Star Formation Histories of Globular Clusters with Multiple Populations.
  I. \omega\ Cen, M22, and NGC 1851
  There is increasing evidence that some massive globular clusters (GCs) host
multiple stellar populations having different heavy element abundances enriched
by supernovae. They usually accompany multiple red giant branches (RGBs) in the
color-magnitude diagrams (CMDs), and are distinguished from most of the other
GCs which display variations only in light element abundances. In order to
investigate the star formation histories of these peculiar GCs, we have
constructed synthetic CMDs for \omega\ Cen, M22, and NGC 1851. Our models are
based on the updated versions of Yonsei-Yale (Y^2) isochrones and horizontal
branch (HB) evolutionary tracks which include the cases of enhancements in both
helium and the total CNO abundances. To estimate ages and helium abundances of
subpopulations in each GC, we have compared our models with the observations on
the Hess diagram by employing a \chi^2 minimization technique. We find that
metal-rich subpopulations in each of these GCs are also enhanced in helium
abundance, and the age differences between the metal-rich and metal-poor
subpopulations are fairly small (~0.3-1.7 Gyr), even in the models with the
observed variations in the total CNO content. These are required to
simultaneously reproduce the observed extended HB and the splits on the main
sequence, subgiant branch, and RGB. Our results are consistent with the
hypothesis that these GCs are the relics of more massive primeval dwarf
galaxies that merged and disrupted to form the proto-Galaxy.
