Cepheid Metallicity in the Leavitt Law (C--MetaLL) survey. X. First spectroscopic characterization of Galactic Type II Cepheids and calibration of the period--Wesenheit--metallicity relations

Type II Cepheids (T2Cs) are Population II pulsating stars that can be used as primary distance indicators thanks to their period--luminosity relation. Together with RR Lyrae stars and the tip of the red giant branch, they can provide an alternative route to the Hubble constant, independently evaluating possible systematic effects in its determination. We aim to build the largest homogeneous spectroscopic sample of Galactic T2Cs with iron and oxygen abundance measurements to investigate the impact of chemical composition on their period--luminosity relations. We observed 80 Galactic T2Cs with the high-resolution spectrograph UVES at the ESO Very Large Telescope. Starting from the spectra for a sample of 74 T2Cs we derived the stellar parameters as well as the iron and oxygen abundances through a self-consistent spectroscopic analysis based on the equivalent widths of the absorption lines. This sample has nearly doubled the number of T2Cs with spectroscopic metallicity determinations available in the literature. The resulting abundance measurements were used to test theoretical predictions for the instability strip and, together with Gaia parallaxes, to derive the period--Wesenheit--metallicity (PWZ) relations. We find, in agreement with model predictions, that the metallicity term (γ) is small and statistically consistent with zero in all investigated PWZ relations, ranging between γ ≃ - 0.02 and $+0.17$ mag dex -1 . We also estimated the distances to 22 Galactic Globular Clusters hosting T2Cs. The derived distances agree, within the uncertainties, with independent literature estimates. Our results indicate that metallicity has at most a minor impact on the pulsation properties and distance scale of T2Cs, confirming recent theoretical predictions and supporting the use of these variables as robust Population II distance indicators.