Our understanding of Jupiter and Saturn goes hand in hand with the availability and accuracy of observational constraints as well as of the equations of state for their main constituents, hydrogen and helium. We show how the current uncertainties in the core mass of Jupiter (0-10 ME) and Saturn (0-20 ME) could be reduced with the help of measured atmospheric oxygen abundances, which is in reach for Jupiter thanks to the Juno mission, and possibly also for Saturn. Given that both planets’ atmospheres are observed to be depleted in helium, we finally discuss the occurrence of H/He demixing with respect to recent ab initio data based H/He phase diagrams and argue that the assumption a layered structure with few layers remains a reasonable approximation. However, we caution that the derived total heavy element fraction is highly subject to our assumption of an adiabatic interior, which may not hold in case of He demixing.
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