Dwarf Cepheids in the Carina dwarf spheroidal galaxy

We have discovered 20 dwarf Cepheids (DCs) in the Carina dwarf spheroidal galaxy from an analysis of individual CCD images obtained for a deep photometric study of the system. These short-period pulsating variable stars are by far the most distant (similar to 100 kpc) and faintest (V similar to 23.0) DCs known. The Carina DCs obey a well-defined period-luminosity relation, allowing us to readily distinguish between overtone and fundamental pulsators in nearly every case. Unlike RR Lyrae stars, the pulsation mode turns out to be uncorrelated with light-curve shape, and the overtone pulsators do not tend toward shorter periods compared with the fundamental pulsators. Using the period-luminosity relations from Nemec, Nemec, & Lutz and McNamara, we derive (m - M)(0) = 20.06 +/- 0.12, for E(B - V) = 0.025 and [Fe/H] = -2.0, in good agreement with recent, independent estimates of the distance/reddening of Carina. The error reflects the uncertainties in the DC distance scale, and in the metallicity and reddening of Carina. The frequency of DCs among upper-main-sequence stars in Carina is approximately 3%. The ratio of dwarf Cepheids to RR Lyrae stars in Carina is 0.13 +/- 0.10, though this result is highly sensitive to the star formation history of Carina and the evolution of the horizontal branch. We discuss how DCs may be useful to search effectively for substructure in the Galactic halo out to Galactocentric distances of less than or similar to 100 kpc.