击败随机性：星系合并中大质量黑洞的合并时标
Defeating stochasticity: coalescence timescales of massive black holes in galaxy mergers
摘要：
星系合并中的大质量黑洞双星的合并是低频引力波的主要来源。目前对激光干涉仪空间天线和脉冲星定时阵列的GW探测率的估计相差三个数量级。为了理解这种变化，我们模拟了等质量偏心星系对与中心大质量黑洞和浅内部密度尖点的合并。我们模拟的形成和硬化的中央BHB使用快速多重法作为力求解器，其特点是$O(N)$缩放与粒子的数量$N$，并获得相当于直接求和模拟的结果。在$N \sim 5\times 10^5$，典型的当代研究，偏心率的BHB可以显着不同的随机实现相同的初始条件，导致合并的时间尺度的实质性变化。这种散射归因于恒星与BHB相遇的随机性，并随着$N$的增加而减小。我们估计，恒星半光半径内的$N \sim 10^7$足以将合并时标中的散射减少到$\sim 10$ \%。我们的研究结果表明，至少有一些低频GW率的不确定性是由于数值分辨率不足。
英文摘要：
The coalescence of massive black hole binaries (BHBs) in galactic mergers is the primary source of gravitational waves (GWs) at low frequencies. Current estimates of GW detection rates for the Laser Interferometer Space Antenna and the Pulsar Timing Array vary by three orders of magnitude. To understand this variation, we simulate the merger of equal-mass, eccentric, galaxy pairs with central massive black holes and shallow inner density cusps. We model the formation and hardening of a central BHB using the Fast Multiple Method as a force solver, which features a $O(N)$ scaling with the number $N$ of particles and obtains results equivalent to direct-summation simulations. At $N \sim 5\times 10^5$, typical for contemporary studies, the eccentricity of the BHBs can vary significantly for different random realisations of the same initial condition, resulting in a substantial variation of the merger timescale. This scatter owes to the stochasticity of stellar encounters with the BHB and decreases with increasing $N$. We estimate that $N \sim 10^7$ within the stellar half-light radius suffices to reduce the scatter in the merger timescale to $\sim 10$\%. Our results suggest that at least some of the uncertainty in low-frequency GW rates owes to insufficient numerical resolution.
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