Hydrogen-Helium Solubility in Gas Giant Interiors

The observation of excess luminosity of giant planets has led to proposals of additional internal energy sources, including de-mixing and rainout of helium from hydrogen. De-mixing is predicted to occur in density functional theory, although the pressure-temperature-composition conditions depend on the details of the calculations and do not always occur at conditions expected in giant planetary interiors. We have re-examined this problem with a new exchange-correlation functional that has been shown to yield better agreement with essentially exact quantum Monte Carlo results than does the generalised gradient approximation (PBE). We perform molecular dynamics based on density functional theory with the vdW-DF2 functional. The simulations are performed in the NPT ensemble giving us a more direct means of assessing chemical equilibrium than previous isochoric simulations. We find, in contrast to recent predictions based on PBE, that hydrogen and helium are soluble at conditions of the Jovian and Saturnian interiors and that helium rainout is not expected to occur in these planets. We explore the underlying reasons for these differences and discuss the implications for giant planetary evolution.