A straightforward test of our new analytic RGBs can be made by generating the same metallicity indices that have been measured on the observed RGBs, and then checking the consistency of the predicted vs. measured quantities. To this aim, for a set of discrete [Fe/H] values a vector was generated, and the combination of the two was used to compute the vector of the giant branch, using Eqs. (2-6). Then for each branch the metallicity indices were measured as it was done for the clusters' fiducials.
In Figs. 8 to 11, the predicted indices are identified by the small open squares (spaced by 0.1 dex) connected by a solid line. The best predictions are for those indices that rely on the brightest part of the RGB (i.e. , and ), while the computations are partially discrepant for those indices that rely on a point that is measured on the faint RGB. This is easily explained by the nature of our fit: since the best match is searched for along the ordinates (for the reasons discussed in Sect. 4), then it is better constrained in the upper part of the RGB, where its curvature becomes more sensitive to metallicity. We must also stress that the metal richest cluster in the reference grid is 47 Tuc ([Fe/H] on the CG scale), whereas NGC 6352 ([Fe/H] on the same scale) is the metal richest cluster for which metallicity indices have been measured. Some of the discrepancies that are seen at the highest metallicities are therefore due to the lack of low-reddening clusters that can be used to extend the reference grid to the larger [Fe/H] values.
The mean differences between the predicted and fitted indices are, on the CG scale, around 0.03 dex for the and indices. They are around 0.08 dex for the , , and S indices. They rise to and dex for the and indices. A similar trend is seen for the comparison on the CG scale. In this case, the mean differences are dex for , , and S; they are dex for and ; and they are 0.12 and 0.27 for the and indices.
We can therefore conclude that, apart from the and indices, our mono-parametric RGB family gives a satisfactory reproduction of the actual changes of the RGB morphology and location, as a function of metallicity. It is then expected that, using this approach, one can exploit the brightest mags of the RGB to determine the mean metallicity, and even more important, the metallicity distribution of the old stellar population of any Local Group galaxy. In a forthcoming paper, we will demonstrate such possibility by re-analyzing our old photometric studies of the dwarf spheroidal galaxies Tucana (Saviane et al. 1996), Phoenix (Held et al. 1999a; Martínez-Delgado et al. 1999b), Fornax (Saviane et al. 1999a), LGS 3 (Aparicio et al. 1997), Leo I (Gallart et al. 1999; Held et al. 1999b) and NGC 185 (Martínez-Delgado et al. 1999a).
© European Southern Observatory (ESO) 2000
Online publication: April 3, 2000