Many proposed scenarios for black hole (BH) mergers involve a tertiary companion that induces von Zeipel–Lidov–Kozai (ZLK) eccentricity cycles in the inner binary. An attractive feature of such mechanisms is the enhanced merger probability when the octupole-order effects, also known as the eccentric Kozai mechanism, are important. This can be the case when the tertiary is of comparable mass to the binary components. Since the octupole strength [∝(1 − q)/(1 + q)] increases with decreasing binary mass ratio q, such ZLK-induced mergers favour binaries with smaller mass ratios. We use a combination of numerical and analytical approaches to fully characterize the octupole-enhanced binary BH mergers and provide semi-analytical criteria for efficiently calculating the strength of this enhancement. We show that for hierarchical triples with semimajor axial ratio a/aout ≳ 0.01–0.02, the binary merger fraction can increase by a large factor (up to ∼20) as q decreases from unity to 0.2. The resulting mass-ratio distribution for merging binary BHs produced in this scenario is in tension with the observed distribution obtained by the LIGO/VIRGO collaboration, although significant uncertainties remain about the initial distribution of binary BH masses and mass ratios.

中文翻译：

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三元双黑洞并合的质量比分布

许多提议的黑洞 (BH) 合并方案都涉及第三伴星，该伴星在内部双星中引发 von Zeipel-Lidov-Kozai (ZLK) 偏心率循环。这种机制的一个吸引人的特征是当八极阶效应（也称为偏心 Kozai 机制）很重要时，合并概率会提高。当三元的质量与二元成分相当时，可能会出现这种情况。由于八极子强度 [∝(1 - q)/(1 + q)] 随着二元质量比 q 的降低而增加，这种 ZLK 诱导的合并有利于质量比较小的二元。我们使用数值和分析方法的组合来充分表征八极增强的二元 BH 合并，并提供半分析标准来有效计算这种增强的强度。我们表明，对于半长轴比 a/aout ≳ 0.01-0.02 的分层三元组，当 q 从单位减小到 0.2 时，二元合并分数可以增加一个很大的因子（高达 ∼20）。在这种情况下产生的合并二元 BH 的质量比分布与 LIGO/VIRGO 合作获得的观察分布存在张力，尽管二元 BH 质量和质量比的初始分布仍存在很大的不确定性。