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Most of the binary black hole (BBH) mergers detected by LIGO and Virgo couldbe explained by first-generation mergers formed from the collapse of stars,while others might come from second (or higher) generation mergers, namelyhierarchical mergers, with at least one of the black holes (BHs) being theremnant of a previous merger. A primary condition for the occurrence ofhierarchical mergers is that the remnant BHs can be retained by the host starcluster. We present a simple formula to estimate the hierarchical merger ratein star clusters. We find this latter to be proportional to the retentionprobability. Further, we show that $\sim 2\%$ of BBH mergers in nuclear starclusters (NSCs) may instead be of hierarchical mergers, while the percentage inglobular clusters (GCs) is only a few tenths of a percent. However, the ratesof hierarchical merger in GCs and NSCs are about the same, namely of $\sim{\mathcal O(10^{-2})}~{\rm Gpc^{-3}~yr^{-1}}$, because the total BBH mergerrate in GCs is larger than that in NSCs. This suggests that if agravitational-wave event detected by LIGO-Virgo is identified as a hierarchicalmerger, then it is equally likely that this merger originated from a GC or anNSC.

Constraining hierarchical mergers of binary black holes detectable with LIGO-Virgo