Numerical models of giant planet formation with rotation

Abstract

We present models of giant planet formation including the accretion and transport of angular momentum. The calculations are carried out in a one-dimensional quasispherical approximation, assuming hydrostatic equilibrium. The approximation of quasisphericity limits the calculations to relatively slowly rotating models. As in previous calculations without rotation (Bodenheimer and Pollack 1986), the so-called “core-accretion” model is adopted. Angular momentum transport is included for both radiative and convective zones. Convective regions are not forced to rotate uniformly at all times, but the angular momentum distribution in those regions is driven to uniform rotation, with transport coefficients based on mixing-length theory. Radiative regions whose angular momentum distributions are unstable according to the Goldreich-Schubert-Fricke criterion are driven to states of marginal stability, on timescales derived from linear theory and previous hydrodynamical modeling. The calculations are carried up to masses approximately equal to that of Saturn. Angular momentum transport is highly effective, producing models with a strong concentration of angular momentum in the outer convective zones that develop at envelope masses above 30 M +. Near the end of the calculation, gas accretion was turned off, and the models allowed to contract. The ratio of centrifugal force to gravity at the outer radius then rises high enough to validate the quasispherical approximation. At that point, mass is assumed to be shed to form a disk. We find that ∼1 M +, and ∼80% of the angular momentum, are lost to a disk. Such values of disk mass and angular momentum are amply sufficient for satellite system formation. As a result of the loss of angular momentum, however, the final planetary models have only one-third to one-half the present-day value of angular momentum of Saturn, indicating that yet larger amounts of angular momentum may have been present during formation.