Follow the wobble: Statistical methods to detect astrometric binary asteroids in Gaia FPR

Context . In a previous study, we leveraged the astrometric accuracy of Gaia DR3 to obtain the first list of astrometric binary asteroid candidates. Some of these candidates have now been confirmed. However, that work did not provide the details of the statistical methods. Aims . Our first aim is to provide methodological details and a performance evaluation of the approach used for detecting binaries. Our second aim is to establish an updated list of binary asteroid candidates from Gaia FPR astrometric residual exploration, accounting for the statistical properties of the Gaia FPR data. Methods . We accounted for the astrometric uncertainties from Gaia FPR and refined the statistical model of the data. We used this model in Monte Carlo simulations to evaluate the strength of the individual detections. We implemented a trend-detection method in the residuals and applied a dedicated period-search algorithm. In addition, we updated the statistical selection process to build the list of candidates. We introduced a method for detecting objects in multiple windows of consecutive observation and refined the estimation of confidence intervals for these parameters, thereby better constraining the physical parameter selection. Results . We detect 343 binary asteroid candidates, corresponding to 410 windows of consecutive observations, in the astrometric data. We show that in noise-only control simulations, the typical number of detections is 88% lower than in the Gaia FPR data. We also detect nine known binaries, 25 candidates that overlap with the Pan-STARRS survey, and 99 candidates that overlap with our previous binary search in Gaia DR3. Finally, we report 45 objects exhibiting residual trends suggestive of wide binary systems. Conclusions . Our results and analyses demonstrate that although detecting binary asteroids is a difficult problem due to their low signal levels, the proposed method provides a reliable list of detections, including systems that are poorly accessible to conventional techniques. This set of targets is valuable for future confirmation with stellar occultations, light curves, and forthcoming LSST data.