Gravitational-wave observations provide the unique opportunity of studying black hole formation channels and histories—but only if we can identify their origin. One such formation mechanism is the dynamical synthesis of black hole binaries in dense stellar systems. Given the expected isotropic distribution of component spins of binary black holes in gas-free dynamical environments, the presence of antialigned or in-plane spins with respect to the orbital angular momentum is considered a tell-tale sign of a merger’s dynamical origin. Even in the scenario where birth spins of black holes are low, hierarchical mergers attain large component spins due to the orbital angular momentum of the prior merger. However, measuring such spin configurations is difficult. Here, we quantify the efficacy of the spin parameters encoding aligned-spin (χ _eff) and in-plane spin (χ _p ) at classifying such hierarchical systems. Using Monte Carlo cluster simulations to generate a realistic distribution of hierarchical merger parameters from globular clusters, we can infer mergers’ χ _eff and χ _p . The cluster populations are simulated using Advanced LIGO-Virgo sensitivity during the detector network’s third observing period and projections for design sensitivity. Using a “likelihood-ratio”-based statistic, we find that ∼2% of the recovered population by the current gravitational-wave detector network has a statistically significant χ _p measurement, whereas no χ _eff measurement was capable of confidently determining a system to be antialigned with the orbital angular momentum at current detector sensitivities. These results indicate that measuring spin-precession through χ _p is a more detectable signature of hierarchical mergers and dynamical formation than antialigned spins.

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旋转医生：如何诊断分层合并的起源

引力波观测为研究黑洞形成通道和历史提供了独特的机会——但前提是我们能够确定它们的起源。其中一种形成机制是致密恒星系统中黑洞双星的动态合成。考虑到在无气体动力学环境中双黑洞分量自旋的预期各向同性分布，相对于轨道角动量的反对齐或面内自旋的存在被认为是合并动力学起源的明显标志。即使在黑洞诞生自旋较低的情况下，由于先前合并的轨道角动量，分层合并也会获得较大的分量自旋。然而，测量这种自旋构型是很困难的。在这里，我们量化了编码对齐自旋的自旋参数的功效（χ _eff ) 和面内自旋 (χ _p ）对这种层次系统进行分类。使用蒙特卡罗聚类模拟从球状聚类生成层次合并参数的真实分布，我们可以推断合并的χ _有效和χ _p 。在探测器网络的第三个观测周期内，使用高级 LIGO-Virgo 灵敏度和设计灵敏度预测来模拟簇群。使用基于“似然比”的统计数据，我们发现当前引力波探测器网络恢复的种群中约有 2% 具有统计显着性χ _p 测量，而没有χ _eff测量能够自信地确定在当前探测器灵敏度下与轨道角动量反对准的系统。这些结果表明，通过测量自旋进动χ _p 与反对齐自旋相比，这是分层合并和动态形成的更容易检测到的特征。