The Von Zeipel–Lidov–Kozai Effect inside Mean Motion Resonances with Applications to Trans-Neptunian Objects
The Von Zeipel–Lidov–Kozai Effect inside Mean Motion Resonances with Applications to Trans-Neptunian Objects
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DOI：
10.3847/1538-3881/ac7c6a
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Hanlun Lei;Jian Li;Xiumin Huang;M. Li
中科院分区：
文献类型：
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作者：
Hanlun Lei;Jian Li;Xiumin Huang;M. Li
平均运动共振（MMR）中的长期动力学在控制海王星外区域的动力学结构和塑造海王星外天体（TNO）的轨道分布方面起着至关重要的作用。在这项研究中，半解析的发展，探讨冯齐佩尔-Lidov-Kozai共振内MMR。为此，从平均理论出发建立了一个半长期模型，然后基于绝热不变性近似得到了一个单自由度可积模型。特别是，我们引入了一个修改的绝热不变量，这是连续周围的分离矩阵的MMR。在长期演化过程中，共振哈密顿量和绝热不变量都保持不变，因此可以通过绘制绝热不变量与给定哈密顿量的能级曲线来绘制相图。相图提供了全局图像来预测近心点的偏心率、倾角和幅角的长期行为。对MMR中一些代表性的TNO（2018 VO 137，2005 SD 278，2015 PD 312，Pluto，2004 HA 79，1996 TR 66和2014 SR 373）的应用表明，全N体模型下的数值传播轨迹与相图中出现的能级曲线之间具有良好的一致性。有趣的是，2018 VO 137和2005 SD 278在长期演化过程中表现出开关行为，目前它们与海王星处于2：5的MMR内。
Secular dynamics inside mean motion resonances (MMRs) plays an essential role in governing the dynamical structure of the trans-Neptunian region and sculpting the orbital distribution of trans-Neptunian objects (TNOs). In this study, semianalytical developments are made to explore the von Zeipel–Lidov–Kozai resonance inside MMRs. To this end, a semi-secular model is formulated from averaging theory and then a single-degree-of-freedom integrable model is achieved based on the adiabatic invariance approximation. In particular, we introduce a modified adiabatic invariant, which is continuous around the separatrices of MMRs. During long-term evolution, both the resonant Hamiltonian and the adiabatic invariant remain unchanged, thus phase portraits can be produced by plotting level curves of the adiabatic invariant with a given Hamiltonian. The phase portraits provide global pictures to predict long-term behaviors of the eccentricity, inclination, and argument of pericenter. Applications to some representative TNOs inside MMRs (2018 VO137, 2005 SD278, 2015 PD312, Pluto, 2004 HA79, 1996 TR66, and 2014 SR373) show good agreements between the numerically propagated trajectories under the full N-body model and the level curves arising in phase portraits. Interestingly, 2018 VO137 and 2005 SD278 exhibit switching behaviors during their long-term evolution and currently they are inside 2:5 MMR with Neptune.