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arXiv 2203.03349astro-ph.EPnlin.CDphysics.space-ph
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1:2:3共振链中的周期轨道及其对Kepler-51行星系轨道动力学的影响

Periodic orbits in the 1:2:3 resonant chain and their impact on the orbital dynamics of the Kepler-51 planetary system

Kyriaki I. Antoniadou, George Voyatzis

摘要:

太空任务已经发现了大量的系外行星在(或接近)平均运动共振(MMR)和共振链中演化。通常,由于观测的局限性,发表的数据表现出非常高的不确定性,这些局限性在特别短或长的时间尺度上将混沌引入系统的演化。我们提出了一种研究这种系统的动力学探索相空间中的特定区域。我们通过研究三行星系统Kepler-51的长期轨道稳定性来验证我们的方法,并支持或限制其数据。这是一个双重过程,分为两个步骤:计算1:2:3共振链中的周期轨道族和通过动态稳定性映射可视化相空间。我们提出了一般四体问题的新结果。稳定的周期轨道只在低偏心率制度。我们展示了三种可能的情况下,保护开普勒-51,每个约束。首先,存在2/1和3/2两体MMR,其中$e_b<0.02$,使得这些两体MMR持续延长的时间跨度。其次,存在1:2:3三体类拉普拉斯共振,其中$e_c<0.016$和$e_d<0.006$是这种链可行的必要条件。第三,对于内行星对,2/1 MMR内部存在1/1次级共振,而对于外行星对,则存在拱点差振荡,只要观测偏心率$e_b$和$e_c$与$e_d\approx 0$一样有利。为了获得一个最佳的扣除的轨道要素,这项研究展示了动力学分析的基础上进行平行的拟合过程中的周期性轨道的需要。

英文摘要:

Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that introduce chaos into the evolution of the system on especially shorter or longer timescales. We propose a study of the dynamics of such systems by exploring particular regions in phase space. We exemplify our method by studying the long-term orbital stability of the three-planet system Kepler-51 and either favor or constrain its data. It is a dual process which breaks down in two steps: the computation of the families of periodic orbits in the 1:2:3 resonant chain and the visualization of the phase space through maps of dynamical stability. We present novel results for the general four-body problem. Stable periodic orbits were found only in the low-eccentricity regime. We demonstrate three possible scenarios safeguarding Kepler-51, each followed by constraints. Firstly, there are the 2/1 and 3/2 two-body MMRs, in which $e_b<0.02$, such that these two-body MMRs last for extended time spans. Secondly, there is the 1:2:3 three-body Laplace-like resonance, in which $e_c<0.016$ and $e_d<0.006$ are necessary for such a chain to be viable. Thirdly, there is the combination comprising the 1/1 secondary resonance inside the 2/1 MMR for the inner pair of planets and an apsidal difference oscillation for the outer pair of planets in which the observational eccentricities, $e_b$ and $e_c$, are favored as long as $e_d\approx 0$. With the aim to obtain an optimum deduction of the orbital elements, this study showcases the need for dynamical analyses based on periodic orbits performed in parallel to the fitting processes.

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