## 3. Photometric metallicity indicators in the V,B-V planeThe position and morphology of the RGB in the
plane are theoretically well tied to the metal content of the stars in
a cluster: the higher the metal content, the cooler the effective
temperature T In principle, for every GC with a good CMD of the brightest evolutionary phases, metallicity indicators may be derived from its RGB. However, to obtain a reliable calibration, homogeneous measurements are needed. We will then select data sets homogeneous enough to match the quality of the calibrating metallicity scale. ## 3.1. The indexThe index (Sandage & Smith 1966) is the de-reddened colour of the RGB at the luminosity level of the HB in the CMD. As one of the most homogeneous available samples, we adopted the one published by Sarajedini and Layden (1997, SL). Their study extended to the plane the Simultaneous Metallicity Reddening method by Sarajedini (1994). They selected high quality CCD photometric studies of 17 globular clusters (15 galactic and 2 Magellanic Clouds clusters), 6 of which were used as primary calibrators. De-reddened colours are adopted from their Table 5. Whenever possible, we try to rest our calibration on the GCs directly analyzed in CG97. Among the 17 SL clusters, only 9 have [Fe/H] values from direct high-resolution spectroscopy; for all other cases, we translated the older ZW value to the new scale with eq. 7 in CG97. The range in metallicity covered by CG97 is [Fe/H] , so all relations here derived are strictly valid only in this interval. We did not try to extend their validity to higher metallicities, e.g. by applying a constant offset given by the difference between ZW and CG97 values at [Fe/H] = -0.54 (the most metal-rich clusters in common): there is in fact the possibility that the strong Ca lines, upon which ZW determinations are based, saturate at very high metallicities. SL used the old ZW scale (ZW; Da Costa & Armandroff 1990; Armandroff et al. 1992). To derive the two expressions for [Fe/H], as a function i) of and ii) of needed to simultaneously solve for metallicity and reddening, they fitted the data using linear regressions. Note however that in previous studies (like Costar & Smith 1988) the linearity of the calibration at the low and high metallicity ends was questioned. We have repeated the calibration, but in terms of [Fe/H] , and results are shown in Fig. 1. Adopting the CG97 scale, this non-linear effect is obviously enhanced, and it is possible to see also by eye that a linear fit is a poor approximation.
The resulting best-fit quadratic relations connecting and [Fe/H] shown in Fig. 1, upper panel, are: when using only the 6 SL primary calibrating clusters (with deviation , and correlation coefficient ) and when using all the 17 SL clusters (, ). Error bars in [Fe/H] can be derived from the CG97 paper: they range from 0.01 to 0.11 dex, with an average value of 0.06 dex. SL apparently did not quote any error associated to their values. To corroborate the visual impression of non linearity, we tested
the statistical significance of the terms of higher order in Eqs. 1
and 2 by a The lower panel of Fig. 1 displays instead the calibration based only upon the 9 CG97 reference clusters; the corresponding relation is: ( and ). In our view, Eq. 3 is the best interpolating fit, since it has the lower formal statistical and higher correlation coefficient. Note however that differences in the derived [Fe/H] values from the one obtained from Eqs. 1 and 2 look negligible (0.01 to 0.02 dex on average, on a range of 0.35 mag in colour). As a check for the validity of the relations found, we used values from two recent high quality photometric studies, namely M3 ( = 0.80; Ferraro et al. 1997) and M5 ( = 0.83; Sandquist et al. 1996), which are not among the clusters used to derive the calibrations. Using Eq. 3 we obtain [Fe/H] for M3, and [Fe/H] for M5. These values have to be compared with (M3) and (M5) obtained from direct analysis by CG97. This test suggests that with the present calibration we are able to establish a very good ranking in cluster metallicities, quite comparable with that given by the CG97 scale. Eq. 3 comes out as best calibration of the parameter as metallicity indicator, and can be adopted as one of the basic equations of the Simultaneous Metallicity Reddening method (SMR, Sarajedini 1994). ## 3.2. The and parametersThe second index we recalibrated is a variation of the classical
parameter, that measures the difference in
These parameters, taken as before from SL Table 5, have been calibrated (see Eqs. 4 and 5), and the case of is presented in Fig. 2 ( has a very similar behaviour and is not shown).
At odds with the case of , there seems to be a clear difference between the calibrations based on the 6 SL primary calibrating clusters and on the whole SL sample. In particular, for a given the first relation gives a lower value of [Fe/H], and the effect seems to be stronger at low/intermediate metallicity, while at higher metallicities the two lines intersect. In fact, using the relation derived from the 6 SL calibrators [Fe/H] values are underestimated on average by 0.08 dex in the interval [Fe/H] , with respect to the other calibration. We have no explanation for this feature; here we only want to note
that SL stated that Finally, we re-calibrated the - metallicity relation using the 9 CG97 primary calibrating clusters. The relation is shown in the lower panel of Fig. 2 and is given by: (, ). This calibration provides [Fe/H] values agreeing very well with those obtained from all the 17 clusters of SL, and clearly represent a good fit to all the data. The case for the index closely reproduces that of ; the resulting calibration based on the 9 CG97 clusters is: (, ). In conclusion, these new calibrations are able to provide metal abundance with a dispersion of about dex, comparable to the errors usually obtained from direct, high resolution spectroscopy of stars in GCs. Eqs. 3 and 4 (or 3 and 5) can be used in the application of the SMR method in the plane. © European Southern Observatory (ESO) 1998 Online publication: December 16, 1997 |