We have discovered 20 dwarf Cepheids (DC) in the Carina dSph galaxy from the
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
(~100 kpc) and faintest (V ~ 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 Lyr
stars, the pulsation mode turns out to be uncorrelated with light-curve shape,
nor do the overtone pulsators tend towards shorter periods compared to the
fundamental pulsators. Using the period-luminosity (PL) relations from Nemec et
al. (1994 AJ, 108, 222) and McNamara (1995, AJ, 109, 1751), 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 Lyr 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 ~100 kpc.Comment: 20 pages of text, 7 figure