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

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3. Metallicity indices

3.1. Definitions

The metallicity indices calibrated in this study are represented and defined in Fig. 1 and Fig. 2. The figures represent the CMD of NGC 1851 and NGC 104 in different color-magnitude planes, and the crosses mark the position of the RGB points used in the measurement of the indices.

The left panel of Fig. 1 shows the apparent colors and magnitudes for NGC 1851: the inclined line helps to identify the first index, S. This was defined, in the [FORMULA] plane, by Hartwick (1968) as the slope of the line connecting two points on the RGB: the first one at the level of the HB, and the second one 2.5 mag brighter. We use the same definition for the [FORMULA] plane here; however, in order to be able to use our metal richest clusters, we redefined S by measuring the second RGB point 2 mag brighter than the HB. Since S is measured on the apparent CMD, it is independent both from the reddening and the distance modulus.

The right panel of the same figure, shows the apparent V magnitude vs. the de-reddened [FORMULA] color. In this panel, four other indices are identified, i.e. [FORMULA], [FORMULA], [FORMULA], and [FORMULA]. The first one is the RGB color at the level of the HB, and the other three measure the magnitude difference between the HB and the RGB at a fixed color [FORMULA], 1.2 and 1.4 mag. The former index was originally defined by Sandage & Smith (1966) and the latter one by Sandage & Wallerstein (1960), in the [FORMULA] plane. The other two indices, [FORMULA] and [FORMULA], are introduced later to measure the metal richest GCs. These indices require an independent color excess determination.

Finally, Fig. 2 shows the CMD of NGC 104 (47 Tuc) in the absolute [FORMULA] plane: the adopted distance modulus, [FORMULA], was obtained by correcting the apparent luminosity of the HB according to Lee et al. (1990; cf. Sect. 6). By comparison, Harris' catalog reports [FORMULA]. Two other indices are represented in the figure: [FORMULA] and [FORMULA]. They are defined as the RGB color at a fixed absolute I magnitude of [FORMULA] (Da Costa & Armandroff 1990) or [FORMULA] (Lee et al. 1993). The latter index was also discussed by Armandroff et al. (1993), and a calibration formula was given in Caldwell et al. (1998). This is based on the DA90 clusters plus M5 and NGC 362 from Lloyd Evans (1983).

Since these two indices are defined on the bright part of the RGB, they can be measured even for the farthest objects of the Local Group (LG). Due to the fast luminosity evolution of the stars on the upper RGB, this part of the branch was typically under-sampled by the early small-size CCDs, so no wide application of these indices has been made for Galactic globulars. However, this is of no concern for galaxy-size stellar systems. It will be shown in Sect. 6 that good accuracies can be obtained even for GCs, provided that the analytic function of Eq. (1) is used.

3.2. Measurement procedures

Colors and magnitudes were measured on a fiducial RGB, which has been found by least-square fitting an analytic function to the observed branch. After some experimenting, it was found that the best solution is to use the following relation:


where x and y represent the color and the magnitude, respectively. One can see from Figs. 1 and 2 that the function is indeed able to represent the giant branch over the typical metallicity range of globular clusters. Moreover, it is shown in Sect. 4 that, when the CMDs are corrected for distance and reddening, the four coefficients can be parametrized as a function of [Fe/H], so that one is able to reproduce the RGB of each cluster, using just one parameter: the metallicity. At any rate, the indices were measured on the original loci, so that an independent check of the goodness of the generalized hyperbolae can be made, by comparison of the measured vs. predicted indices.

All the indices' values that have been measured are reported in Table 2. In this table, the cluster NGC number is given in Column 1; the following columns list, from left to right, [FORMULA], S, [FORMULA], [FORMULA], [FORMULA], and finally the RGB color measured at [FORMULA] and -3.5. The Lee et al. (1990) distance scale was used to compute the last two indices (cf. Sect. 6).


Table 2. The measured metallicity indices

3.3. Internal consistency checks

Before discussing the indices as metallicity indicators, we checked their internal consistency. We will show in Sect. 6 that the index S is the most accurate one, as expected, since it does not require reddening and distance corrections. The rest of the indices are therefore plotted vs. S in Figs. 3 and 4, and we expect that most of the scatter will be in the vertical direction. Second order polynomials were fitted to the distributions, and the rms of the fit was computed for each index. In order to intercompare the different indices, a relative uncertainty has been computed by dividing the rms by the central value of each parameter (this value is identified by a dotted line in each figure).

[FIGURE] Fig. 3. The metallicity indices [FORMULA], [FORMULA], and [FORMULA] are plotted as a function of the index S. The points are ordered such that the metal-poor to metal-rich cluster sequence goes from left to right. The very good correlations between [FORMULA], [FORMULA] and S (the rms of the parabolic fits are 2% and 3% respectively), demonstrate that these indices are very accurate

[FIGURE] Fig. 4. The metallicity indices [FORMULA], [FORMULA], and [FORMULA] as a function of the index S. The points are ordered such that the metal-poor to metal-rich cluster sequence goes from left to right. The dashed line represents a second order polynomial least-square fitted to the data. The typical relative uncertainty on each index has been estimated by taking the ratio of the rms of the fit over the value of the parameter at the level of the horizontal dotted line

In this way, the scatter of the metal index i is [FORMULA], 0.02, 0.04, 0.06, 0.12, and 0.26, for the indices [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA], and [FORMULA], respectively. These values confirm the visual impression of the figures, that [FORMULA] and [FORMULA] are the lowest dispersion indices, followed by [FORMULA] and [FORMULA].

The indices will be calibrated in terms of [Fe/H] in Sect. 6; however, before moving to this section, we want to present a new way to provide "standard" GGC branches in the [FORMULA] plane, along the lines of the classical Da Costa & Armandroff (1990) study. Using this family of RGB branches, we are able to make predictions on the trend of the already defined indices with metallicity; these trends can thus be compared to the observed ones, and therefore provide a further test of the reliability of our RGB family (cf. Sect. 7).

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Online publication: April 3, 2000