On the Origin of Bimodal Horizontal-Branches in Massive Globular Clusters: The Case of NGC 6388 and NGC 6441

Despite the efforts of the past decade, the origin of the bimodal horizontal-branch (HB) found in some globular clusters (GCs) remains a conundrum. Inspired by the discovery of multiple stellar populations in the {\it most massive} Galactic GC, $\omega$ Centauri, we investigate the possibility that two distinct populations may coexist and are responsible for the bimodal HBs in the {\it third} and {\it fifth} brightest GCs, NGC 6388 and NGC 6441. Using the population synthesis technique, we examine two different chemical ``self-enrichment'' hypotheses in which a primordial GC was sufficiently massive to contain two or more distinct populations as suggested by the populations found in $\omega$ Cen: (1) the age-metallicity relation scenario in which two populations with different metallicity and age coexist, following an internal age-metallicity relation, and (2) the super-helium-rich scenario in which GCs contain a certain fraction of helium-enhanced stars, for instance, the second generation stars formed from the helium-enriched ejecta of the first. The comparative study indicates that the detailed color-magnitude diagram morphologies and the properties of the RR Lyrae variables in NGC 6388 and NGC 6441 support the latter scenario; i.e., the model which assumes a minor fraction ($\sim$ 15 %) of helium-excess (Y $\simeq$ 0.3) stars. The results suggest that helium content is the main driver behind the HB bimodality found most often in massive GCs. If confirmed, the GC-to-GC variation of helium abundance should be considered a {\it local} effect, further supporting the argument that age is the {\it global} second parameter of HB morphology.