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Astron. Astrophys. 327, 1054-1069 (1997)

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5. Conclusion

We have presented extensive calculations of VLMS evolution in the range [FORMULA], characteristic metallicities for old globular star clusters and halo field stars. These low-metallicities minimize possible shortcomings of the model atmospheres pertaining to incomplete or inaccurate metallic molecular line lists and grain formation, and provide a stepping stone towards the derivation of more accurate low-mass star models for solar metallicity. The models are examined against available deep photometry color-magnitude diagrams obtained with the Hubble Space Telescope for three globular clusters. The HST CMDs for the clusters span a large range in metallicity, thus providing very stringent tests for the models. Since the parameters characteristic of these clusters, extinction, distance modulus and metallicity are fairly well defined, there is no free parameter left to bring models into agreement with observations. Therefore comparison between theory and observation reflects directly the accuracy of the theory. We stress the importance of eqn.(1) when comparing GC observed and theoretical CMDs. A first generation of the present models (Baraffe et al. 1995) has been used incorrectly by comparing observations at [FORMULA] with a model at the same value of [FORMULA].

The main conclusions of these calculations can be summarized as follows:

[FORMULA] We first note the overall remarkable agreement between the present models and the observations, within less than 0.1 mag, over the whole metallicity range and the entire main sequence from the turn-off to the bottom. The characteristic changes in the slopes of the cluster MS's are reproduced accurately, and assess the validity of the physics involved in the models. This yields an accurate calibration of the observations, i.e. reliable mass-magnitude-effective temperature-age relationships.

We also provide reddening corrections based on accurate LMS synthetic spectra.

[FORMULA] Variations of the mixing length in the stellar interior affect essentially the upper main sequence near the turn-off, i.e. only stars massive enough to develop a large radiative core ([FORMULA]). Variations of the mixing length in the atmosphere is found to be inconsequential on evolutionary models. There is no clear hint for a dependence of the mixing length on the metallicity and our results remain in agreement with all observed sequences, within the error bars, for [FORMULA].

[FORMULA] The Ryan & Norris (1991) prescription to convert solar-mix abundances into oxygen-enriched mixtures characteristic of old stellar populations is accurate. Using the correct [FORMULA] -enhanced mixture (both in the atmosphere and in the interior opacities) leads to results identical to those obtained with the afore-mentioned scaling. Not taking this enrichment into account leads to inconsistent comparisons.

[FORMULA] We derive theoretical sequences in the filters of the NICMOS camera, down to the hydrogen burning limit. This will allow a straightforward analysis of the future HST observations, and provides a stringent test for the accuracy of the present models near the brown dwarf limit. This corresponds to [FORMULA] for the lowest metallicity examined presently, i.e. [FORMULA].

We also predict a photometric signature of the transition from stellar to substellar objects in the infrared, in terms of a severe blue loop near the very bottom of the MS, whereas optical colors keep reddening almost linearly. This photometric signature reflects the overwhelming absorption of molecular hydrogen in the infrared due to many-body collisions, and stems from the increase of the molecular hydrogen fraction and of the density (contraction) near the stellar to substellar transition.

[FORMULA] The models allow a good determination of the metallicty of the observed halo field stars. A striking result is the large metallicity dispersion of these objects, from [FORMULA] = -2 to near solar, although they all have halo kinematic properties. The most extreme halo stars, represented by the Monet et al. (1992) sample, have a metallicity ranging from [FORMULA] to -2.0, with an average value [FORMULA]. We find no evidence for differences in the sequences of halo field subdwarfs and globular star clusters. Both are reproduced with the same isochrones for similar mean metallicity, [FORMULA] to -1.5, i.e. [FORMULA] to -1.8.

We can now affirm that the theory of low-mass stars, at least for metal-depleted abundances, has reached a very good level of accuracy and can be used with confidence to analyse the observations and make reliable predictions. While we cannot honestly exclude the possibility of a discrepancy in the [FORMULA] color predicted by the models (by [FORMULA] mag), it remains within the error bars due to the observations themselves and to the undeterminations of either the extinction or the distance modulus. It may also reflect present uncertainties in the calibration of the [FORMULA] filter.

While it is unfortunate that the hydrogen burning limit remains unreached by the present HST observations, for it is masked by foreground field stars, the next cycles of HST observations will be able to resolve it in the near future. Indeed, known proper motion of the GCs will cause a substantial displacement of cluster stars between 1994 and 1997 which should allow a separation of cluster from field stars (King 1995). Also, as mentioned above, observations in the IR should lead to the observation of the very bottom of - and possibly below - the MS. The present models provide the limit magnitudes to be reached to enter the brown dwarf regime.

The present calculations represent an important improvement in the description of the mechanical and thermal properties of low-mass stars, and of their photometric signature. This provides solid grounds to extend these calculations into the more complicated domain of solar-like metallicities, as will be examined in a forthcoming paper (Allard et al., 1997b). The assessed accuracy of the present models provide reliable mass-luminosity relationships for metal-poor stellar populations in general and for globular clusters in particular. This allows for the first time the derivation of reliable mass-functions for these objects down to the brown dwarf limit (Chabrier and Méra, 1997).

Tables 2-5 are available by anonymous ftp:

ftp ftp.ens-lyon.fr

username: anonymous

ftp [FORMULA] cd /pub/users/CRAL/ibaraffe

ftp [FORMULA] get BCAH97_models

ftp [FORMULA] quit

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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998