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

TL;DR

This paper reveals a degeneracy in astrometric data where a single eccentric planet can mimic a pair of planets in 2:1 resonance, impacting how Gaia data should be interpreted for exoplanet detection.

Contribution

The study derives the astrometric resoeccentric degeneracy, showing how single eccentric planets can be mistaken for resonant planet pairs in Gaia data, and proposes methods to distinguish them.

Findings

Single eccentric planets can mimic 2:1 resonant pairs in astrometry.

Mutual inclination can break the degeneracy.

Bias towards detecting mutually inclined systems.

Abstract

Detections of long-period giant exoplanets will expand dramatically with Gaia Data Release 4 (DR4), 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 ($e_\mathrm{eff}$) of a single planet that mimics a 2:1 configuration, demonstrating that $e_\mathrm{eff} = \, 2^{1/3}(M_{p,2}/M_{p,1})$, 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.