Orbital Parameter Determination for Wide Stellar Binary Systems in the Age of Gaia

The orbits of binary stars and planets, particularly eccentricities and inclinations, encode the angular momentum within these systems. Within stellar multiple systems, the magnitude and (mis)alignment of angular momentum vectors among stars, disks, and planets probes the complex dynamical processes guiding their formation and evolution. The accuracy of the \textit{Gaia} catalog can be exploited to enable comparison of binary orbits with known planet or disk inclinations without costly long-term astrometric campaigns. We show that \textit{Gaia} astrometry can place meaningful limits on orbital elements in cases with reliable astrometry, and discuss metrics for assessing the reliability of \textit{Gaia} DR2 solutions for orbit fitting. We demonstrate our method by determining orbital elements for three systems (DS Tuc AB, GK/GI Tau, and Kepler-25/KOI-1803) using \textit{Gaia} astrometry alone. We show that DS Tuc AB's orbit is nearly aligned with the orbit of DS Tuc Ab, GK/GI Tau's orbit might be misaligned with their respective protoplanetary disks, and the Kepler-25/KOI-1803 orbit is not aligned with either component's transiting planetary system. We also demonstrate cases where \textit{Gaia} astrometry alone fails to provide useful constraints on orbital elements. To enable broader application of this technique, we introduce the python tool \texttt{lofti\_gaiaDR2} to allow users to easily determine orbital element posteriors.