Improving reddening estimates for RR Lyrae stars in the Gaia bands: A machine learning approach to the period-amplitude-color-(metallicity) relation

RR Lyrae stars are essential tracers of old stellar populations and distance indicators across the Milky Way (MW) and nearby galaxies. However, their use as standard candles is limited by uncertainties in extinction, particularly in the optical regime probed by the ESA mission Gaia . In Gaia Data Release 3 (DR3), individual absorption values (A_G) were provided for fundamental-mode RR Lyrae stars (RRab stars) based on an empirical period–amplitude–color (PAC) relation calibrated on a relatively small sample and on passband transformations. We aim to recalibrate extinction relations for RRab stars and, for the first time, establish analogous relations for first-overtone RR Lyrae stars (RRc stars) using Gaia DR3 photometry and pulsation parameters to provide intrinsic colors and interstellar absorption estimates. We used Gaia DR3 mean magnitudes and pulsation properties of RRab and RRc stars from an all-sky reference sample to recalibrate PAC(Z) relations in the Gaia passbands. Intrinsic colors $(G-G_ RP )_0$ and $(G_ BP -G_ RP )_0$ were derived through sequential feature selection combined with linear regression and bootstrap resampling, ensuring statistically consistent estimates of color excess and A_G. We recalibrated PACZ relations for RRab stars and derived, for the first time, PAC relations for RRc stars in the Gaia bands. The new relations reproduce intrinsic colors with residual scatters of ∼0.03–0.04 mag and provide A_G estimates across both pulsation types. Tests on RR Lyrae stars in the MW field, globular clusters, and dwarf galaxy companions show consistent A_G values, with the PAC(Z) relations based on $(G_ ̊m BP -G_ RP )$ appearing to be more reliable than those using (G-G_RP. The new relations provide consistent extinction estimates for both RRab and RRc stars, thus improving on the DR3 implementation and offering a valuable tool for Galactic studies and cosmic-distance scale work in view of Gaia DR4.