Theoretical models for classical Cepheids. VIII. Effects of helium and heavy-element abundance on the Cepheid distance scale

Previous nonlinear fundamental pulsation models for classical Cepheids with metal content Z less than or equal to 0.02 are implemented with new computations at supersolar metallicity (Z = 0.03, 0.04) and selected choices of the helium-to-metal enrichment ratio DeltaY/Delta Z. On this basis, we show that the location into the H-R diagram of the Cepheid instability strip is dependent on both metal and helium abundance, moving toward higher effective temperatures with decreasing metal content (at fixed Y) or with increasing helium content (at fixed Z). The contributions of helium and metals to the predicted period-luminosity and period-luminosity-color relations are discussed as well as the implications on the Cepheid distance scale. We suggest that the adoption of empirical V and I period-luminosity relations, as inferred by Cepheids at the LMC, to get distance moduli with an uncertainty of +/-0.10 mag is fully justified for variables in the short-period range (P less than or equal to 10 days), at least with Z less than or equal to 0.04 and DeltaY/Delta Z in the range of 2-4. Conversely, at longer periods ( P > 10 days) a correction to LMC-based distance moduli may be needed, whose sign and amount depend on the helium and metal content of the Cepheids. Specifically, from fundamental pulsators with Z > 0.008 we derive that the correction (in magnitude) may be approximated as c = -6.03 + 17.80 Y - 2.80 log Z + 8.19 Y log Z, with a total intrinsic uncertainty of +/-0.05 mag, whereas c = -0.23(+/-0.03) log(Z/0.008) if Z < 0.008. Based on these new results, we show that the empirical metallicity correction suggested by Cepheid observations in two fields of the galaxy M101 may be accounted for, provided that the adopted helium-to-metal enrichment ratio is reasonably high (Delta Y/Delta Z similar to 3.5).