A Stability Timescale for Nonhierarchical Three-body Systems
A Stability Timescale for Nonhierarchical Three-body Systems
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DOI：
10.3847/1538-4357/acd782
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
Eric Zhang;S. Naoz;C. Will
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文献类型：
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作者：
Eric Zhang;S. Naoz;C. Will
引力三体问题是物理学中的一个基本问题，在天文学中具有重要的应用。只要系统是分层的，三体构型通常被认为是稳定的；也就是说，两个轨道距离相距甚远。然而，不稳定通常与轨道之间的大量能量交换有关，需要时间来发展。假设两个大质量物体在圆形轨道上，一个测试粒子在偏心轨道上，我们开发了一个分析公式来估计测试粒子的轨道能量自行改变一个量级所需的时间。我们证明了它与 N 体模拟结果的一致性。特别是对于偏心轨道，不稳定性主要不是由测试粒子与其他天体之一的近距离接触驱动的，而是由偏心轨道在其近点交换能量的基本敏感性驱动的。受最近关于银河系中心可能存在一个中等质量黑洞 (IMBH) 作为大质量黑洞 Sgr A* 伴星的启发，我们利用时间尺度来探索参数空间，该空间在 Sgr A* 周围的 S 星团的生命周期内可能包含一个 IMBH。此外，我们表明，在其他轨道交叉恒星存在的情况下，S 星的轨道可以在很长的时间尺度内保持稳定，从而表明 S 星团可能在其成员恒星的生命周期内保持稳定。
The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital distances are well-separated. However, instability, which is often associated with significant energy exchange between orbits, takes time to develop. Assuming two massive objects in a circular orbit and a test particle in an eccentric orbit, we develop an analytical formula estimating the time it takes for the test particle’s orbital energy to change by an order of itself. We show its consistency with results from N-body simulations. For eccentric orbits in particular, the instability is primarily driven not by close encounters of the test particle with one of the other bodies, but by the fundamental susceptibility of eccentric orbits to exchange energy at their periapsis. Motivated by recent suggestions that the galactic center may host an intermediate-mass black hole (IMBH) as a companion to the massive black hole Sgr A*, we use our timescale to explore the parameter space that could harbor an IMBH for the lifetime of the S-cluster of stars surrounding Sgr A*. Furthermore, we show that the orbit of an S-star can be stable for long timescales in the presence of other orbital crossing stars, thus suggesting that the S-cluster may be stable for the lifetimes of its member stars.