论文标题
层次三重系统的拉格朗日与Lyapunov的稳定性：依赖内轨道和外轨道之间的相互倾斜度
Lagrange vs. Lyapunov stability of hierarchical triple systems: dependence on the mutual inclination between inner and outer orbits
论文作者
论文摘要
尽管有许多研究研究了层次三重系统的稳定性，但``稳定性''的含义有些模糊，并且在以前的文献中的解释方式有所不同。本文的重点是``Lagrange稳定性''，该论文与``与``Lyapunov like stane''''的稳定性或``'''''''或``''''''''''''''或``'''''''相反。我们使用直接$ n $ body模拟来计算三重系统的演变，最高$ 10^7 p_ \ mathrm {out} $，它比以前的研究更长（其中$ p_ \ mathrm {out} $是外部外体的初始轨道时期）。我们获得所得的破坏时间尺度$ t_ \ mathrm {d} $作为三重轨道参数的函数，特别注意依赖于内部和外轨道之间的相互倾斜度，$ i_ \ mathrm {mut {mut {mut} $。通过这样做，我们已经明确阐明了拉格朗日和莱普诺诺夫稳定性在天文三元组中的差异。 Furthermore, we find that the von Zeipel-Kozai-Lidov oscillations significantly destabilize inclined triples (roughly with $60^\circ < i_\mathrm{mut} < 150^\circ$) relative to those with $i_\mathrm{mut}=0^\circ$.另一方面，用$ i_ \ mathrm {mut}> 160^\ circ $逆行三元组，随着时间表的较长时间尺寸，circ $变得强烈稳定。我们显示了归一化的破坏时间尺度$ t_ \ mathrm {d}/p_ \ mathrm {out} $的灵敏度对三个系统的轨道参数。所得的$ t_ \ mathrm {d}/p_ \ mathrm {out} $分布在广泛的天文应用中比基于lyapunov Divergence的稳定性标准更有用。
While there have been many studies examining the stability of hierarchical triple systems, the meaning of ``stability'' is somewhat vague and has been interpreted differently in previous literatures. The present paper focuses on ``Lagrange stability'', which roughly refers to the stability against the escape of a body from the system, or ``disruption'' of the triple system, in contrast to ``Lyapunov-like stability'' that is related to the chaotic nature of the system dynamics. We compute the evolution of triple systems using direct $N$-body simulations up to $10^7 P_\mathrm{out}$, which is significantly longer than previous studies (with $P_\mathrm{out}$ being the initial orbital period of the outer body). We obtain the resulting disruption timescale $T_\mathrm{d}$ as a function of the triple orbital parameters with particular attention to the dependence on the mutual inclination between the inner and outer orbits, $i_\mathrm{mut}$. By doing so, we have clarified explicitly the difference between Lagrange and Lyapunov stabilities in astronomical triples. Furthermore, we find that the von Zeipel-Kozai-Lidov oscillations significantly destabilize inclined triples (roughly with $60^\circ < i_\mathrm{mut} < 150^\circ$) relative to those with $i_\mathrm{mut}=0^\circ$. On the other hand, retrograde triples with $i_\mathrm{mut}>160^\circ$ become strongly stabilized with much longer disruption timescales. We show the sensitivity of the normalized disruption timescale $T_\mathrm{d}/P_\mathrm{out}$ to the orbital parameters of triple system. The resulting $T_\mathrm{d}/P_\mathrm{out}$ distribution is practically more useful in a broad range of astronomical applications than the stability criterion based on the Lyapunov divergence.
