Global metallicity of globular cluster stars from colour-magnitude diagrams

We have developed an homogeneous evolutionary scenario for H- and He-burning low-mass stars by computing updated stellar models for a wide metallicity and age range (0.0002$\le Z \le$0.004 and 9$\le t(Gyr) \le$15, respectively) suitable to study globular clusters. This theoretical scenario allows us to provide self-consistent predictions about the dependence of selected observational features of the colour-magnitude diagram, such as the brightness of the Turn Off (TO), Zero Age Horizontal Branch (ZAHB) and Red Giant Branch bump (BUMP), on the cluster metallicity and age. Taking into account these predictions, we introduce a new observable based on the visual magnitude difference between the TO and the ZAHB, and the TO and the RGB-bump, given by $A=\Delta M_V$(TO-BUMP)$-0.566\Delta M_V$(TO-ZAHB). We show that the parameter $A$ does not depend at all on the cluster age, whereas it does strongly depend on the cluster global metallicity. The calibration of the parameter $A$ as a function of $Z$ is then provided, as based on our evolutionary models. We tested the reliability of this result by also considering stellar models computed by other authors,employing different input physics. Eventually, we present clear evidence that the variation of $\Delta M_V$(TO-BUMP) with $\Delta M_V$(TO-ZAHB) does supply a powerful probe of the global metal abundance, at least when homogeneous theoretical frameworks are adopted. We provide an estimate of the global metallicity of 36 globular clusters in the Milky Way, based on our {\it A-Z} calibration, and a large observational database of Galactic GCs. By considering the empirical [Fe/H] scales by both Zinn & West (1984) and Carretta & Gratton (1997), we are also able to provide an estimate of the GC $\alpha-$element enhancement.