非层级三体系统的稳定性时标
A Stability Timescale for Non-Hierarchical Three-Body Systems
AI总结：
本研究针对非层级三体系统，推导了估算试验粒子轨道能量变化一个数量级所需时间的解析公式，经N体模拟验证有效，并将其应用于银心Sgr A*周边S型恒星团与潜在中等质量黑洞的稳定性分析。
摘要：
引力三体问题是物理学中的基础问题，在天文学中具有重要应用。人们通常认为，只要三体构型是层级式的（即两个轨道距离相差悬殊），系统就是稳定的。然而，往往与轨道间显著能量交换相关的不稳定性需要时间才能发展。假设两个大质量天体做圆轨道运动，一个试验粒子做偏心轨道运动，我们推导了一个解析公式，用于估算试验粒子的轨道能量变化一个数量级所需的时间。我们证明了该公式与N体模拟的结果一致。尤其对于偏心轨道，不稳定性的主要驱动因素并非试验粒子与其中一个天体的近距离交会，而是偏心轨道在其近心点处发生能量交换的固有敏感性。受近期“银心可能存在一颗中等质量黑洞（IMBH）作为大质量黑洞Sgr A*的伴天体”这一观点的启发，我们利用我们的时标探究了在围绕Sgr A*的S型恒星团的寿命范围内，可能存在IMBH的参数空间。此外，我们证明，在存在其他轨道交叉恒星的情况下，S型恒星的轨道可以在长时间时标内保持稳定，这表明S型恒星团在其成员恒星的寿命周期内可能是稳定的。
英文摘要：
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.
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