A comparison of the interiors of Jupiter and Saturn

Interior models of Jupiter and Saturn are calculated and compared in the fr amework of the three-layer assumption, which rely on the perception that bo th planets consist of three globally homogeneous regions: a dense core, a m etallic hydrogen envelope, and a molecular hydrogen envelope. Within this f ramework, constraints on the core mass and abundance of heavy elements (i.e . elements other than hydrogen and helium) are given by accounting for unce rtainties on the measured gravitational moments, surface temperature, surfa ce helium abundance, and on the inferred protosolar helium abundance, equat ions of state, temperature profile and solid/differential interior rotation . Results obtained solely from static models matching the measured gravitat ional fields indicate that the mass of Jupiter's dense core is less than 14 M+ (Earth masses), but that models with no core are possible given the cur rent uncertainties on the hydrogen-helium equation of stale. Similarly, Sat urn's core mass is less than 22 M+ but no lower limit can be inferred. The total mass of heavy elements (including that in the core) is constrained to lie between 11 and 42 M+ in Jupiter, and between 19 and 31 M+ in Saturn. T he enrichment in heavy elements of their molecular envelopes is 1-6.5, and 0.5-12 times the solar value, respectively. Additional constraints from evo lution models accounting for the progressive differentiation of helium (Hub bard WE, Guillot T, Marley MS, Burrows A, Lunine JI, Saumon D, 1999. Compar ative evolution of Jupiter and Saturn. Planet. Space Sci. 47, 1175-1182) ar e used to obtain tighter, albeit less robust, constraints. The resulting co re masses are then expected to be in the range 0-10 M+, and 6-17 M+ for Jup iter and Saturn, respectively. Furthermore, it is shown that Saturn's atmos pheric helium mass mixing ratio, as derived from Voyager, Y = 0.06 +/- 0.05 , is probably too low. Static and evolution models favor a value of Y = 0.1 1-0.25. Using, Y = 0.16 +/- 0.05, Saturn's molecular region is found to be enriched in heavy elements by 3.5 to 10 times the solar value, in relativel y good agreement with the measured methane abundance. Finally, in all cases , the gravitational moment J(6) Of models matching all the constraints are found to lie between 0.35 and 0.38 x 10(-4) for Jupiter, and between 0.90 a nd 0.98 x 10(-4) for Saturn, assuming solid rotation. For comparison, the u ncertainties on the measured J(6) are about 10 times larger. More accurate measurements of J(6) las expected from the Cassini orbiter for Saturn) will therefore permit to test the validity of interior models calculations and the magnitude of differential rotation in the planetary interior. (C) 1999 Elsevier Science Ltd. All rights reserved.