Nominal thresholds for good astrometric fits, and prospects for binary detectability, for the full extended Gaia mission

The full extended Gaia mission spans slightly over 10 years, whilst the current data releases represent only a fraction of it, 34 months in Gaia's third data release (DR3). The longer baseline improves the quality of astrometric fits, lowering the noise floor and making consistently bad fits (e.g., due to binarity) more apparent. In this paper, we use simulated binaries from the Gaia Universe Model to examine the long-term astrometric behaviour of single stars and stellar binaries. We calculate nominal upper limits on the spread of goodness of astrometric fits for well-behaved single stars. Specifically, for the RUWE parameter, for upcoming DR4 ($\rm RUWE_{lim}=1.15$) and DR5 ($\rm RUWE_{lim}=1.11$), using the full mission nominal scanning law. These can be used to identify poor astrometric fits and can flag potential binary systems. We show the increase in the number and type of binaries detectable through RUWE. With our updated RUWE thresholds, the number of detectable short-period binaries increases by 5-10% with each subsequent data release, suggesting detections may be possible for orbital periods down to days. The number of detectable long-period systems increases by 10-20%, with periods up to 100 years, causing significant deviations in low and moderate-eccentricity binaries. Very eccentric systems with much longer periods (thousands of years) can still be detected if they pass through periapse during the observing window. Finally, we compare our results to the analytic estimate for the spread in UWE, which we predict from a $\chi$-distribution moderated by the number of observations. These agree with our inferred population limits but suggest that we may be biased by a small number of poorly sampled systems. In regions of the sky that are more frequently observed, lower limits could be employed, potentially bringing even more binaries above the threshold for detectability.