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

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