Unified deep learning approach for estimating the metallicities of RR Lyrae stars using light curves from <i>Gaia</i> Data Release 3

Context. RR Lyrae stars (RRLs) are old population pulsating variables that serve as useful metallicity tracers due to the correlation between their metal abundances and the shape of their light curves. With the advent of ESA’s Gaia mission Data Release 3 (DR3), which provides light curves for approximately 270 000 RRLs, it has become crucial to develop a machine learning technique for estimating metallicities for large samples of RRLs directly from their light curves. Aims. We extend our previous methodological study on RRab stars by developing and validating a unified deep learning (DL) framework capable of accurately estimating metallicities for both fundamental mode (RRab) and first-overtone (RRc) pulsators using their Gaia DR3 G -band light curves. Our goal is to create a single, consistent model to produce a large, homogeneous metallicity catalogue. Methods. We employed a gated recurrent units (GRUs)-based neural network architecture optimised for time-series extrinsic regression. The framework incorporates a rigorous pre-processing pipeline (including phase-folding, smoothing, and sample weighting) and is trained using Gaia DR3 G -band light curves and photometric metallicities of RRLs available in the literature. The model architecture and training implicitly handle the morphological differences between RRab and RRc light curves. Results. Our unified GRU model achieves high predictive accuracy. It successfully confirms the high precision for RRab stars reported in our previous work (RMSE = 0.0765 dex, R 2 = 0.9401) and, crucially, demonstrates even stronger performance for the more challenging RRc stars (RMSE = 0.0720 dex, R 2 = 0.9625). This represents a significant improvement over previous DL benchmarks. We also present a key finding: a clear positive correlation between the number of photometric data points in a light curve and the precision of the final metallicity estimate; this correlation quantifies the value of well-sampled observations. Conclusions. Crucially, we demonstrate that prediction accuracy scales with the number of photometric epochs, establishing that this framework is poised to deliver unprecedented precision with richer future datasets. Applying this methodology to the enhanced light curves from Gaia DR4 and the Vera C. Rubin Observatory will enable us to produce metallicity catalogues of unprecedented scale and fidelity, paving the way for next-generation studies in Galactic archaeology and chemo-dynamics.