标题： exoMMR：一个确认和表征平均运动共振的新Python软件包 显示英文标题

标题： exoMMR: a New Python Package to Confirm and Characterize Mean Motion Resonances

摘要： 轨道共振的研究有助于限制紧凑系统的行星特性。 我们可以通过观察行星的轨道周期来预测系统的共振，因为处于或接近平均运动共振的行星具有简化为小数比值的周期比。 然而，接近共轭的周期比并不保证存在共振；我们必须研究系统的动力学和共振角以确认共振。 由于共振需要深入研究才能确认，且二体共振需要测量偏心率矢量，这非常具有挑战性，因此很少有共振对或链被确认。 因此，我们仍处于小样本统计的时代，尚无法进行大规模种群合成或信息学研究。 为了解决这个问题，我们构建了一个Python包，通过N体模拟来查找、确认和分析平均运动共振。 随后，我们分析了开普勒/K2和TESS目录中所有接近共振的行星，确认了超过60个新的共振对和各种新的共振链。 我们还通过描述开普勒-80g的质量-偏心率退化、探索开普勒-80外部巨行星的可能性以及限制开普勒-305中的行星质量来展示该软件包的功能和潜力。 我们发现，我们的方法高估了共振角的摆动幅度，并且在系统中有多于三颗行星时难以确认共振。 我们识别出一些可能的共振链系统，但无法确认它们，并强调了系外行星共振的下一步研究方向。 显示英文摘要

摘要： The study of orbital resonances allows for the constraint of planetary properties of compact systems. We can predict a system's resonances by observing the orbital periods of the planets, as planets in or near mean motion resonance have period ratios that reduce to a ratio of small numbers. However, a period ratio near commensurability does not guarantee a resonance; we must study the system's dynamics and resonant angles to confirm resonance. Because resonances require in-depth study to confirm, and because two-body resonances require a measurement of the eccentricity vector which is quite challenging, very few resonant pairs or chains have been confirmed. We thus remain in the era of small number statistics, not yet able to perform large population synthesis or informatics studies. To address this problem, we build a python package to find, confirm, and analyze mean motion resonances, primarily through N-body simulations. We then analyze all near-resonant planets in the Kepler/K2 and TESS catalogues, confirming over 60 new resonant pairs and various new resonant chains. We additionally demonstrate the package's functionality and potential by characterizing the mass-eccentricity degeneracy of Kepler-80g, exploring the likelihood of an exterior giant planet in Kepler-80, and constraining the masses of planets in Kepler-305. We find that our methods overestimate the libration amplitudes of the resonant angles and struggle to confirm resonances in systems with more than three planets. We identify various systems that are likely resonant chains but that we are unable to confirm, and highlight next steps for exoplanetary resonances.