellar disks with a wide variety of surface density distributions in order to explore the range of diversity among extra solar planetary systems. We evaluate the cores ’ mass-growth rate ˙ Mc through runaway planetesimal accretion and oligarchic growth. The accretion rate of cores is estimated with a two-body approximation. In the inner regions of disks, the cores ’ eccentricity is effectively damped by the ambient disk gas and their early growth is stalled by “isolation”. In the outer regions, the cores ’ growth rate is much slower. If some cores can acquire more mass than a critical value of several Earth masses during the persistence of the disk gas, they would be able to rapidly accrete gas and evolve into gas giant planets. The gas accretion process is initially regulated by the Kelvin-Helmholtz contraction of the planets ’ gas envelope. Based on the assumption that the exponential decay of the disk-gas mass occurs on the time scales ∼ 10 6 −10 7 years and that the disk