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Metal-rich globular clusters of the Galaxy: morphology of the helium-burning "clump," and the determination of relative ages through the "$ΔV$" method

Morphological aspects of the $V, \bv$ diagram of metal-rich globular clusters are analyzed, on the basis of stellar evolution models for horizontal-branch (HB) and red giant branch stars. These have been incorporated into detailed synthetic HB models, the influence of differential reddening upon which is also discussed. The synthetic HB models are found to be very clumpy in the colour-magnitude diagram, though more extended structures occasionally result due to the effect of evolution away from the zero-age HB. In particular, "sloped" clumps may be naturally expected for sufficiently high helium abundances. Differential reddening is found to have a smaller influence than evolution itself upon the morphology of the clump. The synthetic HB models are also used to study the age difference between metal-rich clusters on the basis of the "$ΔV$" method. We emphasize the importance of knowing in advance the relative abundances of helium and metals in order to estimate this age difference quantitatively. We present chemical evolution models that serve to illustrate the effect, and show that, for two clusters of identical [Fe/H] and $ΔV$, the one enriched predominantly by ejecta from supernovae type II explosions will appear younger than the other which also suffered enrichment from supernovae type Ia ejecta. The implied locations of the red giant branch feature known as the "bump" are also discussed on the basis of recent observational and theoretical results. Our corresponding predictions should be checked against accurate observational data obtained with the Hubble Space Telescope.