Equation of state of water for exoplanetary modeling

An analytical functional form of the Helmholtz free energy valid over the entire density-temperature domain relevant to planetary modeling provides a means to combine various data for use in simulations of interior structure or evolution of planets. For water, this includes ab initio results valid for pressures P≈11000 GPa and temperatures T≈100050000 K supplemented with a low-energy equation of state at P<1 GPa in the vapor and liquid phases as constrained by experimental measurements. For a detailed description, see Here we present a Fortran implementation of this analytical fit (click to download the latest version):
eoswater21.f
Along with the Helmholtz free energy, the code provides its derivatives: pressure, internal energy, specific heat, and pressure derivatives.
(NB: A correction was made in 2021. It affects the entropy, but does not affect the internal energy, pressure, and their derivatives.)
This figure (Fig.5 of the paper) illustrates the domain of applicability of the fit and of the code.
Points in the ρ-T plane where the input data have been used to construct the analytical fit. Different symbols correspond to different phase states: crosses for liquid, asterisks for plasma, upright triangles for superionic state, and reverted triangles for ice X. The colors of the symbols represents the accuracy of the fit (for both pressure and internal energy, i.e., the maximum of the two residuals) according to the palette above the legend. The lines show isentropes of Jupiter (J), according to the models of Leconte & Chabrier (2012) and Nettelmann et al. (2012) (the solid and dashed lines, respectively), Saturn (S), according to Leconte & Chabrier (2012), Neptune (N) according to two models of Nettelmann et al. (2013) (solid and dashed lines), and a planet with M=9MJ (Baraffe et al. 2008, 2010).
fit domain illustration

Collection of equations of states
of the Department of Theoretical Astrophysics
of the Ioffe Institute

Page created by Alexander Potekhin on August 26, 2018, last updated on August 18, 2021.