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

2025/12/01 by Yahalomi, Daniel A., Lu, Tiger, Armitage, Philip J. +4
#Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Physical sciences #Instrumentation and Methods for Astrophysics (astro-ph.IM)

paper · doi:10.48550/arxiv.2512.02007

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_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.

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