Limits on the Core Mass of Jupiter

Abstract:

The core is here defined as the central concentration of elements heavier than hydrogen and helium (it need not be solid and it need not be purely heavy elements and it will not have a sharp boundary). Its determination is a major goal of the Juno mission (2016-17) and it will be difficult to determine because it is expected to be only a few percent of the total mass. It has long been known that there is no prospect of determining the nature of this core (e.g., its density) from gravity measurements, even though the mass can be estimated. By consideration of simple models that are nonetheless faithful to the essential physics, it is further shown that should the core be contaminated with light elements (hydrogen and helium) then the gravity data can tell us the core mass as defined (with some caveats about the fuzziness of its boundary) but not the total mass within some small radius (which could include any light elements mixed in). This is both good and bad news: Good in that the core is thought to be diagnostic of the conditions under which the planet formed but bad in that the admixture also tells us more about both formation process and core erosion. Further, a linear perturbation theory has been developed that provides an easy approximate way of determining how errors in the equation of state (EOS) propagate into errors in the estimated core mass or envelope enrichment in heavies in models that nonetheless satisfy all observables. This theory does not require detailed models of the planet but provides an integral mapping from changes in the EOS into approximate changes in radius at fixed mass, and low degree gravity (or moment of inertia, MOI). This procedure also shows that there exist perturbations that leave the radius, mass and MOI unchanged but cause a change in J2, though in practice the non-uniqueness of structure by this consideration (~0.2% or less in MOI for example) is less than the non-uniqueness arising from likely EOS uncertainties (~1% in total mass, potentially 30% in core mass). Although the likely independent determination of MOI from precession is expected to help in the modeling procedure, the uncertainty in EOS and in the distribution of heavy elements (and resulting non-adiabaticity) will necessarily introduce ambiguity into the determination of core mass.