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Inspection of the CM diagrams of globular clusters having similar heavyelement content shows that the luminosity of the red giant bump relative to theturnoff (Delta V_{TO}^{bump}) differs by more than 0.1 mag between clusterswith different horizontal branch morphology. Unfortunately, carefulconsideration of the data leaves us with only one pair (M3 and M13) of clustersgood for a quantitative discussion. For this pair we consider differences inage and helium content as possible causes for the difference in DeltaV_{TO}^{bump}, and find more convincing support for the latter. A larger heliumcontent in M13 stars (Y~0.28 vs. Y~0.24) accounts for various CM diagramfeatures, such as the difference in the luminosity level of RR Lyr variablesand of the red giant bump with respect to the turnoff luminosity, and thehorizontal branch morphology. This enhanced helium can be tentativelyunderstood in the framework of self--enrichment by massive asymptotic giantbranch stars in the first ~100 Myr of the cluster life. A modestself--enrichment can be present also in M3 and can be the reason for the stillunexplained presence of a not negligible number of luminous, Oosterhoff II typeRR Lyr variables. The hypothesis that a larger helium content is the secondparameter for clusters with very blue horizontal branch morphology could bechecked by an accurate set of data for more clusters giving turnoff, RR Lyrsand bump magnitudes within a unique photometry.Comment: in press on Astronomy and Astrophysic

Helium self-enrichment in globular clusters and the second parameter problem in M 3 and M 13