2 The new solar models

We computed a large number of solar models using the GARching SOlar Model (GARSOM) code which has been described in its latest version in Schlattl (2001). Our standard model has been compared with other contemporary solar models by Turck-Chièze et al. (1998), who found a good agreement between various programs.

The solar photospheric radius and luminosity have been assumed to be $695.51~{\rm Mm}$ (Brown & Christensen-Dalsgaard 1998) and $3.8646\times 10^{33} \;{\rm erg/s}$, respectively. The surface metal ratio has been taken from Grevesse & Noels (1993), thus Z/X=0.0245. The mixing length parameter (Böhm-Vitense 1958), initial helium and metal content have been adjusted in all models to reproduce these values with an accuracy better than 10^-4.

In the actual calculations the latest OPAL-opacities (Iglesias & Rogers 1996) completed in the low-temperature regime by tables of Alexander & Fergusson (1994) have been implemented. The outer boundary condition was determined assuming an Eddington grey atmosphere. Microscopic diffusion of hydrogen, helium and all major metals is taken into account. For the EOS we used either the OPAL- (Rogers et al. 1996) or the MHD-tables (Hummer & Mihalas 1988; Mihalas et al. 1988; Däppen et al. 1988). The original OPAL EOS (OPAL96) has been updated by treating electrons relativistically and by improving the activity expansion method for repulsive interactions (Rogers 2001), denoted OPAL01 in the following.

In the case of MHD EOS the relativistic corrections are not directly included in the tables. We have therefore corrected the adiabatic index $\Gamma _1$ employing the expression of Elliott & Kosovichev (1998),

$$% \frac{\delta\Gamma_1}{\Gamma_1}\equiv {\Gamma_{1, {\rm rel... ...Gamma_1}\simeq - \frac{2+2X}{3+5X}\;\frac{k T}{m_{\rm e} c^2},$$ (1)

where T is the temperature, $m_{\rm e}$ the electron mass, c the light speed in vacuum, k the Boltzmann constant, and X the hydrogen mass fraction. As expected, the correction to $\Gamma _1$ is negative, since its value is 5/3 for the non-relativistic and 4/3 for the extremely relativistic case.

The nuclear reaction rates are taken either from Bahcall et al. (1995) or from Adelberger et al. (1998) with $S_{\rm pp}(0)$ being $3.89 \times 10^{-25}~{\rm MeV ~b}$in the first and $4.00 \times 10^{-25}~{\rm MeV ~b}$in the latter case. Other differences in the reaction rates are not very significant in determining the evolutionary stage of the solar core.