We discuss the effect of clustering for the determination of the merger rate of binary black holes in the LIGO mass range. While for a Poissonian initial distribution, and assuming isolated binaries, the allowed fraction of Primordial Black Holes (PBHs) to dark matter (DM) is a few percent, we show that this bound can be relaxed if PBHs are clustered. More precisely we show that for large clustering the merger rate can drop with increasing fraction of PBHs, introducing a degeneracy in the parameters of the theory consistent with a given present merger rate, and allowing all the DM to be in the form of stellar mass PBHs. This degeneracy can however be broken by looking at the evolution of the merger rate with redshift. For a simple clustering model that we consider, we show that the LIGO projected sensitivity can disentangle, through the observation of a stochastic background of gravitational waves, different clustered distributions having the same present merger rate.

中文翻译：

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LIGO/Virgo 黑洞和暗物质：空间聚类的影响

我们讨论了聚类对确定 LIGO 质量范围内双黑洞合并率的影响。虽然对于泊松初始分布，并假设孤立的双星，原始黑洞 (PBH) 与暗物质 (DM) 的允许比例是几个百分点，但我们表明，如果 PBH 成簇，则可以放宽此界限。更准确地说，我们表明，对于大型星团，合并率会随着 PBH 比例的增加而下降，在与给定的当前合并率一致的理论参数中引入简并性，并允许所有 DM 以恒星质量 PBH 的形式存在. 然而，可以通过观察红移合并率的演变来打破这种退化。对于我们考虑的简单聚类模型，我们表明 LIGO 投影灵敏度可以解开，