The Carina Project IX: on Hydrogen and helium burning variables
  We present new multi-band (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 tale 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 vs 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\pm0.02 (standard error of the
mean) \pm0.05 (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\pm0.007\pm0.07) mag,
\mu=(20.06\pm0.006\pm0.06) mag, \mu=(20.07\pm0.008\pm0.08) mag and
\mu=(20.06\pm0.006\pm0.06) 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 to constrain the evolutionary and
pulsation properties of these transitional variables.
