An Improved Calibration of the Wavelength Dependence of Metallicity on the Cepheid Leavitt law

The Cepheid period-luminosity (PL) relation (or Leavitt law) has served as the first rung of the most widely used extragalactic distance ladder and is central to the determination of the local value of the Hubble constant ($H_0$). We investigate the influence of metallicity on Cepheid brightness, a term that significantly improves the overall fit of the distance ladder, to better define its wavelength dependence. To this aim, we compare the PL relations obtained for three Cepheid samples having distinct chemical composition (in the Milky Way and Magellanic Clouds) and focusing on the use of improved and recent data while covering a metallicity range of about 1 dex. We estimate the metallicity effect (hereafter $\gamma$) in 15 filters from mid-IR to optical wavelengths, including five Wesenheit indices, and we derive a significant metallicity term in all filters, in agreement with recent empirical studies and models, in the sense of metal-rich Cepheids being brighter than metal-poor ones. We describe the contribution of various systematic effects in the determination of the $\gamma$ term. We find no evidence of $\gamma$ changing over the wavelength range $0.5-4.5 \, \rm \mu m$, indicating that the main influence of metallicity on Cepheids is in their luminosity rather than color. Finally, we identify factors that sharpen the empirical constraints on the metallicity term over past studies, including corrections for the depth of the Magellanic Clouds, better-calibrated Cepheid photometry, improved Milky Way extinction estimates, and revised and expanded metallicity measurements in the LMC.