Optimized Jupiter, Saturn, and Uranus interior models

We present models of Jupiter, Saturn, and Uranus which exactly match recent accurate determinations of these planets' gravitational harmonics. The models are computed to third order in the rotational disturbance to the total potential and are based upon a method for inverting the gravitational data. For Jupiter and Saturn, a range of gravity models is calculated to test the possibility of a reduction of density in the outer layers due to helium depletion. The results, which are based upon an improved equation of state for molecular hydrogen, indicate that major helium depletion has not occurred in the outer (molecular hydrogen) layers of Jupiter or Saturn, or if it has, that its effect on the density profile is masked by the presence of other, denser, components. Jupiter is found to be slightly enhanced in heavy elements with respect to solar composition, but the density profile of its hydrogen-rich layers generally agrees rather well with a theoretical profile for solar composition. The deviations from such a profile are more pronounced in the case of Saturn. Uranus models have considerable uncertainty; one successful model resembles the ice-rich model of M. Podolak and R.T. Reynolds (1987, Icarus 70, 31-36), but is fitted to a newer value of J₄. Our Uranus model has a substantial enrichment of heavy elements at depth, but little separation of the ice from the rock component. All of the Jovian planets appear to have central cores of non-hydrogen-helium material which are of similar mass (about 10-15 Earth masses). For Jupiter and Saturn, our calculations yield a gravitational harmonic J₆ which is in agreement with observation, but suggest that this quantity, along with harmonics of higher degree and order, is likely to be more useful for constraining the nature of fluid currents in outer layers rather than deep static structure.