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

1. Introduction

Over the past decade considerable effort, both observational and theoretical, has been directed towards a more accurate determination of the stellar lower main sequence, down to the edge of the sub-stellar domain. Such a determination bears important consequences for our understanding of a wide variety of astrophysical problems, from star formation and stellar structure to galactic formation and evolution. Although the lower main sequence of the disk is relatively well determined since the survey of Monet et al. (1992), the situation is less well defined for the Galactic halo, primarily because of the greater difficulties involved in identifying the halo stars. The task of detecting halo low-mass stars (LMS) and measuring their magnitude is of formidable difficulty with ground-based telescopes. Globular clusters (GCs) have always presented a particular interest for the study of the stellar halo since we can more easily determine their main sequence than for field halo stars. Most of the observations of GCs focussed on the upper main sequence, i.e. the turn-off point, and the red giant branch, for a comparison of this region with theoretical isochrones yields a determination of the age of the clusters, and thus a lower-bound for the age of the Galatic halo. Thanks to the tremendous progress in deep photometry realized recently with the Hubble Space Telescope (HST), which reaches unprecedented magnitude and spatial resolution, the lower main sequence of GCs is now observed nearly down to the hydrogen burning limit. Thanks to the high angular resolution achievable with the HST, accurate photometry is feasible to levels about 4 magnitudes fainter than with ground-based observations, allowing photometry of very faint stars. Several HST observations of globular clusters are now available, spanning a large metallicity-range from solar value to substantially metal-depleted abundances, as will be presented in the next section. The lower main sequence of these clusters is well defined and offers a unique possibility to probe low-mass star evolutionary models for various metallicities down to the hydrogen-burning limit.

In spite of considerable progress in stellar theory - internal structure, model atmospheres and evolution - all the LMS models so far failed to reproduce accurately the observed color-magnitude diagrams (CMD) of disk or halo stars below K, i.e. , depending on the metallicity. All the models predicted too hot an effective temperature for a given luminosity, i.e. were too blue compared to the observations by at least one magnitude (see e.g. Monet, 1992). Such a disagreement stemed essentially from shortcomings both in the physics of the interior, i.e. equation of state (EOS) and thus mass-radius relationship and adiabatic gradient, and in the atmosphere, since all models were based on grey atmospheres and a diffusion approximation. Important progress has been made recently in this field with the derivation of an appropriate EOS for low-mass stars and brown dwarfs (Saumon, Chabrier & Van Horn 1995; see Chabrier and Baraffe 1997), non-grey model atmospheres for M-dwarfs (Allard and Hauschildt 1995, 1997; Brett 1995) and evolutionary models based on a consistent treatment between the interior and the atmosphere profile (Baraffe, Chabrier, Allard & Hauschildt 1995; Chabrier, Baraffe & Plez 1996; Chabrier & Baraffe, 1997). These models now reach quantitative agreement with the observations, as shown in the afore-mentioned papers and presented in Sect. 4.

Globular clusters offer the great advantage of all stars having the same metallicity, determined relatively accurately from bright star spectroscopic measurements. Moreover they are old enough for all the stars to have reached thermal equilibrium, so that age effects do not affect the luminosity of the objects near the bottom of the MS. For these reasons, the mass-luminosity relationship is well determined along the entire MS of GCs, from the turn-off down to the brown dwarf limit, with no dispersion due either to age or metallicity. From the theoretical viewpoint, these properties restrain appreciably the degrees of freedom in the parameter space, so that globular clusters provide a very stringent test to probe the validity of low-mass star evolutionary models and of the related mass-luminosity relationships for various metallicities. Agreement between these models and observations is a necessary condition (but not sufficient !) to assess the validity of these mass-luminosity relationships, a cornerstone to derive reliable mass-functions.

In this paper, we present new evolutionary models for metal-depleted ( ) low-mass stars ( ), based on the most recent non-grey model atmospheres. We compare the results with the observed CMDs of three globular clusters, namely , and , for which HST observations are available. The paper is organized as follows: the observations are summarized in Sect. 2 whereas the theory is outlined in Sect. 3, where comparison is made with other recent LMS models. Comparison between theory and observation is presented in Sect. 4. Sect. 5 is devoted to discussion and conclusion.

The extension of the present calculations to more metal-rich clusters ([Fe/H] -0.5) and field stars, which require more extensive calculations, will be presented in a forthcoming paper (Allard et al. 1997b), as well as the derivation of the mass function for globular star clusters and halo field stars, from the observed luminosity functions (Chabrier & Méra, 1997).

© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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