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

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2. Observations

The decreasing luminosity of stars with mass ([FORMULA] for low-mass stars) renders the observation of the lower main sequence almost impossible from ground-based telescopes. Despite these difficulties, a number of clusters have been investigated with large telescopes by several groups worldwide to determine the bottom of the main sequence. To our knowledge, the most extensive study was conducted by Richer et al. (1991) who determined accurately the MS of six GCs up to a magnitude [FORMULA], i.e. a mass [FORMULA]. Although intrinsically interesting, these observations do not provide any information about the very bottom of the MS, and the shape of the luminosity function near the hydrogen-burning limit. Moreover, for metal-depleted abundances, the afore-mentioned limit magnitude and mass correspond to a temperature [FORMULA] K (see Sect. 4). Above this temperature, the physics of the stellar interiors and atmospheres is relatively well mastered, so that these observations put little constraint on the models, and the related mass-luminosity relationship.

A recent breakthrough in the field has been accomplished with the deep photometry of several GCs obtained with the refurbished Space Telescope. Several observations are now available for [FORMULA] (Paresce, DeMarchi & Romaniello, 1995; Cool, Piotto & King, 1996), [FORMULA] ([FORMULA] ) (DeMarchi & Paresce 1995; Piotto, Cool & King, 1996) and [FORMULA] (Elson, Gilmore, Santiago & Casertano, 1995). Observations for these clusters reach [FORMULA], [FORMULA], almost the very bottom of the main sequence, and thus provide a unique challenge to probe the validity of the LMS models down to the brown dwarf regime.

[FORMULA] Metallicity. All the afore-mentioned clusters are substantialy metal-depleted. Before going any further, it is essential to define what we call "metallicity" in the present context, for different definitions are used in the literature. What is observed in globular clusters is the iron to hydrogen ratio [FORMULA]. The continuous production of oxygen in type II supernovae during the evolution of the Galaxy has led to the well observed enhancement of the oxygen to iron [FORMULA] abundance ratio in old metal-poor stars with respect to the young disk population. Since our basic models assume a solar-mix composition, i.e. [FORMULA], the afore-mentioned oxygen-enhancement must be taken into account to make consistent comparison between theory and observation. We use the prescription derived by Ryan and Norris (1991) for halo subdwarfs, i.e.





Thus a cluster with an observed [FORMULA], for example, corresponds to a model with a metallicity [FORMULA], certainly not [FORMULA]. This latter choice does not take into account the enhancement of the [FORMULA] elements 1and yields inconsistent comparisons, especially at the bottom of the MS where the stellar optical spectra and colors are shaped by H [FORMULA], MgH, CaH and TiO opacities. The Ryan & Norris correction is based on the spectroscopically-determined abundance of 370 kinematically selected halo stars in the solar neighborhood. Although this procedure is not as fully consistent as calculations conducted with the exact mixture, it certainly represents a fairly reasonable correction for the metal-poor star oxygen enrichment. The accuracy of this prescription will be demonstrated in Sect. 3.4, where calculations with the appropriate [FORMULA] -enhanced mixture are presented.

[FORMULA] Photometric conversion. The afore mentioned clusters have been observed with the Wide Field and Planetary Camera-2 (WFPC2) of the HST, using either of the [FORMULA], [FORMULA] or [FORMULA] filters, where [FORMULA] refer to the standard (Johnson-Cousins) filters. Thanks to the courtesy of A. Cool, I. King, G. DeMarchi, F. Paresce, G. Gilmore and R. Elson, we have been able to use the data in these filters, in the so-called WFPC2 Flight system for [FORMULA], [FORMULA] and [FORMULA]. For these clusters, comparison between theory and observations is made directly in the Flight system, thus avoiding any possible uncertainties in the synthetic flight-to-ground photometric transformations of Holtzman et al. (1995). The model magnitudes were calculated using the filter transmissions curves and the observed 2zero points prescribed by Holtzman et al. (1995).

The conversion of apparent m (observation) to absolute M (theory) magnitudes requires the knowledge of the distance modulus ([FORMULA] ), corrected for the interstellar extinction in each filter. In order to minimize the bias in the comparison between theory and observation, we have used the analytical relationships of Cardelli et al. (1989) to calculate the extinctions from the M-dwarf synthetic spectra of Allard & Hauschildt (1997) over the whole frequency-range, from the reddening value [FORMULA] quoted by the observers, and we have compared the observed data with the theoretical models corrected for reddening in the WFPC2 filters, when available. The extinction in each filter was found to depend very weakly on the spectral type ([FORMULA] mag), and thus to be fairly constant over the whole considered temperature range. We believe these determinations, based on accurate synthetic spectra, to yield the most accurate extinction and reddening corrections and the most consistent comparison between theory and observation. These values are given in Table 1, for each cluster, and compared to the values quoted by the observers. Table 1 also summarizes the characteristics adopted for the three clusters of interest. Note that some undetermination remains in the distance modulus of [FORMULA], yielding a difference in the magnitude of [FORMULA] mag, as will be shown in Sect. 4. This stresses the need for a more accurate determination of this parameter.


Table 1. Characteristics of the globular clusters. [FORMULA] is the observed metallicity, [FORMULA] is the metallicity used in the models, which takes into account the [FORMULA] -enrichment following the prescription of Ryan & Norris (see Sect. 2). The fourth and fifth columns denote the bare distance modulus and reddening repectively, as quoted by the refered observers. The last three columns give the extinction in the three respective filters [FORMULA], [FORMULA] and [FORMULA], where J and C denote the standard Johnson-Cousins system. The upper rows give the value chosen by the refered observers whereas the lower rows denote the value used in the present calculations, deduced from the Allard & Hauschildt (1997) synthetic spectra and the Cardelli et al. (1989) extinction law. In all cases the interstellar extinction corresponds to [FORMULA].

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Online publication: April 6, 1998