Orbital Inclination of Astrometric Binaries and the Dearth of Face-on Orbits in Gaia DR3 Solutions

The orbital solutions for astrometric (unresolved) binary stars provided in the Gaia mission DR3 reveal an obvious deficit of face-on orbits with line-of-sight inclinations close to 0 or π. This is shown to be an intrinsic mathematical feature of the orbit estimation technique involving the intermediate Thiele-Innes parameters, which are transformed to the Campbell geometric parameters. A direct condition equation defining the inclination angle via the Thiele-Innes values independently of the other orbital elements is used to investigate the origin of this near-degeneracy for face-on orbits. The emerging bias and correlation of inclination and semimajor axis are illustrated using Monte Carlo simulations for two specific template configurations representing face-on and edge-on orbits. The results have significant impact on the interpretation and follow-up confirmation of Gaia-detected binary systems, including candidate exoplanets and brown dwarf companions.