A Precision Determination of the Effect of Metallicity on Cepheid Absolute Magnitudes in VIJHK Bands from Magellanic Cloud Cepheids

Using high-quality observed period-luminosity (P-L) relations in both Magellanic Clouds in the VIJHKs. bands and optical and near-infrared Wesenheit indices, we determine the effect of metallicity on Cepheid P-L relations by comparing the relative distance between the LMC and SMC as determined from the Cepheids to the difference in distance between the Clouds that has been derived with very high accuracy from late-type eclipsing binary systems. Within an uncertainty of 3%, which is dominated by the uncertainty on the mean difference in metallicity between the Cepheid populations in the LMC and SMC, we find metallicity effects smaller than 2% in all bands and in the Wesenheit indices, consistent with a zero metallicity effect. This result is valid for the metallicity range from -0.35 dex to -0.75 dex corresponding to the mean [Fe/H] values for classical Cepheids in the LMC and SMC, respectively. Yet most Cepheids in galaxies beyond the Local Group and located in the less crowded outer regions of these galaxies do fall into this metallicity regime, making our result important for applications to determine the distances to spiral galaxies well beyond the Local Group. Our result supports previous findings that indicated a very small metallicity effect on the near-infrared absolute magnitudes of classical Cepheids, and resolves the dispute about the size and sign of the metallicity effect in the optical spectral range. It also resolves one of the most pressing problems in the quest toward a measurement of the Hubble constant with an accuracy of 1% from the Cepheid-supernova Ia method.