On the central helium-burning variable stars of the LeoI dwarf
  spheroidal galaxy
  We present a study of short period, central helium-burning variable stars in
the Local Group dwarf spheroidal galaxy LeoI, including 106 RR Lyrae stars and
51 Cepheids. So far, this is the largest sample of Cepheids and the largest
Cepheids to RR Lyrae ratio found in such a kind of galaxy. The comparison with
other Local Group dwarf spheroidals, Carina and Fornax, shows that the period
distribution of RR Lyrae stars is quite similar, suggesting similar properties
of the parent populations, whereas the Cepheid period distribution in LeoI
peaks at longer periods (P \sim 1.26d instead of ~0.5d) and spans over a
broader range, from 0.5 to 1.78d.
  Evolutionary and pulsation predictions indicate, assuming a mean metallicity
peaked within -1.5<= [Fe/H]<=-1.3, that the current sample of LeoI Cepheids
traces a unique mix of Anomalous Cepheids (blue extent of the red--clump,
partially electron degenerate central helium-burning stars) and short-period
classical Cepheids (blue-loop, quiescent central helium-burning stars). Current
evolutionary prescriptions also indicate that the transition mass between the
two different groups of stars is MHeF \sim 2.1 Mo, and it is constant for stars
metal-poorer than [Fe/H]\sim-0.7. Finally, we briefly outline the different
implications of the current findings on the star formation history of LeoI.
