An Equation of State for Supercritical Silicate-Hydrogen Mixtures at Sub-Neptune Interior Conditions

Abstract

Many sub-Neptunes are expected to contain long-lived molten silicate interiors beneath dense H2-rich envelopes. At pressures and temperatures near the atmosphere-interior boundary, MgSiO3 and H2 may become fully miscible, forming a supercritical silicate-hydrogen fluid. Here we use density functional theory molecular dynamics simulations to construct a self-consistent equation of state for supercritical MgSiO3H4, corresponding to 3.86 wt% hydrogen expressed as equivalent H2. We fit the simulation results with a Helmholtz free-energy formulation that yields density, entropy, heat capacity, thermal expansivity, bulk modulus, and Gruneisen parameter from a single thermodynamic surface. We find that the hydrogen-bearing fluid is lower in density than dry MgSiO3 liquid and deviates significantly from ideal specific-volume mixing between MgSiO3 and H2. The resulting excess volume varies with pressure, indicating that the interaction between hydrogen and the silicate framework evolves with compression. Structural analysis shows increasing Si-H coordination and decreasing persistent H-H bonding at high pressure, consistent with a transition away from molecular H2-like bonding toward a more strongly coupled silicate-hydrogen fluid. We incorporate the MgSiO3H4 equation of state into a composition-dependent MgSiO3-H lookup table and apply it to representative sub-Neptune structure models. The models show that hydrogen partitioning between the atmosphere and condensed interior affects the planetary adiabat relative to the MgSiO3 liquidus. These results demonstrate that supercritical silicate-hydrogen fluids have distinct thermodynamic and structural properties that must be accounted for when modeling sub-Neptune interiors.