Secular Evolution of Hierarchical Triple Star Systems
Secular Evolution of Hierarchical Triple Star Systems
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DOI：
10.1086/308815
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发表时间：
1999-05
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影响因子：
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通讯作者：
E. Ford;B. Kozinsky;F. Rasio
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文献类型：
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作者：
E. Ford;B. Kozinsky;F. Rasio
利用经典的哈密顿微扰技术，我们推导出了三重体系的八极级长期微扰方程。我们的方程描述了轨道偏心率和倾角在与轨道周期相比较长的时间尺度上的长期演变。通过将前人的工作推广到先导(四极)序到八极级(即，包括α3阶的项，其中α≡a1/a2<；1是半长轴之比)，我们得到了适用于更广泛范围的参数的表达式。特别是，我们的结果可以应用于高倾角系统和共面系统，并且我们的表达式对于几乎所有系统处于稳定的层次构型的质量比都是有效的。相比之下，标准的Kozai四极能级理论在相对倾角为零的极限下给出了一个消失的结果。经典的行星摄动理论虽然适用于α中的所有阶次，但只适用于低偏心率和低相对倾角的低质量天体围绕共同中心质量运行的轨道。对于包含紧密内双星的三重系统，我们还讨论了经典牛顿微扰与内轨道的广义相对论进动之间可能的相互作用。在某些情况下，我们表明这种相互作用可以导致共振和偏心扰动的最大幅度显着增加。我们通过与三体问题直接数值积分的结果进行详细的比较，证明了我们的解析表达式的有效性。此外，我们还证明了我们的表达式与以前发表的在各种极限条件下的解析结果是一致的。我们还讨论了理论在几个当前感兴趣的观测三星系的背景下的应用，包括M4中的毫秒脉冲星PSR B1620-26，16天鹅座中的巨行星，以及原恒星双星TMR-1。
We derive octupole-level secular perturbation equations for hierarchical triple systems, using classical Hamiltonian perturbation techniques. Our equations describe the secular evolution of the orbital eccentricities and inclinations over timescales that are long compared to the orbital periods. By extending previous work done to leading (quadrupole) order to octupole level (i.e., including terms of order α3, where α ≡ a1/a2 < 1 is the ratio of semimajor axes), we obtain expressions that are applicable to a much wider range of parameters. In particular, our results can be applied to high-inclination as well as coplanar systems, and our expressions are valid for almost all mass ratios for which the system is in a stable hierarchical configuration. In contrast, the standard quadrupole-level theory of Kozai gives a vanishing result in the limit of zero relative inclination. The classical planetary perturbation theory, while valid to all orders in α, applies only to orbits of low-mass objects orbiting a common central mass, with low eccentricities and low relative inclinations. For triple systems containing a close inner binary, we also discuss the possible interaction between the classical Newtonian perturbations and the general relativistic precession of the inner orbit. In some cases we show that this interaction can lead to resonances and a significant increase in the maximum amplitude of eccentricity perturbations. We establish the validity of our analytic expressions by providing detailed comparisons with the results of direct numerical integrations of the three-body problem obtained for a large number of representative cases. In addition, we show that our expressions reduce correctly to previously published analytic results obtained in various limiting regimes. We also discuss applications of the theory in the context of several observed triple systems of current interest, including the millisecond pulsar PSR B1620-26 in M4, the giant planet in 16 Cygni, and the protostellar binary TMR-1.