Synthetic properties of bright metal-poor variables. II. BL Her stars

We investigate the properties of the so-called BL Her stars, i.e., Population II Cepheids with periods shorter than 8 days, using updated pulsation models and evolutionary tracks computed adopting a metal abundance in the range of Z=0.0001 to Z=0.004. We derive the predicted Period-Magnitude (PM) and Period-Wesenheit (PW) relations at the various photometric bands and we show that the slopes of these relations are in good agreement with the slopes determined by observed variables in Galactic globular clusters, independently of the adopted M_V(RR)-[Fe/H] relation to get the cluster RR Lyrae-based distance. Moreover, we show that also the distances provided by the predicted PM and PW relations for BL Her stars agree within the errors with the RR Lyrae based values. The use of the predicted relations with W Vir stars, which are Population II Cepheids with periods longer than 8 days, provides no clear evidence for or against a change in the PM and PW slopes around P~10 days.