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 con vective pulsating models, to predict the reddening and true distance modulu s 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 theore tical predictions agree to the values obtained by the Extragalactic Distanc e Scale Key Project on the basis of empirical Period-Luminosity relations r eferenced 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) decrea se as the adopted metal content increases. This suggests a metallicity corr ection to LMC-based distances as given by Delta mu(0)/Delta log Z similar t o -0.27 mag dex(-1), where Delta log Z is the difference between the metall icity of the Cepheids whose distance we are estimating and the LMC value Z= 0.008. Such a theoretical correction appears supported by an existing, alth ough weak, correlation between the Cepheid distance and the [O/H] metallici ty of galaxies within a given group or cluster, as well as by a similar cor relation between the H-0 estimate and the [O/H] metallicity of the galaxies which calibrate the SNIa luminosity. On the contrary, the metallicity corr ections earlier suggested on empirical grounds seem to be excluded. Eventua lly we suggest that the average value [H-0] similar to 67 km s(-1) Mpc(-1) provided by the Key Project team should increase at least up to similar to 69 km s(-1) Mpc(-1). Further observational evidences in support of the pred icted scenario are finally presented.