We present new multiband (UBVI) time-series data of helium burning variables in the Carina dwarf spheroidal galaxy. The current sample includes 92 RR Lyrae --six of them are new identifications-- and 20 Anomalous Cepheids, one of which is new identification. The analysis of the Bailey diagram shows that the luminosity amplitude of the first overtone component in double-mode variables is located along the long-period tail of regular first overtone variables, while the fundamental component is located along the short-period tail of regular fundamental variables. This evidence further supports the transitional nature of these objects. Moreover, the distribution of Carina double-mode variables in the Petersen diagram (P_1_/P_0_ versus P_0_) is similar to metal-poor globulars (M15, M68), to the dwarf spheroidal Draco, and to the Galactic Halo. This suggests that the Carina old stellar population is metal-poor and affected by a small spread in metallicity. We use trigonometric parallaxes for five field RR Lyrae stars to provide an independent estimate of the Carina distance using the observed reddening free Period-Wesenheit [PW,(BV)] relation. Theory and observations indicate that this diagnostic is independent of metallicity. We found a true distance modulus of {mu}=20.01+/-0.02 (standard error of the mean)+/-0.05 (standard deviation) mag. We also provided independent estimates of the Carina true distance modulus using four predicted PW relations (BV, BI, VI, BVI) and we found: {mu}=(20.08+/-0.007+/-0.07)mag, {mu}=(20.06+/-0.006+/-0.06)mag, {mu}=(20.07+/-0.008+/-0.08)mag, and {mu}=(20.06+/-0.006+/-0.06)mag. Finally, we identified more than 100 new SX Phoenicis stars that together with those already known in the literature (340) make Carina a fundamental laboratory for constraining the evolutionary and pulsation properties of these transitional variables.

Cone search capability for table J/ApJ/814/71/table3 (Catalog of candidate variable stars that according to the current investigation are not variable)

Cone search capability for table J/ApJ/814/71/table2 (Catalog of Carina variable stars)

Cone search capability for table J/ApJ/814/71/table12 (Pulsation properties of the new Carina SX Phe)

Cone search capability for table J/ApJ/814/71/table13 (Pulsation properties of the known Carina SX Phe)