标题： 最负的$χ_\mathrm{eff}$系统对分层黑洞合并的限制 显示英文标题

标题： Limits on hierarchical black hole mergers from the most negative $χ_\mathrm{eff}$ systems

摘要： 它已被提出，一些双黑洞（BBH）系统中的黑洞（BHs）是通过“层级合并”（HM）形成的；即较小黑洞的早期合并。这些HM产物具有自旋大小$\chi \sim 0.7$，如果它们动态地组成BBH系统，它们的自旋方向有时会与二元轨道角动量反向对齐。事实上，如 Baibhav 等人（2020）所示，包含HM产物的BBH系统的$\sim16\%$将具有有效 inspiral 自旋参数，$\chi_\mathrm{eff} < -0.3$。然而，LIGO-Virgo-Kagra（LVK）引力波（GW）探测器尚未观测到具有$\chi_\mathrm{eff} \lesssim -0.2$的BBH系统，这导致了种群中HM产物比例的上限。我们拟合了BBH系统的天体物理质量和自旋分布，并测量了具有$\chi_\mathrm{eff} < -0.3$的BBH系统的比例，这暗示了HM比例的上限。我们发现，在基础的BBH种群中，少于$26\%$的系统包含HM产物（90%可信度）。即使在主要质量为$m_1=60\,M_\odot$的BBH系统中，HM比例也小于69%，这可能限制了成对不稳定性质量间隙的位置。 随着300 GW事件（预计在LVK的下一次观测运行中将出现），如果我们未能观测到具有$\chi_\mathrm{eff} < -0.3$的BBH，我们可以得出结论，即HM成分小于$2.5^{+9.1}_{-2.2}\%$。 显示英文摘要

摘要： It has been proposed that some black holes (BHs) in binary black hole (BBH) systems are born from "hierarchical mergers" (HM); i.e. earlier mergers of smaller BHs. These HM products have spin magnitudes $\chi \sim 0.7$, and, if they are dynamically assembled into BBH systems, their spin orientations will be sometimes anti-aligned with the binary orbital angular momentum. In fact, as Baibhav et al. (2020) showed, $\sim16\%$ of BBH systems that include HM products will have an effective inspiral spin parameter, $\chi_\mathrm{eff} < -0.3$. Nevertheless, the LIGO-Virgo-Kagra (LVK) gravitational-wave (GW) detectors have yet to observe a BBH system with $\chi_\mathrm{eff} \lesssim -0.2$, leading to upper limits on the fraction of HM products in the population. We fit the astrophysical mass and spin distribution of BBH systems and measure the fraction of BBH systems with $\chi_\mathrm{eff} < -0.3$, which implies an upper limit on the HM fraction. We find that fewer than $26\%$ of systems in the underlying BBH population include HM products (90\%. credibility). Even among BBH systems with primary masses $m_1=60\,M_\odot$, the HM fraction is less than 69\%, which may constrain the location of the pair-instability mass gap. With 300 GW events (to be expected in the LVK's next observing run), if we fail to observe a BBH with $\chi_\mathrm{eff} < -0.3$, we can conclude that the HM fraction is smaller than $2.5^{+9.1}_{-2.2}\%$.