The ACS LCID Project. I. Short-Period Variables in the Isolated Dwarf
  Spheroidal Galaxies Cetus & Tucana
  (abridged) We present the first study of the variable star populations in the
isolated dwarf spheroidal galaxies (dSph) Cetus and Tucana. Based on Hubble
Space Telescope images obtained with the Advanced Camera for Surveys in the
F475W and F814W bands, we identified 180 and 371 variables in Cetus and Tucana,
respectively. The vast majority are RR Lyrae stars. In Cetus we also found
three anomalous Cepheids, four candidate binaries and one candidate long-period
variable (LPV), while six anomalous Cepheids and seven LPV candidates were
found in Tucana. Of the RR Lyrae stars, 147 were identified as fundamental mode
(RRab) and only eight as first-overtone mode (RRc) in Cetus, with mean periods
of 0.614 and 0.363 day, respectively. In Tucana we found 216 RRab and 82 RRc
giving mean periods of 0.604 and 0.353 day. These values place both galaxies in
the so-called Oosterhoff Gap, as is generally the case for dSph. We calculated
the distance modulus to both galaxies using different approaches based on the
properties of RRab and RRc, namely the luminosity-metallicity and
period-luminosity-metallicity relations, and found values in excellent
agreement with previous estimates using independent methods:
(m-M)_{0,Cet}=24.46+-0.12 and (m-M)_{0,Tuc}=24.74+-0.12, corresponding to
780+-40 kpc and 890+-50 kpc. We also found numerous RR Lyrae variables
pulsating in both modes simultaneously (RRd): 17 in Cetus and 60 in Tucana.
Tucana is, after Fornax, the second dSph in which such a large fraction of RRd
(~17%) has been observed. We provide the photometry and pulsation parameters
for all the variables, and compare the latter with values from the literature
for well-studied dSph of the Local Group and Galactic globular clusters.
