The effect of dense cores on the structure and evolution of Jupiter and Saturn

Abstract

We have calculated evolutionary and static models of Jupiter and Saturn with homogeneous solar composition mantles and dense cores of material consisting of solar abundances of SiO 2, MgO, Fe, and Ni. Evolutionary sequences for Jupiter were calculated with cores of mass 2, 4, 6, and 8% of the Jovian mass. Evolutionary sequences for Saturn were calculated with cores of mass 16, 18, 20, and 22% of total mass. Two envelope mixtures, representative of the solar abundances were used: X (mass fraction of hydrogen) = 0.74, Y (mass fraction of helium) = 0.24 and X = 0.77 and Y = 0.21. For Jupiter, the observations of the temperature at 1 bar pressure ( T 1bar), radius and internal luminosity were best fit by evolutionary models with a core mass of ∼6.5% and chemical composition of X = 0.77, Y = 0.21. The calculated cooling time for Jupiter is approximately 4.9 × 10 9 years, which is consistent, within our error bars, with the known age of the solar system. For Saturn, the observations of the radius, internal luminosity and T 1BAR can be best fit by evolutionary models with a core mass of ∼21% and chemical composition of X = 0.77, Y = 0.21. The cooling time calculated for Saturn is approximately 2.6 × 10 9 years, almost a factor 2 less than the present age of the solar system. Static models of Jupiter and Saturn were calculated for the above chemical compositions in order to investigate the sensitivity of the calculated gravitational moments, J 2 and J 4, to the mass of the dense core, T 1BAR and hydrogen/helium ratio. We find for Jupiter that a model having a core mass of approximately 7% gives values of J 2, J 4, and T 1BAR that are within observational limits, for the mixture X = 0.77, Y = 0.21. The static Jupiter models are completely consistent with the evolutionary results. For Saturn, the quantities J 2, J 4, and J 6 determined from the static models with the most probable T 1BAR of 140°K, using modeling procedures which result in consistent models for Jupiter, are considerably below the observed values.