The effect of equation of state thermodynamic consistency on simulated planet evolution

An equation of state (EOS) is thermodynamically consistent if it satisfies the first law of thermodynamics and its derivatives (see e.g. Paxton et al. 2019). Most EOS in widespread use are not perfectly thermodynamically consistent, because other considerations, including fidelity to experiment and smoothness of numerical derivatives, often take priority over thermodynamic consistency. As such, the specific effect of thermodynamic inconsistency on the evolution of stellar or planet models has not yet been evaluated, although it is posited to make structure and evolution models less accurate. Here, we present a procedure for adjusting an EOS table to improve its thermodynamic consistency, based on the work of Timmes & Swesty 2000. We apply this procedure to a set of EOS commonly used for planet modeling: the H/He EOS of Chabrier et al. 2019, with non-ideal mixing terms from Howard & Guillot 2023, and a heavy element EOS based on AQUA H2O (Haldemann et al. 2020) and SESAME rock (Lyon & Johnson 1992). We show that the adjusted, thermodynamically consistent versions are compatible with experimental Hugioniot measurements, where available. Finally, we compare planet models evolved with (1) the original EOS presented in the literature; (2) thermodynamically consistent versions of the EOS; and (3) "control" versions of the EOS, which have roughly the same thermodynamic consistency as the originals, but deviate roughly as much from the original tabulated values as version (2).