Evolutionary and pulsation properties of Type II Cepheids
  We discuss the observed pulsation properties of Type II Cepheids (TIICs) in
the Galaxy and Magellanic Clouds. The period (P) distributions, luminosity
amplitudes and population ratios of the three different sub-groups (BL
Herculis[BLH, P<5 days], W Virginis [WV, 5<P<20 days], RV Tauri [RVT, P>20
days]) are quite similar in different stellar systems, suggesting a common
evolutionary channel and a mild dependence on both metallicity and environment.
We present a homogeneous theoretical framework based on Horizontal Branch (HB)
evolutionary models, envisaging that TIICs are mainly old (t<10 Gyr), low-mass
stars. The BLHs are predicted to be post early asymptotic giant branch (PEAGB)
stars (double shell burning) on the verge of reaching their AGB track (first
crossing of the instability strip), while WVs are a mix of PEAGB and post-AGB
stars (hydrogen shell burning) moving from cool to hot (second crossing). Thus
suggesting that they are a single group of variable stars. RVTs are predicted
to be a mix of post-AGB stars along their second crossing (short-period tail)
and thermally pulsing AGB stars (long-period tail) evolving towards their white
dwarf cooling sequence.
  We also present several sets of synthetic HB models by assuming a bimodal
mass distribution along the HB. Theory suggests, in agreement with
observations, that TIIC pulsation properties marginally depend on metallicity.
Predicted period distributions and population ratios for BLHs agree quite well
with observations, while those for WVs and RVTs are almost a factor of two
smaller and larger than observed, respectively. Moreover, the predicted period
distributions for WVs peak at periods shorter than observed, while those for
RVTs display a long period tail not supported by observations.
  We investigate several avenues to explain these differences, but more
detailed calculations are required to address them.
