Gaia DR3 Cepheids [Fe/H] and Fourier param.

The reference sample comprises 398 CCs from Gaia data release 3, for which high-resolution spectroscopic metallicities are available in the literature, covering the typical pulsation period range of CCs. Focusing exclusively on fundamental mode pulsators, we modelled each light curve with a truncated Fourier series to derive characteristic parameters, such as amplitude ratios and phase differences. A random forest algorithm was applied to this reference set as a feature selection tool to identify the most influential predictors, which were subsequently used to derive an empirical relation for estimating [Fe/H] from photometric properties.

We inferred an empirical relation that combines characteristic Fourier parameters extracted from the multi-band Gaia light curves to enable the estimation of the [Fe/H] of fundamental-mode CCs. As a consistency check, we applied this relation to an independent target sample of Cepheids in the Milky Way, the Large Magellanic Cloud, and the Small Magellanic Cloud. The resulting metallicity distributions exhibit three clearly separated peaks, centred near the currently accepted [Fe/H] values of these stellar systems, supporting the predictive capability and external validity of the derived relation.