A pilot study on the CSST astrometric capability: Detecting astrometric binaries with Gaia synergy via simulated data
Context. The China Space-station Survey Telescope (CSST) will provide deep, wide-field epoch astrometry during its 10-year mission. Astrometric binary orbits constrain the masses of stellar and compact-object components. Orbital recovery depends on astrometric precision and temporal coverage. Combining CSST and Gaia data extends the baseline and improves binary detection. Aims. We evaluate CSST, Gaia, and joint astrometry for binary-candidate selection and 12-parameter (12p) orbit fitting at faint magnitudes ($g>17.8$). We also test how regular CSST cadences affect the yield of 12p fits satisfying our criteria. Methods. We constructed a mock catalog, simulated CSST and Gaia epoch astrometry, and fitted five-parameter (5p) single-star models to derive astrometric diagnostics, proper-motion anomaly features, and observational-sampling features. A four-stage histogram-based gradient-boosting classifier used these features to select candidates for 12p orbit fitting and assessment. Results. On the independent test set, the classifier reaches a precision of 0.802 and a recall of 0.181 among eligible true binaries. In the scenario-specific fitted samples, joint astrometry raises the fiducial fraction from 6.76% for Gaia alone to 10.46%; for fitted binaries with $P_{\rm true}>15{\rm yr}$, it rises from 2.37% to 6.78%. The current CSST schedule yields few fiducial fits, while idealized regular cadences increase the yield mainly at $g\lesssim21$. Conclusions. In the simulation, joint CSST and Gaia epoch astrometry yields higher fractions of fitted unresolved binaries satisfying the stated criteria than Gaia-only solution. A practical strategy is to select candidates from 5p diagnostics and astrometric anomalies, obtain more regular CSST follow-up observations, and then fit 12p orbital models and apply the selection criteria.