## 4. Comparing different stellar evolutionary modelsDuring the last decades there have been several attempts to reproduce the evolution of stars, motivated, in part, by the increasing power of computers and the continuous improvement of the input physics. In Table 1 some of the most recent models are listed. Differences between them are due to the use of different physical ingredients in their calculation, such as the free parameter of the mixing length theory for the convection treatment, the free parameter which allows us to consider the effect of overshooting as a mechanism to extend the convective shells, the nuclear reactions rates, the mean opacities, or the mass loss rates. Since the ages and masses obtained with our algorithm will depend on the SEM we use, a classical test has been developed to decide which of these recent models is more realistic. Comparison only consider solar composition models.
The most accurate information on fundamental parameters of stars
(mass and radii) is obtained from the analysis of the light and
radial-velocity curves of detached, double-lined eclipsing binary
systems. Based on Andersen's (1991) and Popper's (1980) compilations
of these kinds of binary stars, we constructed a sample of 61 stars
with masses between 1 and 3 , covering in
this way the Main Sequence A-type range. According to Andersen (1991)
the mean precision in From The main evaluation of the models of Table 1 is based on the hypothesis of "same age" for the two components of every binary system. We define as follows: where is the number of binary systems in our sample, are weights given by and and are the
errors propagated directly from the individual errors in In addition, the comparison between and the observed value gives us a secondary test. Let us define as: where is the number of stars. The use of weights in this case is not recommended, since in practice they depend on the errors in the determination of the observational , which are quite arbitrarily estimated. The smaller and are, the closer the agreement between the SEM and these accurate observations. In fact, the first quantity is more reliable since it has been calculated solely from fundamental stellar parameters. After rejecting ten stars located below the ZAMS we calculated and for three subsamples to evaluate the SEM fit in different HR-diagram regions:
Fig. 4 shows the for different SEM. It
is obvious from this figure that those models that do not take into
account the overshooting effect on the convective layers (VAN and CCS)
assign quite different ages to the components of the binary systems,
especially for the most evolved ones [sample
The general fit does not change markedly for
samples
From left to right, the general trend in Figs. 4 and 5 is to improve the match between observational information and the set of SEM, which almost implies a chronological improvement. An important contribution to this improvement is the application of the overshooting effect to better define the limits of the convective regions of stars. In particular, the best fits are obtained for SSMM and BFBC models. Some new studies on dynamo action in stratified convection with overshooting (Nordlund et al., 1992) and rotational effect on convection (Pulkkinen et al., 1993) will introduce important advances in the description of stellar evolution in the near future. © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |