Calculations of the accretion and evolution of giant planets: The effects of solid cores

The evolution of the giant planets is calculated under the general hypothesis that the solid cores formed first, by accretion of small particles, and that these cores later gravitationally attracted their gaseous envelopes from the solar nebula. The evolution passes through the following phases. (1) Planetesimals accrete to form a core of rocky and icy material. (2) When the core mass has grown to a few tenths of an Earth mass, a gaseous envelope in hydrostatic equilibrium begins to form around the core. (3) The core and envelope continue to grow until the “critical” core mass is reached, beyond which point the envelope increases in mass much more rapidly than the core. (4) The envelope mass increases quickly to its present value and prodices a relatively high luminosity, derived from gravitational contraction. (5) Accretion of both core and envelope terminates, and the planet contracts and cools to its present state on a time scale of 5 × 109 years. Evolutionary calculations of phases (2) through (5) are presented, based on solutions of the time-dependent stellar structure equations in spherical symmetry. The physical considerations that determine the critical core mass are discussed; its value is found to depend strongly on the core accretion rate but only weakly on surface boundary conditions. Evolutionary tracks up to the present state are presented for objects of Uranus and Saturn mass.