Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber
Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber
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DOI：
10.1051/0004-6361/201935220
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发表时间：
2019-04
影响因子：
6.5
通讯作者：
G. El'ia;M. Zanardi;A. Dugaro;S. Naoz
中科院分区：
文献类型：
--
作者：
G. El'ia;M. Zanardi;A. Dugaro;S. Naoz
目标。分析了椭圆型限制性三体问题中外粒子近心幅角ω2的行为，重点讨论了ω2共振或逆Lidov-Kozai共振.方法.首先，我们计算了四极、八极和十六极项对外粒子ω2进动率（dω2 scind τ）的贡献。然后，我们推导出了在不同的内扰动偏心率e1值下，ω2四极进动率（dω2/dτ）quad消失的解析判据。最后，我们使用这样的分析考虑，并描述了从以前的工作中开发的N体模拟中提取的外部粒子的ω2的行为。结果我们的分析研究表明，与消失的（dω2/dτ）quad相关联的外粒子的倾角i2和升交点经度Ω2的值强烈地依赖于内微扰的偏心率e1.事实上，如果e1 0.40825），（dω2/dτ）quad仅对于Ω2循环的粒子（自由振动）消失。当e1在0.25 ~ 0.40825之间时，对于任意粒子，只要选择合适的对（Ω2，i2），（dω2/dτ）quad就可以消失。我们的N体模拟分析表明，逆Lidov-Kozai共振是可能的小，中等，高值的e1。此外，这种共振在粒子在（Ω2，i2）平面的演化中产生了独特的特征。事实上，如果ω2做平动，Ω2做循环，那么i2在Ω2 = 90°和270°的极值不会达到相同的值，而如果ω2和Ω2做平动，那么粒子在（Ω2，i2）平面上的演化轨迹显示出相对于i2 = 90°不对称的证据。在N体模拟中，与外粒子相关的ω2的演化可以很好地用我们研究中得到的分析判据来解释。
Aims. We analyze the behavior of the argument of pericenter ω2 of an outer particle in the elliptical restricted three-body problem, focusing on the ω2 resonance or inverse Lidov-Kozai resonance. Methods. First, we calculated the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle’s ω2 precession rate (dω2∕dτ). Then, we derived analytical criteria that determine the vanishing of the ω2 quadrupole precession rate (dω2/dτ)quad for different values of the inner perturber’s eccentricity e1. Finally, we used such analytical considerations and described the behavior of ω2 of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i2 and the ascending node longitude Ω2 associated with the outer particle that vanish (dω2/dτ)quad strongly depend on the eccentricity e1 of the inner perturber. In fact, if e1 0.40825), (dω2/dτ)quad is only vanished for particles whose Ω2 circulates (librates). For e1 between 0.25 and 0.40825, (dω2/dτ)quad can be vanished for any particle for a suitable selection of pairs (Ω2, i2). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate, and high values of e1. Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω2, i2) plane. In fact, if ω2 librates and Ω2 circulates, the extremes of i2 at Ω2 = 90° and 270° do not reach the same value, while if ω2 and Ω2 librate, the evolutionary trajectory of the particle in the (Ω2, i2) plane shows evidence of an asymmetry with respect to i2 = 90°. The evolution of ω2 associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation.