Weak Galactic Halo--Fornax dSph Connection from RR Lyrae Stars
  For the first time accurate pulsation properties of the ancient variable
stars of the Fornax dwarf spheroidal galaxy (dSph) are discussed in the broad
context of galaxy formation and evolution. Homogeneous multi-band $BVI$ optical
photometry of spanning {\it twenty} years has allowed us to identify and
characterize more than 1400 RR Lyrae stars (RRLs) in this galaxy. Roughly 70\%
are new discoveries. We investigate the period-amplitude distribution and find
that Fornax shows a lack of High Amplitude (A$_V\gsim$0.75 mag) Short Period
fundamental-mode RRLs (P$\lsim$0.48 d, HASPs). These objects occur in stellar
populations more metal-rich than [Fe/H]$\sim$-1.5 and they are common in the
Galactic halo (Halo) and in globulars. This evidence suggests that old (age
older than 10 Gyr) Fornax stars are relatively metal-poor.
  A detailed statistical analysis of the role of the present-day Fornax dSph in
reproducing the Halo period distribution shows that it can account for only a
few to 20\% of the Halo when combined with RRLs in massive dwarf galaxies
(Sagittarius dSph, Large Magellanic Cloud). This finding indicates that
Fornax-like systems played a minor role in building up the Halo when compared
with massive dwarfs. We also discuss the occurrence of HASPs in connection with
the luminosity and the early chemical composition of nearby dwarf galaxies. We
find that, independently of their individual star formation histories, bright
(M$_V\lsim$-13.5 mag) galaxies have HASPs, whereas faint ones (M$_V\gsim$-11
mag) do not. Interestingly enough, Fornax belongs to a luminosity range
(--11$<$M$_V<$--13.5 mag) in which the occurrence of HASPs appears to be
correlated with the early star formation and chemical enrichment of the host
galaxy.
