The Astrometric Resoeccentric Degeneracy: Eccentric Single Planets Mimic 2:1 Resonant Planet Pairs in Astrometry

Abstract Detections of long-period giant exoplanets will expand dramatically with Gaia Data Release 4, but interpreting these signals will require care. We derive the astrometric resoeccentric degeneracy: an astrometric analogue of the well-known radial velocity degeneracy in which a single eccentric planet can mimic two circular planets near a 2:1 period ratio. To first order in eccentricity, the sky-projected motion of a single eccentric orbit decomposes into a fundamental mode and first harmonic with an amplitude proportional to that eccentricity. A pair of coplanar, circular planets in a 2:1 orbital resonance produces the same harmonic structure: the outer planet sets the fundamental mode, while the inner planet supplies an apparent first harmonic. We present a mapping between the harmonic amplitudes and effective eccentricity ( e eff ) of a single planet that mimics a 2:1 configuration, demonstrating that e eff = 2 1/3 ( M p ,2 / M p ,1 ), the masses of the inner and outer planets, respectively. Using simulated Gaia data, we show that (1) coplanar 2:1 systems are statistically indistinguishable from a single eccentric planet and (2) mutual inclination can break this degeneracy. This bias favors detecting mutually inclined systems, often fingerprints of a dynamically hot history—traces for processes such as planet–planet scattering or secular chaos. Determining the planetary architectures in which this degeneracy holds will be essential for measuring cool-giant occurrence rates with Gaia and for inferring their dynamical evolution histories.