Theoretical models for classical Cepheids. VII. Metallicity effects on the Cepheid distance scale

We use theoretical Period-Luminosity and Period-Luminosity-Color relations in the VI passbands, as based on nonlinear, nonlocal and time-dependent convective pulsating models, to predict the reddening and true distance modulus of distant Cepheids observed with the Hubble Space Telescope. By relying on the pulsating models with metal content Z=0.008, we find that the theoretical predictions agree to the values obtained by the Extragalactic Distance Scale Key Project on the basis of empirical Period-Luminosity relations referenced to LMC variables. In the meantime, from the theoretical relations with Z=0.004 and 0.02 we find that the predicted E(B-V) and mu_0 decrease as the adopted metal content increases. This suggests a metallicity correction to LMC-based distances as given by Delta mu_0 /Delta log Z ~ -0.27 mag dex^-1, where Delta log Z is the difference between the metallicity of the Cepheids whose distance we are estimating and the LMC value Z=0.008. Such a theoretical correction appears supported by an existing, although weak, correlation between the Cepheid distance and the [O/H] metallicity of galaxies within a given group or cluster, as well as by a similar correlation between the H_0 estimate and the [O/H] metallicity of the galaxies which calibrate the SNIa luminosity. On the contrary, the metallicity corrections earlier suggested on empirical grounds seem to be excluded. Eventually we suggest that the average value < H_0> ~ 67 km s^-1 Mpc^-1 provided by the Key Project team should increase at least up to ~ 69 km s^-1 Mpc^-1. Further observational evidences in support of the predicted scenario are finally presented.