Synthetic properties of bright metal-poor variables. I. "Anomalous" Cepheids

We present new grids of evolutionary models for the so-colled ``Anomalous'' Cepheids (ACs), adopting Z=0.0001 and various assumptions on the progenitor mass and mass-loss efficiency. These computations are combined with the results of our previous set of pulsation models and used to build synthetic populations of the predicted pulsators as well as to provide a Mass-Luminosity relation in the absence of mass-loss. We investigate the effect of mass-loss on the predicted boundaries of the instability strip and we find that the only significant dependence occurs in the Period-Magnitude plane, where the synthetic distribution of the pulsators is, on average, brighter by about 0.1 mag than the one in absence of mass-loss. Tight Period-Magnitude relations are derived in the K band for both fundamental and first overtone pulsators, providing a useful tool for distance evaluations with an intrinsic uncertainty of about 0.15 mag, which decreases to about 0.04 mag if the mass term is taken into account. The constraints provided by the evolutionary models are used to derive evolutionary (i.e, mass-independent) Period-Magnitude-Color relations which provide distance determinations with a formal uncertainty of the order of about 0.1 mag, once the intrinsic colors are well known. We also use model computations from the literature to investigate the effect of metal content both on the instability strip and on the evolutionary Period-Magnitude-Color relations. Finally, we compare our theoretical predictions with observed variables and we confirm that a secure identification of actual ACs requires the simultaneous information on period, magnitude and color, that also provide constraints on the pulsation mode