Does the mixing length parameter depend on metallicity? Further tests of evolutionary sequences using homogeneous databases

This paper is a further step in the investigation of the morphology of the color-magnitude diagram of Galactic globular clusters, and the fine-tuning of theoretical models, made possible by the recent observational efforts to build homogeneous photometric databases. In particular, we examine here the calibration of the morphological parameter W-HB vs. metallicity, originally proposed by Brocato et al. (1998; B98), which essentially measures the color position of the red-giant branch. We show that the parameter can be used to have a first-order estimate of the cluster metallicity, since the dispersion around the mean trend with [Fe/H] is compatible with the measurement errors. The tight W-HB-[Fe/H] relation is then used to show that variations in helium content or age do not affect the parameter, whereas it is strongly influenced by the mixing-length parameter alpha (as expected). This fact allows us, for the first time, to state that there is no trend of alpha with the metal content of a cluster. A thorough examination of the interrelated questions of the alpha-elements enhancement and the color-T-eff transformations, highlights that there is an urgent need for an independent assessment of which of the two presently accepted metallicity scales is the true indicator of a cluster's iron content. Whatever scenario is adopted, it also appears that a deep revision of the V-I-temperature relations is needed.