Unified Deep Learning Approach for Estimating the Metallicities of RR Lyrae Stars Using light curves from Gaia Data Release 3

RR Lyrae stars (RRLs) are old pulsating variables widely used as metallicity tracers due to the correlation between their metal abundances and light curve morphology. With ESA Gaia DR3 providing light curves for about 270,000 RRLs, there is a pressing need for scalable methods to estimate their metallicities from photometric data. We introduce a unified deep learning framework that estimates metallicities for both fundamental-mode (RRab) and first-overtone (RRc) RRLs using Gaia G-band light curves. This approach extends our previous work on RRab stars to include RRc stars, aiming for high predictive accuracy and broad generalization across both pulsation types. The model is based on a Gated Recurrent Unit (GRU) neural network optimized for time-series extrinsic regression. Our pipeline includes preprocessing steps such as phase folding, smoothing, and sample weighting, and uses photometric metallicities from the literature as training targets. The architecture is designed to handle morphological differences between RRab and RRc light curves without requiring separate models. On held-out validation sets, our GRU model achieves strong performance: for RRab stars, MAE = 0.0565 dex, RMSE = 0.0765 dex, R^2 = 0.9401; for RRc stars, MAE = 0.0505 dex, RMSE = 0.0720 dex, R^2 = 0.9625. These results show the effectiveness of deep learning for large-scale photometric metallicity estimation and support its application to studies of stellar populations and Galactic structure.