The variable stars and blue horizontal branch of the metal-rich globular cluster NGC 6441

We present time-series VI photometry of the metal-rich ([Fe/H] = -0.53) glo bular cluster NGC 6441. Our color-magnitude diagram shows that the extended blue horizontal branch seen in Hubble Space Telescope data exists in the o utermost reaches of the cluster. About 17% of the horizontal-branch stars l ie blueward and brightward of the red clump. The red clump itself slopes ne arly parallel to the reddening vector. A component of this slope is due to differential reddening, but part is intrinsic. The blue horizontal-branch s tars are more centrally concentrated than the red clump stars, suggesting m ass segregation and a possible binary origin for the blue horizontal-branch stars. We have discovered similar to 50 new variable stars near NGC 6441, among them eight or more RR Lyrae stars that are highly probable cluster me mbers. Comprehensive period searches over the range 0.2-1.0 days yielded un usually long periods (0.5-0.9 days) for the fundamental pulsators compared with held RR Lyrae of the same metallicity. Three similar long-period RR Ly rae are known in other metal-rich globular clusters. With over 10 examples in hand, it seems that a distinct subclass of long-period, metal-rich RR Ly rae stars is emerging. It appears that these stars have the same intrinsic colors as normal RR Lyrae. Using the minimum-light color of the RR Lyrae, w e determine the mean cluster reddening to be E(B-V) = 0.45 +/- 0.03 mag, wi th a significant variation in reddening across the face of the cluster. The observed properties of the horizontal-branch stars are in reasonable agree ment with recent models that invoke deep mixing to enhance the atmospheric helium abundance, while they conflict with models that assume high initial helium abundance. The Light curves of the c-type RR Lyrae seem to have unus ually long rise times and sharp minima. Reproducing these light curves in s tellar pulsation models may provide another means of constraining the physi cal variables responsible for the anomalous blue horizontal-branch extensio n and sloped red clump observed in NGC 6441.