BIMODALITY AND GAPS ON GLOBULAR-CLUSTER HORIZONTAL BRANCHES - II - THE CASES OF NGC-6229, NGC-1851, AND NGC-2808

The outer halo globular cluster NGC 6229 has a peculiar horizontal-bra nch (HE) morphology, with clear indications of a bimodal HE and a ''ga p'' on the blue HE. In this paper, we present extensive synthetic HE s imulations to determine whether peculiar distributions in the underlyi ng physical parameters are needed to explain the observed HE morpholog y. We find that a unimodal mass distribution along the HE can satisfac torily account for the observed HE bimodality, provided the mass dispe rsion is substantially larger than usually inferred for the Galactic g lobular clusters. In this case, NGC 6229 should have a well-populated, extended blue tail. A truly bimodal distribution in HE masses can als o satisfactorily account for the observed HE morphology, although in t his case the existence of an extended blue tail is not necessarily imp lied. The other two well-known bimodal-HB clusters, NGC 1851 and NGC 2 808, are briefly analyzed. While the HE morphology of NGC 1851 can als o be reproduced with a unimodal mass distribution assuming a large mas s dispersion, the same is not true of NGC 2808, for which a bimodal, a nd possibly multimodal, mass distribution seems definitely required. T he problem of gaps on the blue HE is also discussed. Applying the stan dard Hawarden and Newell chi(2) test, we find that the NGC 6229 gap is significant at the 99.7% level. However, in a set of 1000 simulations , blue-HE gaps comparable to the observed one are present in similar t o 6%-9% of all cases. We employ a new and simple formalism, based on t he binomial distribution, to explain the origin of this discrepancy, a nd conclude that Hawarden's method, in general, substantially overesti mates the statistical significance of gaps.