The Astrometric Resoeccentric Degeneracy: Eccentric Single Planets Mimic 2:1 Resonant Planet Pairs in Astrometry
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908828449112064 |
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| author | Yahalomi, Daniel A. Lu, Tiger Armitage, Philip J. Bedell, Megan Casey, Andrew R. Price-Whelan, Adrian M. Rice, Malena |
| author_facet | Yahalomi, Daniel A. Lu, Tiger Armitage, Philip J. Bedell, Megan Casey, Andrew R. Price-Whelan, Adrian M. Rice, Malena |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Astrometric Resoeccentric Degeneracy: Eccentric Single Planets Mimic 2:1 Resonant Planet Pairs in Astrometry Yahalomi, Daniel A. Lu, Tiger Armitage, Philip J. Bedell, Megan Casey, Andrew R. Price-Whelan, Adrian M. Rice, Malena Earth and Planetary Astrophysics Instrumentation and Methods for Astrophysics 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. |
| title | The Astrometric Resoeccentric Degeneracy: Eccentric Single Planets Mimic 2:1 Resonant Planet Pairs in Astrometry |
| topic | Earth and Planetary Astrophysics Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2512.02007 |