Hierarchical mergers in young, globular and nuclear star clusters: black hole masses and merger rates

Hierarchical mergers are one of the distinctive signatures of binary black hole (BBH) formation through dynamical evolution. Here, we present a fast Monte Carlo approach to simulate hierarchical mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs). Hierarchical mergers are orders of magnitude more common in NSCs than they are in both GCs and YSCs, because of the different escape velocity. In our fiducial model, the fraction of hierarchical mergers over all mergers is 0.15, 6×103 and 104 in NSCs, GCs and YSCs, respectively. The mass distribution of hierarchical BBHs strongly depends on the properties of first-generation BBHs, such as their progenitor’s metallicity. In our fiducial model, we form black holes (BHs) with masses up to 103 M in NSCs and up to 102 M in both GCs and YSCs. When escape velocities in excess of 100 km s1 are considered, BHs with mass >103 M are allowed to form in NSCs. Hierarchical mergers lead to the formation of BHs in the pair instability mass gap and intermediate-mass BHs (IMBHs), but only in metal-poor environments. In our fiducial model, at metallicity Z0.0002, the fraction of BBH mergers with primary BH in the pair instability mass gap is 7×103, 3×104 and 5×106 in NSCs, GCs and YSCs, respectively. In metal-poor NSCs, the fraction of BBH mergers with primary mass in the IMBH regime is 5×104. The local BBH merger rate in our models ranges from 10 to 60 Gpc3 yr1; hierarchical BBHs in NSCs account for 1020.2 Gpc3 yr1, with a strong upper limit of 10 Gpc3 yr1