Thermodynamics of MgSiO3 Fluid and Radius Inflation of Hot Exoplanets

Many of the exoplanets observed so far are likely to have hot interiors dominated by silicate fluids. These include lava or magma ocean super-Earths with molten or vaporized surfaces, and sub-Neptunes or water worlds with a silicate magma layer beneath an H2- or H2O-rich envelope. Hot, fluid interiors may be maintained by stellar radiation, tidal heating, internal heat retained from formation, or the insulating effect of overlying atmospheres. A major limitation to our understanding of these bodies is our lack of knowledge of the thermodynamics of silicate fluids over the wide range of relevant conditions, from the liquid-vapor transition to high-pressure metallic states. We present the results of new first-principles molecular dynamics simulations of the MgSiO3 fluid over a wide range of conditions, from the vapor phase to 4,000 GPa, temperatures from 2,000 to 20,000 K, and densities from 0.5 to 13 g/cm3. We have found a self-consistent analytical thermodynamic description that captures the physical properties and phase equilibria of the MgSiO3 system over this range of conditions. We use this thermodynamic description to compute the isentropes of the MgSiO3 fluid at surface potential temperatures of 2,000–10,000 K and to determine the radii for planets with a single-layer model of the MgSiO3 fluid, a two-layer model of the MgSiO3 fluid with an Fe liquid core, and a three-layer model of the MgSiO3 fluid with an Fe liquid core and an H2- or H2O- envelope. Our results show that temperature effects can increase the radii of these low-mass exoplanets by 5–20%, especially for planets with significant masses of low-density silicate fluid, such as very hot lava worlds.