Period-age-metallicity and period-age-colour-metallicity relations for classical Cepheids: an application to the Gaia EDR3 sample

Based on updated pulsation models for classical Cepheids, computed for various assumptions about the metallicity and helium abundance, roughly representative of pulsators in the Small Magellanic Cloud (Z = 0.004 and Y = 0.25), Large Magellanic Cloud (Z = 0.008 and Y = 0.25), and M31 (Z = 0.03 and Y = 0.28), and self-consistent updated evolutionary predictions, we derived period-age and multi-band period-age-colour relations that also take into account variations in the mass-luminosity (ML) relation. These results, combined with those previously derived for Galactic Cepheids, were used to investigate the metallicity effect when using these variables as age indicators. In particular, we found that a variation in the metal abundance affects both the slope and the zero-point of the above-mentioned relations. The new relations were applied to a sample of Gaia Early Data Release 3 classical Cepheids. The retrieved distribution of the individual ages confirms that a brighter ML relation produces older ages and that first overtone pulsators are found to be concentrated towards older ages with respect to the fundamental ones at a fixed ML relation. Moreover, the inclusion of a metallicity term in the period-age and period-age-colour relations slightly modifies the predicted ages. In particular, the age distribution of the selected sample of Galactic Cepheids is found to be shifted towards slightly older values, when the F-mode canonical relations are considered, with respect to the case at a fixed solar chemical composition. A marginally opposite dependence can be found in the non-canonical F-mode and canonical FO-mode cases.