Mass and rate of hierarchical black hole mergers in young, globular and nuclear star clusters

Michela Mapelli, Filippo Santoliquido, Yann Bouffanais, Manuel Arca Sedda, Maria Celeste Artale, Alessandro Ballone

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


Hierarchical mergers are one of the distinctive signatures of binary black hole (BBH) formation through dynamical evolution. Here, we present a fast semi-analytic approach to simulate hierarchical mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs). Hierarchical mergers are more common in NSCs than they are in both GCs and YSCs because of the different escape velocity. 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 s−1 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, but only in metal-poor environments. The local BBH merger rate in our models ranges from ∼10 to ∼60 Gpc−3 yr−1; hierarchical BBHs in NSCs account for ∼10−2–0.2 Gpc−3 yr−1, with a strong upper limit of ∼10 Gpc−3 yr−1 . When comparing our models with the second gravitational-wave transient catalog, we find that multiple formation channels are favored to reproduce the observed BBH population.

Original languageEnglish
Article number1678
Issue number9
Publication statusPublished - Sept 2021
Externally publishedYes


  • Astrophysical black holes
  • Gravitational waves
  • Intermediate-mass black holes
  • Star clusters

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • General Mathematics
  • Physics and Astronomy (miscellaneous)


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