Classical Cepheid pulsation models. XI. Effects of convection and chemical composition on the period-luminosity and period-Wesenheit relations

In spite of the relevance of classical Cepheids as primary distance indicators, a general consensus on the dependence of the period-luminosity (PL) relation on the Cepheid chemical composition has not yet been achieved. From the theoretical point of view, our previous investigations were able to reproduce some empirical tests for suitable assumptions on the helium-to-metal relative enrichment, but these results relied on specific assumptions concerning the mass-luminosity relation and the efficiency of the convective transfer in the pulsating envelopes. In this paper, we investigate the effects of the assumed value of the mixing-length parameter l/H_p on the pulsation properties and we release the assumption of a fixed mass-luminosity relation. To this purpose, new nonlinear convective fundamental pulsation models have been computed for various chemical compositions (Z=0.004, 0.008, 0.01 and 0.02) and adopting l/H_p=1.7-1.8, which is larger than that (1.5) used in our previous papers. From the extended model set, synthetic PL relations in the various photometric bands are derived using the predicted instability strip together with recent evolutionary tracks. We show that as the l/H_p value increases the pulsation region gets narrower, mostly due to the blueward shift of the red edge for fundamental pulsation, with the effect becoming stronger at the higher metal contents (Z≥ 0.01). However, the comparison of the new models with previously computed models shows that the l/H_p variation has no consequence on the predicted period-Wesenheit (PW) relations, which instead are influenced by the pulsator metal content. On this basis, we present a straightforward way to infer the distance and metal content of variables with observed BVI or BVK magnitudes. As for the PL relations, we show that either the zero-point and the slope are very slightly modified by the l/H_p variation, at constant chemical composition. We also confirm that: (1) moving from visual to longer wavelengths, the predicted period-magnitude distribution for a given metal content becomes narrower and its slope becomes steeper; (2) decreasing the metal content, the PL relations become steeper and brighter, with the amount of this metallicity effect decreasing from optical to near-infrared bands. Overall, we show that our pulsation relations appear fully consistent with the observed properties of Galactic and Magellanic Cloud Cepheids, supporting the predicted steepening and brightening of the PL relations when moving from metal-rich to metal-poor variables. Moreover, we show that the distances inferred by the predicted PW relations agree with recently measured trigonometric parallaxes, whereas they suggest a correction to the values based on the Infrared Surface Brightness technique, as already found from an independent method. Finally, also the pulsation metal contents suggested by the predicted PW relations appear in statistical agreement with spectroscopic [Fe/H] measurements.