Gas accretion onto a protoplanet and formation of a gas giant planet

We investigate gas accretion on to a protoplanet, by considering the thermal effect of gas in three-dimensional hydrodynamical simulations, in which the wide region from a protoplanetary gas disc to a Jovian radius planet is resolved using the nested grid method. We estimate the mass accretion rate and growth time-scale 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 ≡ 0.036M_Jup(ap/1au)0.75, and MJup and ap are the Jovian mass and the orbital radius, respectively. This accretion rate is typically two orders of magnitude smaller than that in two-dimensional simulations. The growth time-scale of a gas giant planet or the time-scale of the gas accretion on to the protoplanet is about 10⁵ yr, that is two orders of magnitude shorter than the growth time-scale 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 disc. 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 time-scale of gas giant planets.