The second-parameter effect in metal-rich globular clusters

Recent Hubble Space Telescope observations have found that the horizontal branches (HBs) in the metal-rich globular clusters NGC 6388 and NGC 6441 slope upward with decreasing B - V. Such a slope is not predicted by canonical HE models and cannot be produced by either a greater cluster age or enhanced mass loss along the red giant branch (RGB). The peculiar HE morphology in these clusters may provide an important clue for understanding the second-parameter effect. We have carried out extensive evolutionary calculations and numerical simulations in order to explore three noncanonical scenarios for explaining the sloped HBs in NGC 6388 and NGC 6441: (1) a high cluster helium abundance scenario, in which the HE evolution is characterized by long blue loops; (2) a rotation scenario, in which internal rotation during the RGB phase increases the HE core mass; and (3) a helium-mixing scenario, in which deep mixing on the RGB enhances the envelope helium abundance. All three of these scenarios predict sloped HBs with anomalously bright RR Lyrae variables. We compare this prediction with the properties of the two known RR Lyrae variables in NGC 6388. Additional observational tests of these scenarios are suggested.