Hide and Seek with Gaia. Detectability of Predicted Thin-Disc Metal-Rich RR Lyrae Binaries in Gaia DR3 and DR4

RR Lyrae stars (RRLs) are classical tracers of old stellar populations, yet growing evidence suggests the presence of a metal-rich ([Fe/H]>-0.5), intermediate-age (2-7 Gyr) sub-population in the Milky Way disc. Binary evolution, particularly stable mass transfer, has been proposed as a viable formation channel, predicting that most metal-rich, intermediate-age (<9 Gyr) RRLs should reside in binaries with orbital periods of ~900-2000 days. However, no genuine RRL binaries have been robustly identified, including in the Gaia DR3 astrometric binary catalogues, despite Gaia being sensitive to the predicted orbital-period range. We investigate whether the lack of detections in Gaia DR3 reflects an intrinsically low binary fraction or instead arises from observational biases. We analyse a carefully selected sample of 100 Gaia DR3 RRLs designed to trace the metal-rich population with thin-disc kinematics and compare them with predictions from binary evolution models. We generate realistic Gaia observation mocks, including variability-induced astrometric biases, and assess the detectability of binaries and the posterior constraints on the hidden binary fraction using astrometric quality indicators, such as RUWE, and a robust Bayesian inference. While current uncertainties prevent a definitive rejection of a high fraction of hidden binaries, our results reveal tensions between existing binary evolution predictions and the Gaia DR3 non-detections. This suggests either the presence of unaccounted systematics in the modelling of Gaia observations or the need to revise assumptions in binary evolution models. We predict that Gaia DR4 will significantly improve the binary detectability and provide powerful new constraints on the post-interaction binary populations.