On a new parameter to estimate the helium content in old stellar systems

We introduce a new parameter {\Delta}{\xi} - the difference in magnitude between the red giant branch (RGB) bump and a point on the main sequence (MS) at the same color as the bump, the "benchmark" - to estimate the helium content in old stellar systems. Its sensitivity to helium is linear over the entire metallicity range, it is minimally affected by age, uncertainties in the photometric zero-point, reddening or the effects of evolution on the horizontal branch. The two main drawbacks are the need for precise and large photometric data sets, and a strong dependence of the {\Delta}Y/{\Delta}{\xi} slope on metallicity. To test the {\Delta}{\xi} parameter we selected 22 Galactic Globular Clusters (GGCs) with low foreground reddening, a broad range of iron abundance and precise, relatively deep, and homogeneous multi-band (B,V,I) photometry. We found that the observed {\Delta}{\xi} and those predicted from {\alpha}-enhanced models agree quite well if we assume Y=0.20. Comparison with canonical primordial helium content models (Y=0.245, {\Delta}Y/{\Delta}Z=1.4) indicates that the observed {\Delta}{\xi} values are systematically smaller than predicted. The outcome is the same if predicted parameters are based on models that take into account also CNO enhancements and becomes even larger if we consider He-enhanced models. These findings suggest that current stellar evolutionary models overestimate the luminosity of the RGB bump. We also found that including envelope overshooting can eliminate the discrepancy, as originally suggested by Alongi et al. (1993, aaps, 97, 851). The {\Delta}{\xi} parameter of GGCs, in spite of the possible limitations concerning the input physics of current evolutionary models, provides an independent detection of pre-stellar helium at least at the 5{\sigma} level.