大质量黑洞周围的强质量分离：低频引力波天体物理学的意义
On strong mass segregation around a massive black hole: Implications for lower-frequency gravitational-wave astrophysics
摘要：
我们提出，第一次，一个明确的$N$体实现的{\it强质量分离}解决方案的恒星分布周围的大质量黑洞。我们比较了我们的$N$体的结果与那些通过求解轨道平均的Fokker-Planck（FP）方程在能量空间。$N$-体分离比FP解稍强，但两者都证实了当重恒星的数量分数（实际上）占总星群的一小部分时，强分离状态的{\it鲁棒性}。鉴于最近的观测揭示了在银河系的亚秒差距区域的巨星缺乏，我们表明，与尖点再生长的时间尺度不长于$(0.1-0.25) \times T_{rlx}(r_h)$。这些时间尺度是短于哈勃时间的黑洞质量$\mbul \lesssim 4 \times 10^6 M_\odot$，我们得出结论，准稳定，质量分离，恒星尖点可能是常见的MBH在这个质量范围内。由于EMRI的速率标度为$\mbul^{-α}$，加上$α\in [1\4,1]$，这些事件中有很大一部分应该来自强烈分离的恒星尖点。
英文摘要：
We present, for the first time, a clear $N$-body realization of the {\it strong mass segregation} solution for the stellar distribution around a massive black hole. We compare our $N$-body results with those obtained by solving the orbit-averaged Fokker-Planck (FP) equation in energy space. The $N$-body segregation is slightly stronger than in the FP solution, but both confirm the {\it robustness} of the regime of strong segregation when the number fraction of heavy stars is a (realistically) small fraction of the total population. In view of recent observations revealing a dearth of giant stars in the sub-parsec region of the Milky Way, we show that the time scales associated with cusp re-growth are not longer than $(0.1-0.25) \times T_{rlx}(r_h)$. These time scales are shorter than a Hubble time for black holes masses $\mbul \lesssim 4 \times 10^6 M_\odot$ and we conclude that quasi-steady, mass segregated, stellar cusps may be common around MBHs in this mass range. Since EMRI rates scale as $\mbul^{-α}$, with $α\in [1\4,1]$, a good fraction of these events should originate from strongly segregated stellar cusps.
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