FINAL MASSES OF GIANT PLANETS. II. JUPITER FORMATION IN A GAS-DEPLETED DISK

Abstract

ABSTRACT First, we study the final masses of giant planets growing in protoplanetary disks through capture of disk gas, by employing empirical formulae for the gas capture rate and a shallow disk gap model, which are both based on hydrodynamic simulations. We find that, for planets less massive than 10 Jupiter masses, their growth rates are mainly controlled by the gas supply through the global disk accretion, and the gap opening does not limit the accretion. The insufficient gas supply compared with the rapid gas capture causes a depletion of the gas surface density even at the outside the gap, which can create an inner hole in the disk. Second, our findings are applied to the formation of our solar system. For the formation of Jupiter, a very low-mass gas disk of several Jupiter masses is required at the beginning of its gas capture because of the continual capture. Such a low-mass gas disk with sufficient solid material can be formed through viscous evolution from a compact disk of initial size ∼10 au. By viscous evolution with a moderate viscosity of α ∼ 10−3, most of the disk gas accretes onto the Sun and a widely spread low-mass gas disk remains when the solid core of Jupiter starts gas capture at t ∼ 107 yr. A very low-mass gas disk also provides a plausible path where type I and II planetary migrations are both suppressed significantly. In particular, the type II migration of Jupiter-size planets becomes inefficient because of the additional gas depletion due to the rapid gas capture by such planets.