Gas Accretion onto a Protoplanet and Formation of a Gas Giant Planet

We investigate gas accretion onto a protoplanet, by considering the thermal effect of gas in three-dimensional hydrodynamical simulations, in which the wide region from a protoplanetary gas disk to a Jovian radius planet is resolved using the nested-grid method. We estimate the mass accretion rate and growth timescale of gas giant planets. The mass accretion rate increases with protoplanet mass for M_p < M_cri, while it becomes saturated or decreases for M_p > M_cri, where M_cri = 0.036 M_Jup (a_p/1AU)^0.75, and M_Jup and a_p are the Jovian mass and the orbital radius, respectively. The growth timescale of a gas giant planet or the timescale of the gas accretion onto the protoplanet is about 10^5 yr, that is two orders of magnitude shorter than the growth timescale of the solid core. The thermal effects barely affect the mass accretion rate because the gravitational energy dominates the thermal energy around the protoplanet. The mass accretion rate obtained in our local simulations agrees quantitatively well with those obtained in global simulations with coarser spatial resolution. The mass accretion rate is mainly determined by the protoplanet mass and the property of the protoplanetary disk. We find that the mass accretion rate is correctly calculated when the Hill or Bondi radius is sufficiently resolved. Using the oligarchic growth of protoplanets, we discuss the formation timescale of gas giant planets.