Cepheid Metallicity in the Leavitt Law (C–MetaLL) survey

Context. The C-MetaLL project has provided homogeneous spectroscopic abundances of 290 Classical Cepheids (DCEPs) for which we have the intensity-averaged magnitudes in multiple optical and NIR bands, periods, pulsation modes, and Gaia parallaxes corrected for individual zero-point (ZP) biases. Aims. Our goal is to derive updated period–Wesenheit–metallicity (PWZ) relations using the largest and most homogeneous metallicity sample ever used for such analyses, covering a range of −1.3 < [Fe/H] < +0.3 dex, and to assess the metallicity dependence of these relations. Methods. We computed several optical and NIR Wesenheit magnitudes adopting both Cardelli et al. (1989, ApJ, 345, 245) and Fitzpatrick (1999, PASP, 111, 63) reddening laws, and transformed Johnson-Cousins Wesenheit magnitudes into their HST equivalents using empirical relations. Using 275 DCEPs with reliable parallaxes, we applied a robust photometric parallax technique, which simultaneously fits all parameters – including the global ZP counter-correction to Gaia parallaxes – and handles outliers via a Cauchy likelihood to account for the sample’s excess variance. Results. We find a stronger metallicity dependence ( γ ≈ −0.5 mag/dex in optical, −0.4 mag/dex in NIR) than recent literature reports. Gaia parallax ZP counter-correction ( ϵ ) varies moderately across bands, with an average value of ∼10 μas, aligning with previous determinations. Applying our PWZ relations to ∼4500 LMC Cepheids yields distances generally consistent within 1 σ with geometric estimates. The choice of reddening law has a small impact, while using only fundamental-mode pulsators significantly increases the uncertainties. Including α element corrections increases | γ | and reduces ϵ . However, we find 1 σ consistency γ values with the literature, particularly for the Wesenheit magnitude in the HST bands, by restricting the sample to brighter (i.e. closer) objects, or by including only pulsators with −0.7 < [Fe/H] < 0.2 dex. Our results hint at a large γ or a non-linear dependence on metallicity of DCEP luminosities at the metal-poor end, which is difficult to quantify with the precision of parallaxes of the present dataset.