Theoretical Models for Classical Cepheids. IV. Mean Magnitudes and Colors and the Evaluation of Distance, Reddening, and Metallicity

We discuss the metallicity effect on the theoretical visual and near-infrared period-luminosity (PL) and period-luminosity-color (PLC) relations of classical Cepheids, as based on nonlinear, nonlocal, and time-dependent convective pulsating models at varying chemical composition. In view of the two usual methods of averaging (magnitude-weighted and intensity-weighted) observed magnitudes and colors over the full pulsation cycle, in the first part of the paper we briefly discuss the differences between static and mean quantities. We show that the behavior of the synthetic mean magnitudes and colors fully reproduces the observed trend of Galactic Cepheids, supporting the validity of the model predictions. In the second part of the paper we show how the estimates of the mean reddening, E_B-V, and true distance modulus, μ₀, of a galaxy from Cepheid VK photometry depend on the adopted metal content, in the sense that larger metallicities drive the host galaxy to lower extinctions and distances. Conversely, self-consistent estimates of the Cepheid mean reddening, distance, and metallicity may be derived if three-filter data (in this paper BVK) are taken into account. By applying the theoretical PL and PLC relations to available BVK data of Cepheids in the Magellanic Clouds, we eventually obtain Z~0.008, E_B-V~0.02 mag, and μ₀~18.63 mag for the LMC; and Z~0.004, E_B-V~0.01 mag, and μ₀~19.16 for the SMC. The discrepancy between such reddenings and the current values based on BVI data (E_B-V~0.074 mag for the LMC and ~0.054 mag for the SMC) is briefly discussed.