Multiple populations in globular clusters: Unified efforts from stellar evolution and chemical evolution models

Recent stellar evolution models for globular clusters (GCs) in multiple population paradigm suggest that horizontal-branch (HB) morphology and mean period of type ab RR Lyrae variables are mostly determined by He & CNO abundances and relative ages for subpopulations. These parameters are also provided by chemical evolution models constructed to reproduce the Na-O anti-correlation. Therefore, a consistency check is possible between the synthetic HB and chemical evolution models. Furthermore, by combining them, a better constraint might be attained for star formation history and chemical abundances of subpopulations in GCs. We find, from such efforts made for four GCs, M4, M5, M15, and M80, that consistent results can be obtained from these two independent studies. In our unified model, He and Na abundances gradually increase over the generation, and therefore, the various extensions observed in both HB morphology and Na-O chemical pattern depend on the presence of later generation stars after the second generation. It is schematically shown that this observed diversity, however, would not be naturally explained by the models requiring dilution. Further spectroscopic observations are required, for metal-poor GCs in particular, to obtain a more detailed constraint from this approach.