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-branch (HE) morphology, with clear indications of a bimodal HE and a "gap" on the blue HE. In this paper, we present extensive synthetic HE simulations to determine whether peculiar distributions in the underlying physical parameters are needed to explain the observed HE morphology. We find that a unimodal mass distribution along the HE can satisfactorily account for the observed HE bimodality, provided the mass dispersion is substantially larger than usually inferred for the Galactic globular clusters. In this case, NGC 6229 should have a well-populated, extended blue tail. A truly bimodal distribution in HE masses can also satisfactorily account for the observed HE morphology, although in this case the existence of an extended blue tail is not necessarily implied. The other two well-known bimodal-HB clusters, NGC 1851 and NGC 2808, are briefly analyzed. While the HE morphology of NGC 1851 can also be reproduced with a unimodal mass distribution assuming a large mass dispersion, the same is not true of NGC 2808, for which a bimodal, and possibly multimodal, mass distribution seems definitely required. The problem of gaps on the blue HE is also discussed. Applying the standard 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 to 6%-9% of all cases. We employ a new and simple formalism, based on the binomial distribution, to explain the origin of this discrepancy, and conclude that Hawarden's method, in general, substantially overestimates the statistical significance of gaps.