## 7. Evolutionary modelsBasically the physics employed for the calculation of models is the same as in Morel et al. (1997b). The ordinary assumptions of stellar modeling are made, i.e. spherical symmetry, no rotation, no magnetic field, no mass loss. It has been already claimed, see Morel et al. (2000a), that stellar models of about one solar mass, computed with the same physics but initialized either on pre main-sequence or at zero-age homogeneous main-sequence are almost identical after a few years, a small quantity with respect to the expected age of the Cen system. To save computations, along the search of a solution with the minimization, we have initialized each evolution with a homogeneous zero-age main-sequence model. The models presented in Table 5 include the pre main-sequence evolution. They are initialized with homogeneous zero-age stellar model in quasi-static contraction with a central temperature close to the onset of the deuteron burning, i.e. MK. ## 7.1. Nuclear and diffusion networkWe have taken into account the most important nuclear reactions of
PP+CNO cycles (Clayton 1968). The relevant nuclear reaction rates
are taken from the NACRE compilation (Angulo et al. 1999) with
the reaction taken from the
compilation of Adelberger et al. (1998). Weak screening
(Salpeter 1954) is assumed. We have used the meteoritic value
(Grevesse & Sauval 1998) for the initial lithium abundance,
. For the calculations of the
depletion, lithium is assumed to be in its most abundant isotope
form. The initial abundance of each
isotope is derived from isotopic fractions and initial values of
and Microscopic diffusion is described by the simplified formalism of
Michaud & Proffitt (1993) with heavy elements as trace
elements. We have neglected the radiative accelerations as they amount
only to a tiny fraction of gravity in the radiative part for stars
with masses close to the solar one (Turcotte et al. 1998). We
assume that changes of with is the iron mass fraction
within ## 7.2. Equation of state, opacities, convection and atmosphereWe have used the CEFF equation of state (Christensen-Dalsgaard
& Däppen 1992) and the opacities of Iglesias &
Rogers (1996) complemented at low temperatures by Alexander &
Ferguson (1994) opacities for the solar mixture of Grevesse &
Noels (1993). We have not taken into account the changes of
abundance ratios between the metals within In the convection zones the temperature gradient is computed
according to either MLT At the end of the pre main-sequence both components, have for a few million years, a temporary convective core. For Cen A, slightly more massive than the Sun, a second convective core is formed during the main-sequence due to the onset of the CNO burning (e.g. Guenther & Demarque 2000). Following the prescriptions of Schaller et al. (1992) we have calibrated models with overshooting of convective cores over the distance where is the core radius. The atmosphere is restored using a grid of
laws, provided by
Cayrel (2000), ( is the
Rosseland optical depth) derived from atmosphere models with the solar
mixture of Grevesse & Noels (1993) and metallicity
. The atmosphere models were
computed with the Kurucz (1991) ATLAS12 package. The connection
with the envelope is made at the optical depth
where the diffusion approximation
for radiative transfer becomes valid (Morel et al. 1994). A
smooth connection of the gradients is insured between the uppermost
layers of the envelope and the optically thick convective bottom of
the atmosphere. It is an important requirement for the calculation of
eigenmode frequencies. The radius
of any model is taken at the optical depth
where
. Typically,
increases from
in the initial pre main-sequence
model, until at the present time.
The mass of the star is defined as
the mass enclosed in the sphere of radius
. The external boundary is located
at the optical depth , where the
density is fixed to its value in the atmosphere model
g cm ## 7.3. NumericsModels have been computed using the CESAM code (Morel 1997a). The numerical schemes are fully implicit and their accuracy is of the first order for the time and third order for the space. Each model is described by about 600 mass shells, this number increases up to 2100 for the models used in seismological analysis. Evolutions are described by about 80 models. About half of them concerns the pre main-sequence evolution. © European Southern Observatory (ESO) 2000 Online publication: December 11, 2000 |