Demixing of Hydrogen and Helium at Megabar Pressures

We present results of ab initio finite-temperature density functional theory molecular dynamics simulations for fluid hydrogen-helium mixtures at megabar pressures. The location of the miscibility gap is derived from the equation of state data. We find a close relation between hydrogen-helium phase separation and the continuous nonmetal-to-metal transition in hydrogen. Our calculations predict that demixing of hydrogen and helium occurs in Saturn and probably also in Jupiter. These results will have a strong impact on interior models of giant solar and extrasolar planets.

Figure 1

Gibbs free energy of mixing for a pressure of 4 Mbar. For temperatures below 11 000 K a region with negative curvature occurs for which the common double tangent construction is applied (dashed lines).

Figure 2

Miscibility gap in the hydrogen-helium system for three pressures. Our results (solid lines) show a strongly asymmetric slope in contrast to CP-MD results [9] (dashed lines). The dotted line represents the mean helium fraction in Jupiter. The calculated melting temperatures $T_m$ of solid helium are indicated on the right side for each pressure.

Figure 3

Melting line and phase diagram of helium. Our results (colored points) agree well with the extrapolation (dashed line) of the measurements by Loubeyre et al. [28] and Datchi et al. [29]. The three isobares considered are also shown. Note that the temperatures inside the planets are higher than those on the melting line so that no solid helium occurs there.

Figure 4

Region of demixing in the $P\mathrm{\text{−}}T$ plane and isentropes for Jupiter and Saturn. Our new FT-DFT-MD results (with error bars) in combination with the low-pressure result of Schouten et al. [7] are compared with the LDA-DFT calculations [8] for a solid H-He alloy and the CP-MD curve [9].