DeepHubble Space TelescopeImaging of IC 1613. I. Variable Stars and Distance

We present WFPC2 VI photometry of a field in the halo of IC 1613, finding 13RR Lyraes and 11 Cepheids. Our photometry of the red giant branch tip and redclump is used to derive distances to IC 1613, which are consistent with eachother and with distances based on the variable stars. We compare these valueswith similarly-measured distances for the Magellanic Clouds, and are able tomeasure metallicity dependencies of the RR Lyrae and Cepheid distances byrequiring consistent relative distance measurements from the four techniques.For metallicities of [Fe/H] = -1.3 (RR Lyraes) and -1.0 (Cepheids), we find arelatively steep slope of 0.34 +/- 0.20 magnitudes per dex for the RR Lyraesand a shallow slope of -0.07 +/- 0.16 mag/dex for the Cepheids, both valueswithin the range of theoretical and empirical results in the literature. Wefind that a dependence of the red clump absolute magnitude on age, in additionto metallicity, is required to produce self-consistent relative distancesbetween IC 1613 and the Magellanic Clouds. Adopting such a red clumpcalibration and self-consistent calibrations for the other three distanceindicators, we find that the distances to all three objects are in excellentagreement. Our best distance modulus to IC 1613 is mu_0 = 24.31 +/- 0.06,corresponding to a distance of 730 +/- 20 kpc. This distance produces an RRLyrae absolute magnitude of MV = 0.61 +/- 0.08.Comment: To appear in March ApJ 36 pages, 10 figure