Equations of State for Stellar Partial Ionization Zones
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Abstract
view Abstract Citations (203) References (35) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Equations of State for Stellar Partial Ionization Zones Fontaine, G. ; Graboske, H. C., Jr. ; van Horn, H. M. Abstract A composite numerical equation of state has been developed to compute thermodynamic surfaces covering the density-temperature domain of interest for stellar partial ionization zones. Emphasis has been placed on the thermodynamic constraints of stability and consistency in obtaining the ionization equilibrium conditions for nonideal, multicomponent gases. Two different theoretical models have been used. First, in the low-density regime, the ionization equilibrium has been obtained by the free-energy minimization technique. This method explicitly minimizes the free energy of a statistical mechanical model by finding the equilibrium concentrations of all atomic and ionic species. This particular model includes electron degeneracy, Coulomb interactions, fluid interactions, and electronic perturbations. Second, in the high-density regime where material properties are dominated by the electron gas, a hot Thomas-Fermi model has been employed. Both these models become inaccurate in the low-temperature, intermediate- density domain, and interpolation was used to approximately describe the properties of matter in this complex region. However, by making use of Maxwell's relations, thermodynamic consistency was preserved even in this interpolation region. The results are presented in the form of extensive tables listing the pressure, the internal energy, the adiabatic gradient, and the pressure derivatives as functions of the temperature and the density. Other thermodynamic quantities of astrophysical interest such as specific heats and adiabatic exponents can easily be derived from the listed data. Each table consists of 54 isotherms spaced by A log TI = 0.08, and each isotherm contains 20 to 30 density points spaced by IA log I = 31 The data cover a skewed grid in the ranges -9 < log p < 5 and 3.30 < log T < 7.54. Data are given for three mixtures with nearly pure chemical compositions, having element abundances XH = 0.999, XHe = 0.999, and Xc = 0.999. Different methods of composition interpolation have been investigated and it is found that an "additive volume" law is to be preferred. The present results are relevant to studies of pulsational properties and outer layers of white dwarfs, and also to evolutionary calculations of low-mass main-sequence stars, red giants, and white dwarfs. Subject headings: equation of state stars: interiors - stars: white dwarfs Publication: The Astrophysical Journal Supplement Series Pub Date: 1977 DOI: 10.1086/190482 Bibcode: 1977ApJS...35..293F full text sources ADS |