The phase diagram and transport properties for hydrogen-helium fluid planets

Abstract

Hydrogen and helium are the major constituents of Jupiter and Saturn, and phase transitions can have important effects on the planetary structure. In this paper, the relevant phase diagrams and microscopic transport properties are analyzed in detail. The following paper (Paper II) applies these results to the evolution and present dynamic structure of the Jovian planets. Pure hydrogen is first discussed, especially the nature of the molecular-metallic transition and the melting curves for the two phases. It is concluded that at the temperatures and pressures of interest (T ≈ 10^4 K, P ≈ 1-10 Mbar), both phases are fluid, but the transition between them might nevertheless be first-order. The insulator-metal transition in helium occurs at a much higher pressure (~ 70 Mbars) and is not of interest. The phase diagrams for both molecular and metallic hydrogen-helium mixtures are discussed. In the metallic mixture, calculations indicate a miscibility gap for T ≾ 10^4 K. Immiscibility in the molecular mixture is more difficult to predict but almost certainly occurs at much lower temperatures. A fluid-state model is constructed which predicts the likely topology of the threedimensional phase diagram. The greater solubility of helium in the molecular phase leads to the prediction that the He/H mass ratio is typically twice as large in the molecular phase as in the coexisting metallic phase. Under these circumstances a inversion is possible in which the molecular phase becomes more dense than the metallic phase. The partitioning of minor constituents is also considered: The deuterium/hydrogen mass ratio is essentially the same for all coexisting hydrogen-helium phases, at least for T ≳ 5000 K. The partitioning of H_2O, CH_4, and NH_3 probably favors the molecular (or helium-rich) phase. Substances with high conduction electron density (e.g., AI) may partition into the metallic phase. Electronic and thermal conductivities, viscosity, helium diffusivity, and Soret coefficient are evaluated for the fluid molecular and metallic phases, all to at least order-of-magnitude accuracy. The properties of the metallic phase are typical of a liquid alkali metal, and those of the molecular phase are typical of a dense neutral fluid (except that the conductivities may be almost metallic at the transition pressure). The opacities of molecular hydrogen and solar-composition mixtures are discussed for T ≈ 500 K, where molecular hydrogen alone may be insufficiently opaque to ensure convection in the Jovian planets. Sufficient opacity to initiate convection is probably supplied by the minor constituents. Current uncertainties are assessed.