Theoretical Models for Classical Cepheids. II. Period-Luminosity, Period-Color, and Period-Luminosity-Color Relations

We present and discuss theoretical predictions concerning the pulsational properties of classical Cepheids. Masses and luminosities provided by stellar evolutionary calculations are used as input parameters of nonlinear, nonlocal, and time-dependent convective pulsating models, and accurate determinations of both the blue and red edge of the instability strip are derived, together with theoretical light curves for a suitable grid of models. The computations have been performed for three different chemical compositions (Y=0.25, Z=0.004; Y=0.25, Z=0.008; Y=0.28, Z=0.02), taken as representative of Cepheids in the Magellanic Clouds (MCs) and in the Galaxy. Bolometric light curves have been transformed into visual and near-infrared magnitudes, and the intensity-weighted mean magnitudes of the pulsators over a full pulsation cycle (<M_V> and <M_K>, respectively) have been derived. We obtain that both in the log P-<M_V> and in the log P-<M_K> planes the predicted edges of instability strip are in excellent agreement with the observed distribution of Galactic and Magellanic Cepheids, providing a preliminary estimate of the distance to these galaxies. Moreover, we show that the models are in agreement with several empirical period-luminosity (PL) relations given in the literature, even though the theoretical distribution in the log P-<M_V> plane is better represented by a quadratic PL relation. We also show that both the zero point and the slope of the predicted PL relations are significantly dependent on metallicity, with the amplitude of the metallicity effect decreasing at the longer wavelength. At variance with several empirical suggestions appeared in the literature, we find that at fixed period the metal-rich pulsators should be fainter than the metal-poor ones. Tight period-luminosity-color (PLC) relations are derived for both visual and near-infrared photometric bands. Also in this case the effect of metallicity decreases with increased wavelength. By applying our theoretical relations to Magellanic Cepheids, we confirm that, within the statistical errors, the distance modulus obtained from different PL and PLC relations is marginally correlated with the adopted relation, but the associated uncertainty decreases when infrared magnitudes are taken into account. Finally the whole pulsational scenario is briefly discussed in light of the adopted evolutionary framework.