Abstract
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, nonlinear 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.
Highlights
The equation of state (EOS) of ionized matter is a key ingredient in models of stars, gas giant planets, accretion disks, and many other astrophysical systems
We demonstrate Skye in action in the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution software instrument by computing white dwarf cooling curves
Yj, j where fmliqixuid captures non-ideal corrections to the mixing free energy in the liquid phase, the fOCP,j terms represent the free energy of a one-component plasma (OCP) made entirely of species j, and fi−e,j accuonts for electron-ion interactions for species j
Summary
The equation of state (EOS) of ionized matter is a key ingredient in models of stars, gas giant planets, accretion disks, and many other astrophysical systems. While HELM does not include the sophisticated non-ideal corrections which are a defining strength of PC, it provides a tabulated Helmholtz free energy treatment of an ideal quantum electron-positron plasma, obtained by highprecision evaluation of the relevant Fermi-Dirac integrals (Cloutman 1989; Aparicio 1998; Gong et al 2001b). Fideal e−e+ represents an ideal gas of non-interacting electrons and positrons, obtained from biquintic Hermite polynomial interpolation of a table (Timmes & Swesty 2000, see Baturin et al 2019). This single table captures both relativistic and degeneracy effects and is valid for any fully ionized composition. Fideal mix captures the ideal free energy of mixing for ions, given by
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