We introduce a new parameter \Delta \xi —the difference in magnitude between the red giant branch ( RGB ) bump and the point on the main sequence ( MS ) at the same color as the bump ( which we call the “ benchmark ” ) —to estimate the helium content in old stellar systems .
The \Delta \xi parameter is a helium indicator since an increase in helium makes , at fixed age and iron abundance , the RGB bump brighter and the MS benchmark fainter .
Moreover , its sensitivity to helium is linear over the entire metallicity range . \Delta \xi is also minimally affected by changes of a few Gyr in cluster age , by uncertainties in the photometric zero-point , by the amount of reddening , or by the effects of evolution on the horizontal branch .
The two main drawbacks of the \Delta \xi parameter include the need for precise and large photometric data sets from the RGB bump down to the MS benchmark , and a strong dependence of the \Delta \hbox { Y } / \Delta \xi slope on metallicity .
To provide an empirical basis for the \Delta \xi parameter we selected almost two dozen relatively bright Galactic Globular Clusters ( GGCs ) with low foreground reddening , and a broad range of iron abundance ( -2.45 \leq [ Fe/H ] \leq - 0.70 dex ) .
Moreover , the selected GGCs have precise , relatively deep , and homogeneous multi-band ( BVI ) photometry .
We found that the observed \Delta \xi parameters and those predicted from \alpha -enhanced evolutionary models agree reasonably well if we assume a primordial helium content of Y=0.20 ( abundance by mass ) .
The discrepancy in the photometric B band becomes of the order of 4 \sigma ( \Delta B = 0.20 Â mag ) only in the metal-poor regime .
Comparison with evolutionary prescriptions based on a canonical primordial helium content ( Y=0.245 , \Delta Y/ \Delta Z [ helium-to-metal enrichment ratio ] =1.4 ) indicates that the observed \Delta \xi values are systematically smaller than predicted .
This discrepancy ranges from 5 \sigma ( \Delta B = 0.26 Â mag ) in the metal-rich regime to 10 \sigma ( \Delta B = 0.51 Â mag ) in the metal-poor regime .
The outcome is the same if predicted \Delta \xi parameters are based on evolutionary models with CNO enhancements in addition to \alpha enhancements .
The discrepancy becomes even larger if we extend the comparison to He-enhanced models .
These findings support previous results ( Meissner & Weiss 2006 , A & A , 456 , 1085 ; Di Cecco et al. 2010 , ApJ , 712 , 527 ; Cassisi et al. 2011 , A & A , 527 , A59 ) suggesting 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 , A & AS , 97 , 851 ) ; atomic diffusion and mass loss play smaller roles .
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 .