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Astron. Astrophys. 355, 966-978 (2000)

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1. Introduction

In very recent times, new determinations of Galactic globular cluster (GGC) metallicities have provided us with new homogeneous [FORMULA] scales. In particular, Carretta & Gratton (1997; CG) obtained metallicities from high resolution spectroscopy for 24 GGCs, with an internal uncertainty of 0.06 dex. For an even larger sample of 71 GGCs, metallicities have been obtained by Rutledge et al. (1997; RHS97) based on spectroscopy of the CaII infrared triplet. The equivalent widths of the CaII triplet have been calibrated by RHS97 on both the CG scale and the older Zinn & West (1984; ZW) scale. The compilation by RHS97 is by far the most homogeneous one which is currently available.

In the same period, we have been building the largest homogeneous [FORMULA] photometric sample of Galactic globular clusters (GGC) based on CCD imaging carried out both with Northern (Isaac Newton Group, ING) and Southern (ESO) telescopes (Rosenberg et al. 1999b, 1999c). The main purpose of the project is to establish the relative age ranking of the clusters, based on the methods outlined in Saviane et al. (1997, 1999b; SRP97, SRP99) and Buonanno et al. (1998; B98). The results of this investigation are presented in Rosenberg et al. (1999a; RSPA99). Here suffice it to say that for a set of 52 clusters we obtained V vs. [FORMULA] color-magnitude diagrams (CMD), which cover a magnitude range that goes from a few mags below the turnoff (TO) up to the tip of the red giant branch (RGB).

At this point both a spectroscopic and photometric homogeneous databases are available: the purpose of this study is to exploit them to perform a thorough analysis of the morphology of the RGB as a function of the cluster's metallicity. As a first step, we want to obtain a new improved calibration of a few classical photometric metallicity indices. Secondly, we want to provide to the community a self-consistent, analytic, family of giant branches, which can be used in the analysis of old stellar populations in external galaxies.

1.1. Metallicity indices

Photometric indices have been widely used in the past to estimate the mean metallicities of those stellar systems where direct determinations of their metal content are not feasible. In particular, they are used to obtain [FORMULA] values for the farthest globulars and for those resolved galaxies of the Local Group where a significant Pop II is present (e.g. the dwarf spheroidal galaxies).

The calibration of [FORMULA] indices is particularly important, since with comparable exposure times, deeper and more accurate photometry can be obtained for the cool, low-mass stars in these broad bands than in [FORMULA]. Moreover, our huge CMD database allows a test of the new CG scale on a large basis: we are able to compare the relations obtained for both the old ZW and new scale, and check which one allows to rank GGCs in the most accurate way. Indeed, the most recent calibration of the [FORMULA] indices (Carretta & Bragaglia 1998) is based on just 8 clusters.

1.2. Old stellar populations in Local Group galaxies

A reliable metallicity ranking of GGC giant branches also allows studies that go beyond a simple determination of the mean metallicity of a stellar population. As an illustration, we may recall the recent investigation of the halo metallicity distribution function (MDF) of NGC 5128 (Harris et al. 1999), which was based on the fiducial GC lines obtained by Da Costa & Armandroff (1990, hereafter DA90). These studies can be made more straightforward by providing a suitable analytic representation of the RGB family of GGCs. Indeed, assuming that most of the GGCs share a common age (e.g. Rosenberg et al. 1999a), one expects that there should exist a "universal" function of [FORMULA] able to map any [FORMULA] coordinate pair into the corresponding metallicity (provided that an independent estimate of the distance and extinction of the star are available). We will show here that such relatively simple mono-parametric function can actually be obtained, and that this progress is made possible thanks to the homogeneity of both our data set and analysis.

In order to enforce a proper use of our calibrations, we must clearly state that, in principle, the present relations are valid only for rigorously old stellar populations (i.e. for stars as old as the bulk of Galactic globulars). At fixed abundance, giant branches are somewhat bluer for younger ages (e.g. Bertelli et al. 1994). Moreover, in real stellar systems AGB stars are also present on the blue side of the RGB (cf. Fig. 2). Both effects must be taken into account when dealing with LG galaxies, since they could lead to systematic effects in both the mean abundances and the abundance distributions (e.g. Saviane et al. 1999a).

1.3. Layout of the paper

The observational sample, on which this investigation is based, is presented in Sect. 2. Sect. 3 is devoted to the set of indices which are to be calibrated. They are defined in Sect. 3.1. The reliability of our sample is tested in Sect. 3.3, where we demonstrate that our methodology produces a set of well-correlated indices. In Sect. 4 we show that, once a distance scale is assumed for the GGCs, our whole set of RGBs can be approximated by a single analytic function, which depends on the metallicity alone. This finding allows a new and easier way to determine the distances and mean metallicities of the galaxies of the Local Group, extending the methods of Da Costa & Armandroff (1990), and Lee et al. (1993). The metallicity indices are calibrated in Sect. 6, where analytic relations are provided both for the ZW and for the CG scales. Using these indices, we are able to test our analytic RGB family in Sect. 7. Our conclusions are in Sect. 8.

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Online publication: April 3, 2000