Astrometric Identification of Nearby Binary Stars I: Predicted Astrometric Signals

We examine the capacity to identify binary systems from astrometric errors and deviations alone. Until the release of the fourth Gaia data release we lack the full astrometric time series that the satellite records, but as we show can still infer the presence of binaries from the best fit models, and their error, already available. We generate a broad catalog of simulated binary systems within 100 pc, and examine synthetic observations matching the Gaia survey's scanning law and astrometric data processing routine. We show how the Unit Weight Error (UWE) and Proper Motion Anomaly (PMA) vary as a function of period, and the properties of the binary. Both UWE and PMA peak for systems with a binary period close to the time baseline of the survey. Thus UWE can be expected to increase or remain roughly constant as we observe the same system over a longer baseline, and we suggest $UWE_{eDR3}>1.25$ and $\Delta UWE/UWE_{eDR3}>-0.25$ as criteria to select astrometric binaries. For stellar binaries we find detectable significant astrometric deviations for 80-90\% of our simulated systems in a period range from months to decades. We confirm that for systems with periods less than the survey's baseline the observed $UWE$ scales $\propto \ \varpi$ (parallax), $a$ (semi-major axis) and $\Delta =\frac{|q-l|}{(1+q)(1+l)}$ where $q$ and $l$ are the mass and light ratio respectively, with a modest dependence on viewing angle. For longer periods the signal is suppressed by a factor of roughly $\propto P^{-2}$ (period). PMA is largest in orbits with slightly longer periods but obeys the same approximate scaling relationships.