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As a first step toward a multi-phase equation of state for dense water, wedevelop a temperature-dependent equation of state for dense water covering theliquid and plasma regimes and extending to the super-ionic and gas regimes.This equation of state covers the complete range of conditions encountered inplanetary modeling.  We use first principles quantum molecular dynamics simulations and itsThomas-Fermi extension to reach the highest pressures encountered in giantplanets several times the size of Jupiter. Using these results, as well as thedata available at lower pressures, we obtain a parametrization of the Helmholtzfree energy adjusted over this extended temperature and pressure domain. Theparametrization ignores the entropy and density jumps at phase boundaries butwe show that it is sufficiently accurate to model interior properties of mostplanets and exoplanets.  We produce an equation of state given in analytical form that is readilyusable in planetary modeling codes and dynamical simulations (a fortranimplementation can be found at http://www.ioffe.ru/astro/H2O/). The EOSproduced is valid for the entire density range relevant to planetary modeling,for densities where quantum effects for the ions can be neglected, and fortemperatures below 50,000K. We use this equation of state to calculate themass-radius relationship of exoplanets up to 5,000M_Earth, explore temperatureeffects in ocean and wet Earth-like planets, and quantify the influence of thewater EOS for the core on the gravitational moments of Jupiter.

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