On the impact of Helium abundance on the Cepheid Period-Luminosity and Wesenheit relations and the Distance Ladder

This work analyses the effect of the Helium content on synthetic Period-Luminosity Relations (PLRs) and Period-Wesenheit Relations (PWRs) of Cepheids and the systematic uncertainties on the derived distances that a hidden population of He-enhanced Cepheids may generate. We use new stellar and pulsation models to build a homogeneous and consistent framework to derive the Cepheid features. The Cepheid populations expected in synthetic color-magnitude diagrams of young stellar systems (from 20 Myr to 250 Myr) are computed in several photometric bands for Y = 0.25 and Y = 0.35, at a fixed metallicity (Z = 0.008). The PLRs appear to be very similar in the two cases, with negligible effects (few %) on distances, while PWRs differ somewhat, with systematic uncertainties in deriving distances as high as about 7% at log P < 1.5. Statistical effects due to the number of variables used to determine the relations contribute to a distance systematic error of the order of few percent, with values decreasing from optical to near-infrared bands. The empirical PWRs derived from multi-wavelength datasets for the Large Magellanic Cloud (LMC) is in a very good agreement with our theoretical PWRs obtained with a standard He content, supporting the evidence that LMC Cepheids do not show any He effect.