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Astron. Astrophys. 364, 157-164 (2000)

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1. Introduction

The equation of state (EOS) is one of the most important physical inputs for the study of stellar envelopes and interiors. Although a simple ideal-gas model of the plasma of the solar interior, the so-called EFF equation of state (Eggleton et al. 1973), was adequate before the advent of helioseismology, the use of high-quality helioseismic data requires much greater accuracy in the EOS (Christensen-Dalsgaard & Däppen 1992). The calculation of the EOS of a multicomponent quantum plasma, consisting of charged particles interacting via the Coulomb potential, is of theoretical and practical interest.

The gas in the solar interior is only weakly coupled and weakly degenerate; however, non-ideal effects, especially Coulomb corrections, significantly influence the structure of the solar interior. The Coulomb correction due to the sum of all pair interactions between charged particles (electrons, nuclei and compound ions), is conventionally described in the Debye-Hückel approximation. The simplest improved EOS is the so-called CEFF equation of state, obtained by adding Debye-Hückel terms to the EFF model (Christensen-Dalsgaard et al. 1988; Stix & Skaley 1990; Christensen-Dalsgaard & Däppen 1992). To estimate the possible deficiencies of this approximation, a more realistic expression for the higher-order corrections is required. The specific form of [FORMULA] correction based on the assumption of a constant ion radius to the Debye-Hückel term was adopted in the MHD equation of state (Hummer & Mihalas 1988; Mihalas et al. 1988; Däppen et al. 1988; Gabriel 1994). However, the influence of this [FORMULA] correction is too large to be realistic for a stellar plasma. Recent studies have addressed specific non-ideal effects beyond the Debye-Hückel approximation (Pols et al. 1995; Christensen-Dalsgaard et al. 1996; Stolzmann & Blöcker 1996; Däppen 1998; Nayfonov & Däppen 1998), and there is clearly a strong interest in further development of the EOS.

The EOS presented in this paper is formulated for a hydrogen-helium mixture and takes into account the physical processes of electron degeneracy and Coulomb coupling based on the free energy minimization method in the chemical picture (Harris et al. 1960; Graboske et al. 1969). A simple thermodynamic model of the hydrogen-helium mixture is presented in Sect. 2. In Sect. 3, we establish the detailed processes of Coulomb coupling, and propose simple approximations for the non-ideal free energies of the plasma. The calculated results and comparisons are presented in Sect. 4. A brief summary is given in Sect. 5.

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© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000