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Astron. Astrophys. 317, 90-98 (1997)

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6. Discussion and conclusions

As very recently stated in the paper by Baraffe et al. (1995), till recent times the theoretical framework for VLM stars appeared far from being satisfactory, "all the existing theoretical models failing to reproduce the observed magnitude-color diagram for the faintest objects, predicting temperature that are too large for a given luminosity". As a matter of fact, the history of VLM models is the history of the continuous decrease of model effective temperatures driven by the continuous improvement in the evaluation of the input physics (see, e.g. Dorman et al. 1989). In this context, solar metallicity models appear as the most difficult objects to be theoretically reproduced, just because of the difficult task of taking into the right account the proper influence of metals on both opacity and EOS.

[FIGURE]Fig. 10. Mass-luminosity relations for VLM objects for the labeled assumptions on the star metallicity, as obtained in this work (lines), by Baraffe et al. (1995) and by Chabrier et al. (1996). Observational data are from Henry & McCarthy (1993).

Numerical experiments (Ciacio 1994) as well as inspection of the results already appeared in the literature, show that the treatment of the atmosphere or the improved physical inputs mainly affect the stellar temperature, with only a minor influence on the model luminosity. As a consequence, it could be suggested that theoretical mass-luminosity relations should have reached a reasonable degree of reliability. However, recently Chabrier et al. (1996) have emphasized the need to use accurate boundary conditions (nongray model atmospheres) between the atmosphere and the interior structure to derive more reliable mass - luminosity relationship. Nevertheless, one has to notice that not negligible differences still exist between different sets of model atmospheres (Bessel 1995, Chabrier et al. 1996) due mainly to the different methods adopted in the opacity calculations (straight-mean approximation versus opacity-sampling technique). In Fig. 10, we compare theoretical predictions from the present paper, by Baraffe et al. (1995) and by Chabrier et al. (1996) with observational data by Henry & McCarthy (1993). It is worth noting that our models are in good agreement with the observations and also with the theoretical mass-luminosity relation by Chabrier et al. (1996) obtained adopting the most accurate model atmospheres (Allard et al. 1996, Brett 1995) presently available. This evidence reinforces the suggestion, given in the previous sections, that the use of a [FORMULA] relation in computing stellar models has to be regarded as a first order but not-too-bad approximation to the expected evolutionary behavior. This result is, of course, a very important point since the mass - luminosity relation is at the basis of the significant problems concerning the investigation of the initial mass function in galactic globular clusters and, more in general, in stellar systems.

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