The mosaic multiple stellar populations in $\omega$ Centauri : the
  Horizontal Branch and the Main Sequence
  We interpret the stellar population of $\omega$ Centauri by means of a
population synthesis analysis, following the most recent observational
guidelines for input metallicities, helium and [(C+N+O)/Fe] contents. We deal
at the same time with the main sequences, sub-giant and horizontal branch data.
The reproduction of the observed colour magnitude features is very satisfying
and bears interesting hints concerning the evolutionary history of this
peculiar stellar ensemble. Our main results are: 1) no significant spread in
age is required to fit the colour-magnitude diagram. Indeed we can use coeval
isochrones for the synthetic populations, and we estimate that the ages fall
within a $\sim 0.5$ Gyr time interval; in particular the most metal rich
population can be coeval (in the above meaning) with the others, if its stars
are very helium--rich (Y$\sim$0.37) and with the observed CNO enhancement
([(C+N+O)/Fe] = + 0.7); 2) a satisfactory fit of the whole HB is obtained,
consistent with the choice of the populations providing a good reproduction of
the main sequence and sub giant data. 3) the split in magnitude observed in the
red HB is well reproduced assuming the presence of two stellar populations in
the two different sequences observed: a metal poor population made of stars
evolving from the blue side (luminous branch) and a metal richer one whose
stars are in a stage closer to the zero age HB (dimmer branch). This
modelization also fits satisfactorily the period and the [Fe/H] distribution of
the RR Lyrae stars.
