By performing Monte Carlo simulations of the evolution of binary primordial black hole (PBH) systems, we estimate the effect of distant encounters with single PBHs upon the coalescence time and merger rate of binary PBHs. We find that, for models where PBHs compose a large fraction of dark matter, $\fPBH\sim 1$, the expected fractional change in coalescence time is negligible, of order $10^{-6}$ for most binaries. For models with significantly lower PBH abundances, $\fPBH\ll 1$, we find that the average change in binary lifetime due to encounters can be as large as $\mathcal{O}(10^{-2})$, with a small number of binaries experiencing an order unity change in lifetime. In the absence of encounters, we also compare the use of an analytic approximation for the coalescence time to numerically evolving the binary system, finding that the analytic approximation results in an order $10\%$ error in the coalescence time. However, when these effects are taken into consideration, there is a negligible change to the calculated merger rate, placing previous constraints on the PBH abundance arising from observed gravitational wave signals from merging binary black holes on a more secure footing.

中文翻译：

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远距离飞越对二元原始黑洞并合率的影响

通过对二元原始黑洞 (PBH) 系统的演化进行蒙特卡罗模拟，我们估计了与单个 PBH 的远距离相遇对二元 PBH 的合并时间和合并率的影响。我们发现，对于 PBH 构成大部分暗物质 $\fPBH\sim 1$ 的模型，聚结时间的预期分数变化可以忽略不计，对于大多数双星来说，其数量级为 $10^{-6}$。对于具有显着较低 PBH 丰度 $\fPBH\ll 1$ 的模型，我们发现由于遭遇导致的双星寿命平均变化可能与 $\mathcal{O}(10^{-2})$ 一样大，其中少数二进制文件在生命周期中经历了顺序统一变化。在没有遇到的情况下，我们还将对聚结时间的解析近似的使用与数值演化二元系统进行比较，发现解析近似导致聚结时间出现 $10\%$ 级误差。然而，当考虑到这些影响时，计算出的合并率的变化可以忽略不计，这对在更安全的基础上合并双黑洞时观测到的引力波信号产生的 PBH 丰度施加了先前的限制。