Skye: A Differentiable Equation of State

Abstract

Stellar evolution and numerical hydrodynamics simulations depend critically on access to fast, accurate, thermodynamically consistent equations of state. We present Skye, a new equation of state for fully-ionized matter. Skye includes the effects of positrons, relativity, electron degeneracy, Coulomb interactions, non-linear mixing effects, and quantum corrections. Skye determines the point of Coulomb crystallization in a self-consistent manner, accounting for mixing and composition effects automatically. A defining feature of this equation of state is that it uses analytic free energy terms and provides thermodynamic quantities using automatic differentiation machinery. Because of this, Skye is easily extended to include new effects by simply writing new terms in the free energy. We also introduce a novel thermodynamic extrapolation scheme for extending analytic fits to the free energy beyond the range of the fitting data while preserving desirable properties like positive entropy and sound speed. We demonstrate Skye in action in the MESA stellar evolution software instrument by computing white dwarf cooling curves.