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arXiv 2011.07103astro-ph.EPnlin.CD
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递阶三体问题的稳定点

The Stationary Points of the Hierarchical Three Body Problem

Bradley M. S. Hansen, Smadar Naoz

备注：
27 pages, 36 figures
发表信息：
MNRAS, 499, 1682 (2020)
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摘要：

本文研究了行星极限（m_2，m_3 << m_1）下四极和八极级层次三体问题的不动点。我们证明了在小的外偏心率e_2的限制下，八极序的扩展保持了四极解的主不动点，但在逆和逆的情况下都出现了新的稳定不动点族。最重要的新平衡是那些从四极解分支出来并延伸到大e_2的平衡。这些家族的拱点排列是质量和内行星离心率的函数，并且由四极水平上ω_1和ω_2的相对进动方向决定。这些新的平衡也是最能抵御相对论性岁差的不稳定影响的。我们发现额外的平衡，使天平动的内行星参数的pericentre在径向轨道的限制，并恢复非线性模拟的拉普拉斯-拉格朗日解的共面极限。最后，我们表明，与偏心Kozai Lidov机制及其变体确定的混沌扩散和轨道翻转可以理解的驻点在这里讨论。

英文摘要：

We study the stationary points of the hierarchical three body problem in the planetary limit (m_2, m_3 << m_1) at both the quadrupole and octupole orders. We demonstrate that the extension to octupole order preserves the principal stationary points of the quadrupole solution in the limit of small outer eccentricity e_2 but that new families of stable fixed points occur in both prograde and retrograde cases. The most important new equilibria are those that branch off from the quadrupolar solutions and extend to large e_2. The apsidal alignment of these families is a function of mass and inner planet eccentricity, and is determined by the relative directions of precession of omega_1 and omega_2 at the quadrupole level. These new equilibria are also the most resilient to the destabilizing effects of relativistic precession. We find additional equilibria that enable libration of the inner planet argument of pericentre in the limit of radial orbits and recover the non-linear analogue of the Laplace-Lagrange solutions in the coplanar limit. Finally, we show that the chaotic diffusion and orbital flips identified with the Eccentric Kozai Lidov mechanism and its variants can be understood in terms of the stationary points discussed here.

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