AI 中文总结
本研究通过数值模拟探究反冲黑洞引发的潮汐瓦解与引力波爆发，发现事件发生率依赖反冲速度、黑洞质量与核星团密度轮廓，这类可观测信号可用于探测并合后核星团并检验数值相对论。
AI 中文摘要
我们旨在研究大质量黑洞双星在星系中心并合后不久，且残留黑洞被逐出星系时发生的潮汐瓦解事件和引力波事件。我们采用计算方法，对嵌入核星团中、质量分别为$M_{\bullet}=10^{5}$ M$_\bullet$和$4\times10^{5}$ M$_\bullet$的黑洞，以$v_k=300$和$600$ km s$^{-1}$的速度施加反冲踢动。系统采用4阶Hermite格式积分$0.1$ Myr的时长。反冲踢动会瞬间重新填充损失锥，引发强烈的潮汐瓦解事件和引力波并合爆发。受缚恒星拱点取向的各向异性会延长这一爆发阶段。反冲速度$v_k$越低、黑洞质量$M_{\bullet}$越大、并合时刻核星团的密度轮廓越陡，事件发生率就越高。假设双黑洞在并合过程中会冲刷出Bahcall-Wolf密度轮廓，那么质量处于$10^{5}\leq M_{\bullet}$ [M$_\bullet] \times10^{5}$范围内的被逐出残留黑洞，在红移$z=3$以内产生的可观测偏移事件的预测发生率为$\bar{N}\times290$ yr$^{-1}$。若并合时刻核星团的毫秒差距尺度由浅密度轮廓（$\bar{\nu}=1$）描述，该发生率会降至$\bar{N}\times30$ yr$^{-1}$。这类可观测信号对初始密度轮廓和反冲踢动的强依赖性，使其成为探测大质量黑洞双星并合后核星团状态的有力工具，也为数值相对论提供了检验途径。
英文摘要
We aim to investigate the tidal disruption and gravitational wave events shortly after a massive black hole binary merges in the galactic centre and whose remnant black hole is ejected from the galaxy. Using computational methods, black holes of mass $M_{\bullet}=10^{5}$ M$_\odot$ and $4\times10^{5}$ M$_\odot$ embedded in a nuclear star cluster are kicked at velocities of $v_k=300$ and $600$ km s$^{-1}$. Systems are integrated for $0.1$ Myr using a $4$th-order Hermite scheme. The kick instantaneously repopulates the loss cone, producing a strong burst of tidal disruption events and gravitational wave mergers. The anisotropy in the apsidal orientation of bound stars prolongs this burst phase. Rates increase for lower $v_k$, larger $M_{\bullet}$ and for steeper nuclear star cluster density profiles at moment of merger. Assuming binary black holes scour a Bahcall-Wolf density profile during coalescence, ejected remnants with mass between $10^{5}\leq M_{\bullet}$ [M$_\odot] \leq 4\times10^{5}$ generate observable offset events at a forecasted rate of $\dot{N}\lesssim290$ yr$^{-1}$ up to redshift $z=3$. If, at the moment of merger, the milliparsec scales of the nuclear star cluster are described by a shallow density profile ($γ=1$), this decreases to $\dot{N}\lesssim30$ yr$^{-1}$. The strong dependence on the initial density profile and recoil kick makes observables powerful probes of the nuclear star cluster post-massive black hole binary coalescence, and provides test for numerical relativity.
Comments10 pages, 5 figures
