论文标题
来自球状簇的黑洞二进制文件的合并速率：理论误差线和与GWTC-2的重力波数据的比较
Merger rate of black hole binaries from globular clusters: theoretical error bars and comparison to gravitational wave data from GWTC-2
论文作者
论文摘要
在球状簇中动态形成的黑洞二进制物被认为是宇宙中引力波的主要来源之一。在这里，我们使用新的人口综合代码CBHBD来确定合并速率密度和球状簇中形成的黑洞二进制组的红移演变。我们模拟$ \ sim 2 $ $ $ $ $，以探索与真实群集和所有质量尺度相关的参数空间。我们表明，当正确考虑了初始群集质量函数和密度的不确定性时，它们将成为设定合并率的理论误差栏的两个主要因素。其他模型参数（例如，出生踢，黑洞质量，金属性）几乎对局部合并速率密度没有影响，尽管它们会影响合并黑洞的质量。建模合并速率密度作为红移的函数为$ r（z）= r_0（1+z）^κ$ in $ z <2 $，并在不确定性上进行边缘化，我们发现：$ r_0 = 7.2^{+21.5} _ { - 5.5} _ { - 5.5} { - 5.5} $κ= 1.6^{+0.4} _ { - 0.6} $（$ 90 \％$可信度）。在簇内部合并的二进制的速率参数为$ {r} _ {\ rm 0，in} = 1.6^{+1.9} _ { - 1.0} {\ rm gpc^{ - rm gpc^{ - 3} in} = 2.3^{+1.3} _ { - 1.0} $;这些形式的$ \ sim 20 \％$是引力波捕获的结果，这意味着来自球形簇的偏心合并贡献了$ \ lissim 0.4 \ rm gpc gpc^{ - 3} yr^{ - 1} $对本地费率。 Ligo-Virgo报告的合并率的比较表明，在球状簇中形成大多数检测到的黑洞合并的情况与当前的约束是一致的，并且需要初始群集半质量密度$ \ gtrsim 10^4 M_ \ odot \ odot \ odot \ odot \ odot \ rm pc^{-3} $。这样的模型还重现了质量$ 13-30 m_ \ odot $的推断的主要黑洞质量分布，但在此范围之外的数据不足。
Black hole binaries formed dynamically in globular clusters are believed to be one of the main sources of gravitational waves in the Universe. Here, we use our new population synthesis code, cBHBd, to determine the redshift evolution of the merger rate density and masses of black hole binaries formed in globular clusters. We simulate $\sim 2$ million models to explore the parameter space that is relevant to real clusters and over all mass scales. We show that when uncertainties on the initial cluster mass function and density are properly taken into account, they become the two dominant factors in setting the theoretical error bars on merger rates. Other model parameters (e.g., natal kicks, black hole masses, metallicity) have virtually no effect on the local merger rate density, although they affect the masses of the merging black holes. Modelling the merger rate density as a function of redshift as $R(z)=R_0(1+z)^κ$ at $z<2$, and marginalizing over uncertainties, we find: $R_0=7.2^{+21.5}_{-5.5}{\rm Gpc^{-3}yr^{-1}}$ and $κ=1.6^{+0.4}_{-0.6}$ ($90\%$ credibility). The rate parameters for binaries that merge inside the clusters are ${R}_{\rm 0,in}=1.6^{+1.9}_{-1.0}{\rm Gpc^{-3}yr^{-1}}$ and $κ_{\rm in}=2.3^{+1.3}_{-1.0}$; $\sim 20\%$ of these form as the result of a gravitational-wave capture, implying that eccentric mergers from globular clusters contribute $\lesssim 0.4 \rm Gpc^{-3}yr^{-1}$ to the local rate. A comparison to the merger rate reported by LIGO-Virgo shows that a scenario in which most of the detected black hole mergers are formed in globular clusters is consistent with current constraints, and requires initial cluster half-mass densities $\gtrsim 10^4 M_\odot \rm pc^{-3}$. Such models also reproduce the inferred primary black hole mass distribution for masses $13-30 M_\odot$, but under-predict the data outside this range.
