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Astron. Astrophys. 326, 187-194 (1997)

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1. Introduction

Recent improvements concerning radiative opacities and equation of state removed significant discrepancies between observations and theory of stellar evolution. Updated solar models (Turck-Chièze et al. 1993; Charbonnel & Lebreton 1993; Gabriel 1994a; Basu & Thompson 1996) are in good agreement with the solar helioseismic data.

In this work models are constructed for the Sun starting when model becomes stable against gravitational contraction, with different EOS and opacities, by using Ezer's stellar evolutionary code (EC) (Ezer & Cameron 1967; Yldz& Kzloglu 1995). EOS of MHD (Mihalas et al. 1990; and references therein) which uses an approach known as chemical picture is based on minimization of the free energy and is applicable for stellar modeling. We have chosen opacity tables of OPAL (Iglesias et al. 1992). Since those tables do not extend to low temperatures, Alexander & Ferguson opacity (1994) is used for outer layers of the stars. The models computed for comparison are obtained using Cox & Stewart (1970) (CS) opacity and EC EOS which takes into account degenerate electrons and pressure ionization in an artificial way. Since OPAL opacity, near the bottom of the convective zone, is larger than the CS opacity by a factor of about two, it strongly affects the structure of the convective zone. In performing the solar calibration, the lower luminosity due to enhancement of the opacity also in radiative regions is balanced by decreasing H (or increasing He) abundance. Thus, the abundance of H by mass may also be significantly altered.

It was shown that the MHD EOS removes significantly the discrepancies between the observational and the theoretical frequencies of the solar oscillations (Christensen-Dalsgaard et al. 1988). However we do not mention about the solar oscillations. The incorporation of the Coulomb interaction in EOS reduces both of the pressure and the energy. To compensate this reduction in pressure, the mean molecular weight per free particle, that is He abundance, becomes smaller, in contrast to the effect of OPAL opacity. The application of MHD EOS requires the calculation of ionization and internal energy of each chemical species. Avoiding the time consuming calculation of the Saha equation for the heavy elements, we use two different methods, namely, Henyey (Gabriel 1994b) method and Gabriel & Yldz method (1995).

In Sect. 2 we present the basic features of the code. The EOS with its computational method and opacity used in the construction of the solar models are given in Sect 3. Sect. 4 is devoted to the influence of MHD EOS including the results of the two methods for the ionization and internal energy of heavy elements. In Sect. 5 we give the results of the solar models with different EOS and opacity.

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998