Orbital inclination of astrometric binaries and the dearth of face-on orbits in Gaia DR3 solutions

TL;DR

Gaia DR3 astrometric binary solutions show a bias against face-on orbits due to the mathematical properties of the orbit estimation method, affecting interpretation of binary and exoplanet detections.

Contribution

This paper identifies and explains the intrinsic bias against face-on orbits in Gaia DR3 astrometric solutions caused by the orbit estimation technique.

Findings

Bias against face-on orbits in Gaia DR3 data

Mathematical origin of the inclination bias

Impact on binary and exoplanet detection interpretations

Abstract

The orbital solutions for astrometric (unresolved) binary stars provided in the Gaia mission Data Release 3 reveal an obvious deficit of face-on orbits with line-of-sight inclinations close to 0 or $\pi$. 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.