双星的Jacobi俘获起源及其在地月系统和星系核黑洞中的应用
On the Jacobi capture origin of binaries with applications to the Earth-Moon system and black holes in galactic nuclei
摘要：
圆盘中两个天体的近距离相遇往往会导致一次轨道偏转。然而，在他们的雅可比体积内，两个物体和中心物体之间的引力变得相互竞争，多次近距离接触的临时捕获成为可能的结果：雅可比捕获。我们进行3体模拟，以便在飞机上的Jacobi捕获的动力学。我们发现，相空间结构类似于一个康托样集的分形维数约为0.4。寿命分布呈指数下降，而最近的分离的分布遵循指数为0.5的幂律。在我们的第一个应用中，我们考虑Jacobi捕获月球。我们证明，潮汐捕获和巨大的影响是可能的结果。碰撞速度很好地近似为抛物线碰撞，而碰撞角遵循均匀光束对圆形目标的碰撞角。雅可比捕获在较大的日心距离更有可能导致潮汐捕获。在我们的第二个应用中，我们发现雅可比捕获与引力波耗散可以导致形成的星系核中的二元黑洞。偏心率分布是近似超热的，包括顺时针和逆时针方向。我们的结论是，耗散Jacobi捕获形成一个有效的通道，形成二进制，这激励进一步的研究，以建立跨多个天体物理尺度的Jacobi捕获的普遍性。
英文摘要：
Close encounters between two bodies in a disc often result in a single orbital deflection. However, within their Jacobi volumes, where the gravitational forces between the two bodies and the central body become competitive, temporary captures with multiple close encounters become possible outcomes: a Jacobi capture. We perform 3-body simulations in order to characterise the dynamics of Jacobi captures in the plane. We find that the phase space structure resembles a Cantor-like set with a fractal dimension of about 0.4. The lifetime distribution decreases exponentially, while the distribution of the closest separation follows a power law with index 0.5. In our first application, we consider the Jacobi capture of the Moon. We demonstrate that both tidal captures and giant impacts are possible outcomes. The impact speed is well approximated by a parabolic encounter, while the impact angles follow that of a uniform beam on a circular target. Jacobi captures at larger heliocentric distances are more likely to result in tidal captures. In our second application, we find that Jacobi captures with gravitational wave dissipation can result in the formation of binary black holes in galactic nuclei. The eccentricity distribution is approximately super-thermal and includes both prograde and retrograde orientations. We conclude that dissipative Jacobi captures form an efficient channel for binary formation, which motivates further research into establishing the universality of Jacobi captures across multiple astrophysical scales.
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