High resolution spectroscopy of classical Cepheids and multiwavelength calibration of PLZ and PWZ relations

Classical Cepheids are a type of variable stars critical for establishing distances in the Local Group. These stars are young, intermediate-mass stars evolving through a specific phase of the star evolution in which radial pulsation is excited, resulting in a change of brightness. What makes them one of the primary tools in estimating distances is the correlation between their intrinsic luminosities and pulsational periods. For this reason, they are usually referred to as "standard candles". This property, known as the Period-Luminosity (PL) relation, enables Cepheids to serve as fundamental anchors on the cosmic distance ladder, which allows us to determine the scale of the Universe. On the other hand, they represent powerful tools as tracers of the young population in the Milky Way disc, with the possibility to study variations in their chemical abundances as a function of their location in the Galaxy. The first part of this dissertation revolves around the description of the astrophysical characteristics of Cepheids, their progenitors, evolution and ultimate fate. The origin of stellar pulsation is explored, starting from the basics of stellar structure to the development of a pulsational theory. The main objective is to discover which mechanisms ignite pulsation, which are the constraints that define the region in the Hertzspring-Russell diagram, called the instability strip, where these mechanisms become relevant and what are the main implications and uses of the PL relation. Furthermore, we will navigate through the basics of spectroscopic analysis, the elements necessary to build an atmospheric model and which physical quantities play a relevant role in influencing the photosphere and need to be determined in order to characterise a star. The remaining chapters are based on three peer-reviewed published papers and part of the C-MetaLL project survey: In Chapter 2 we have collected high-resolution spectroscopy with UVES@VLT for a sample of 65 DCEPs. The majority of them are the faintest DCEPs ever observed in the Milky Way. For each target, we derived accurate atmospheric parameters, radial velocities, and abundances for 24 different species. The resulting iron abundances range between +0.3 and -1.1 dex with the bulk of stars at [Fe/H] -0.5 dex. Our sample includes the most metal-poor DCEPs observed so far with high-resolution spectroscopy. Exploiting the role of Cepheids as tracers of young population stars, the radial metallicity gradient is studied together with the distribution of the sample in the disc. In Chapter 3 we quantify the metallicity dependence of the PL and PW relations of the Galactic DCEPs for a variety of photometric bands, ranging from optical to near-infrared. We gathered a sample of 910 DCEPs with available [Fe/H] values from high-resolution spectroscopy or metallicities from the Gaia Radial Velocity Spectrometer. For all these stars, we collected photometry in the GBP, GRP, G, I, V, J, H, and KS bands and astrometry from Gaia Data Release 3 (DR3). We used these data to investigate the metal dependence of both the intercepts and slopes of a variety of PL and PW relations at multiple wavelengths. In Chapter 4, a follow-up of Chapter 2, we enlarge the sample of DCEPs with accurate abundances from high-resolution spectroscopy. We present the results of the analysis of 331 spectra obtained for 180 individual DCEPs with a variety of high-resolution spectrographs. As already done in Chapter 2 we derived accurate atmospheric parameters, radial velocities, and abundances for up to 29 different species. A robust sample is obtained, distributed almost homogeneously in both distance and metallicity ranges. The radial metallicity gradient is studied for all the chemical species, highlighting the role of Cepheids as a powerful means to trace spiral arms not yet well constrained.