1997A&A...317..171B

Pulsating convective models and evolutionary tracks are used to constrain mass, luminosity, and effective temperature of metal-poor (Z in the range of 0.0001 to 0.001) low-mass (0.52M_☉-0.80M_☉) fundamental pulsators connected with the horizontal branch and asymptotic branch phase. On this basis the fundamental period P(F) and the absolute blue magnitude B of the pulsators are calculated. We show that, by scaling the blue magnitude of the pulsator to the value B(3.83) of the zero age horizontal branch at the mean effective temperature of the RR Lyrae strip (logTe=3.83), the distribution of theoretical fundamental pulsators in the B(3.83)-B vs P(F) plane is independent of metallicity. The limits of this distribution, which depend on the adopted edges of the instability strip, conform well with data of known type II Cepheids and show that these variables are fundamental pulsators with mass in the range of 0.59M_☉ to 0.52M_☉. Moreover, since for fundamental pulsating models there is a linear correlation of the blue magnitude with period and blue amplitude A(B), we are able to predict that the period-luminosity-blue amplitude relation for type II Cepheids with P≤15days is B(3.83)-B=-0.12+1.39logP+0.57A(B). The comparison with the theoretical evolutionary tracks yields that the mass of type II Cepheids decreases with increasing the period and that the brightest variables with P≥10days should likely belong to the very rapid phases of the 0.52M_☉ and 0.53M_☉ evolution. The agreement between observations and calculated expectations turns out to be almost satisfactory, suggesting that the pulsational and evolutionary scenario is capable to match the properties of metal-poor pulsating stars.