boundary, which depends on the planet's total mass. The overall evolutionary time scale is generally determined by the length New numerical simulations of the formation of the giant of the second phase. planets are presented, in which for the first time both the gas and
The actual rates at which the giant planets accreted small planetesimal accretion rates are calculated in a self-consistent, planetesimals is probably intermediate between the constant interactive fashion. The simulations combine three elements: rates assumed in most previous studies and the highly variable (1) three-body accretion cross sections of solids onto an isolated rates used here. Within the context of the adopted model of planetary embryo, (2) a stellar evolution code for the planet's planetesimal accretion, the joint constraints of the time scale gaseous envelope, and (3) a planetesimal dissolution code for dissipation of the solar nebula and the current high-Z masses within the envelope, used to evaluate the planet's effective of the giant planets lead to estimates of the initial surface capture radius and the energy deposition profile of accreted density ( init ) of planetesimals in the outer region of the solar material. Major assumptions include: The planet is embedded nebula. The results show that init ศ 10 g cm ุ2 near Jupiter's in a disk of gas and small planetesimals with locally uniform orbit and that init ุ a ุ2 , where a is the distance from the Sun. initial surface mass density, and planetesimals are not allowed These values are a factor of 3 to 4 times as high as that of to migrate into or out of the planet's feeding zone.
the ''minimum-mass'' solar nebula at Jupiter's distance and a All simulations are characterized by three major phases. Durfactor of 2 to 3 times as high at Saturn's distance. The estimates ing the first phase, the planet's mass consists primarily of solid for the formation time of Jupiter and Saturn are 1 to 10 million material. The planetesimal accretion rate, which dominates years, whereas those for Uranus fall in the range 2 to 16 million that of gas, rapidly increases owing to runaway accretion, then years. These estimates follow from the properties of our Solar decreases as the planet's feeding zone is depleted. During the System and do not necessarily apply to giant planets in other second phase, both solid and gas accretion rates are small planetary systems.