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Astron. Astrophys. 364, 879-886 (2000)

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1. Introduction

The modeling of high-quality helioseismic data requires great accuracy in an equation of state (EOS), thus providing a basis for checking input physics about stellar envelopes and interiors. Although nonideal effects are fairly weak in the Sun, they influence the structure of solar interior significantly. The complexity of physical effects mainly includes two processes, i.e., Coulomb coupling and pressure ionization, both of which should be incorporated into the equation of state of stellar evolutionary codes covering a wide range of density and temperature variables.

Several equations of state have been developed in order to include nonideal effects for fully ionized or partially ionized plasmas. A theoretical description of improved equations of state beyond the ideal gas law can be based either on the physical or the chemical picture of the plasma. In the chemical picture, the simplest improved equation of state is the so called CEFF equation of state (Christensen-Dalsgaard et al. 1988; Christensen-Dalsgaard & Däppen 1992) by adding Debye-Hückel free energy term to the EFF model (Eggleton et al. 1973). Mihalas et al. (Hummer & Mihalas 1988; Mihalas et al. 1988; Däppen et al. 1988) have presented the so called MHD equation of state which takes into account the effect of excited levels of atoms and ions on the properties of the plasma. The MHD equation of state considers only the lowest-order Coulomb coupling term through the Debye-Hückel approximation. In contrast to the chemical picture, there exists a more complicated physical picture, in which nuclei and electrons (free or bound) are the only fundamental constituents of the thermodynamic ensemble, as employed in the OPAL equation of state (Rogers 1986; Rogers et al. 1996).

The MHD equation of state and the OPAL equation of state are given with their results in tabular form and can not be called directly. This is because the complex formalism and time-consuming calculation of the EOS stem from many physical processes. Although a number of shortcomings in the EFF equation of state have been known for a long time, the EFF equation of state possesses many advantages over tabulated EOSs due to its being analytical. Its obvious merit is flexibility in varying compositions, which have been routinely dealt with, and the possibility of introducing and investigating new physics. In order to model high accurate EOS, we attempt to present an algorithm for explicit and simplified expressions of the improved EFF equation of state under the solar interior conditions on the basis of free-energy minimization method in the chemical picture (Harris et al. 1960; Graboske et al. 1969). The EOS presented in this paper is formulated for a hydrogen-helium mixture and takes into account the physical processes of electron degeneracy, Coulomb coupling and pressure ionization.

The paper is organized as follows. A thermodynamic model of the hydrogen-helium mixture is presented in Sect. 2. In Sect. 3, we propose simple and accurate analytic approximations for the non-ideal free energies of the plasma arising from Coulomb coupling and pressure ionization. The algorithm for calculating thermal equilibrium is given in Sect. 4. In Sect. 5 the calculated results of the EOS are compared with those of other EOSs.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001