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arXiv 2512.02007astro-ph.EPastro-ph.IM
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轨道共振退化:单颗偏心行星在测光学中可以模仿2:1共振行星对

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

Center for Computational Astrophysics, Flatiron Institute(计算天体物理学中心,平顿研究所);Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology(卡弗里天体物理与空间研究所,麻省理工学院);Department of Physics and Astronomy, Stony Brook University(物理与天文系,石溪大学);School of Physics & Astronomy, Monash University(物理与天文学院,蒙纳士大学)

Daniel A. Yahalomi, Tiger Lu, Philip J. Armitage, Megan Bedell, Andrew R. Casey, Adrian M. Price-Whelan, Malena Rice

AI总结:

研究发现单颗偏心行星在测光学中可模仿2:1共振行星对,相互倾角可打破这一退化,对行星架构研究和动态演化历史推断具有重要意义。

摘要:

长周期巨行星的检测将随着Gaia数据释放4(DR4)大幅增加,但解释这些信号需要谨慎。我们推导出轨道共振退化:这是已知的径向速度退化的测光学类比,其中单颗偏心行星可以模仿一个近2:1轨道比的两个圆形行星。在偏心率的一阶近似中,单颗偏心轨道的天空投影运动分解为基本模式和第一谐波,其振幅与偏心率成正比。一对共面的圆形行星在2:1轨道共振中产生相同的谐波结构:外行星设定基本模式,而内行星提供一个 apparent 第一谐波。我们展示了单颗行星的谐波振幅与有效偏心率(e_eff)之间的映射,该单颗行星可以模仿2:1配置,证明e_eff = 2^(1/3)(M_p,2/M_p,1),其中M_p,2和M_p,1分别是内行星和外行星的质量。使用模拟的Gaia数据,我们显示(1)共面的2:1系统在统计上与单颗偏心行星无法区分;(2)相互倾角可以打破这种退化。这种偏差倾向于检测相互倾斜的系统,通常是动态热历史的指纹——如行星-行星散射或长期混沌等过程的痕迹。确定这种退化存在的行星架构对于用Gaia测量冷巨星发生率以及推断其动态演化历史至关重要。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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