Ab initio based equation of state of dense water for planetary and exoplanetary modeling

Abstract

Context. The modeling of planetary interiors requires accurate equations of state (EOSs) for the basic constituents with proven validity in the difficult pressure–temperature regime extending up to 50 000 K and hundreds of megabars. While EOSs based on first-principles simulations are now available for the two most abundant elements, hydrogen and helium, the situation is less satisfactory for water where no wide-range EOS is available despite its requirement for interior modeling of planets ranging from super-Earths to planets several times the size of Jupiter. Aims. As a first step toward a multi-phase EOS for dense water, we develop a temperature-dependent EOS for dense water covering the liquid and plasma regimes and extending to the super-ionic and gas regimes. This equation of state covers the complete range of conditions encountered in planetary modeling. Methods. We use first-principles quantum molecular dynamics simulations and the Thomas-Fermi extension to reach the highest pressures encountered in giant planets several times the size of Jupiter. Using these results, as well as the data available at lower pressures, we obtain a parametrization of the Helmholtz free energy adjusted over this extended temperature and pressure domain. The parametrization ignores the entropy and density jumps at phase boundaries but we show that it is sufficiently accurate to model interior properties of most planets and exoplanets. Results. We produce an EOS given in analytical form that is readily usable in planetary modeling codes and dynamical simulations (a fortran implementation is provided). The EOS produced is valid for the entire density range relevant to planetary modeling, for densities where quantum effects for the ions can be neglected, and for temperatures below 50 000K. We use this EOS to calculate the mass-radius relationship of exoplanets up to 5000 MEarth, explore temperature effects in the wet Earth-like, ocean planets and pure water planets, and quantify the influence of the water EOS for the core on the gravitational moments of Jupiter.