Classical Cepheid pulsation models. III. The predictable scenario

Within the current uncertainties in the treatment of the coupling between pulsation and convection, the limiting amplitude, nonlinear, convective models appear the only viable approach for providing theoretical predictions about the intrinsic properties of radial pulsators. In this paper we present the results of a comprehensive set of Cepheid models computed within such theoretical framework for selected assumptions on their original chemical composition. We first discuss the location of the instability strip in the HR diagram, showing that nonlinear predictions on the effective temperature of the instability boundaries substantially differ from similar predictions available in the literature. This discrepancy is mainly due to the nonlinear effects introduced by the interaction between radial and convective motions and to the different physical assumptions adopted for constructing pulsation models. We found that both the blue (hot) and the red (cool) boundaries of fundamental pulsators appear, for each given metallicity, fairly independent of the adopted mass-luminosity relation. As a consequence, it turns out that they can be approximated over a wide luminosity range by a logarithmic relation between stellar luminosity and effective temperature. We discuss the occurrence of first overtone pulsators and provide an analytical relation for the effective temperature of the predicted blue boundary in metal-poor structures. We also found that predicted fundamental periods based on different assumptions about the mass-luminosity relation can be all nicely fitted, for each given metallicity, by a logarithmic relation which connects the period of the pulsator to mass, luminosity, and effective temperature. Theoretical predictions concerning pulsation amplitudes in luminosity, radius, velocity, gravity, and effective temperature are discussed and then compared with data available in the current literature. Even though these observables are affected by non-negligible observational uncertainties, the agreement between theory and observations is rather satisfactory. Finally, we found that the predicted ratio of the amplitudes in the I and in the V bands appears in very good agreement with the empirical value (A(I)/A(V) = 0.6), with a mild dependence on metallicity.