Hierarchical binary black hole mergers in globular clusters: Mass function and evolution with redshift^⋆

¹ Institut für Theoretische Astrophysik, ZAH, Universität Heidelberg, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany
e-mail: stefano.torniamenti@unipd.it, mapelli@uni-heidelberg.de
² Physics and Astronomy Department Galileo Galilei, University of Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
³ INFN – Padova, Via Marzolo 8, 35131 Padova, Italy
⁴ INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁵ Gran Sasso Science Institute (GSSI), 67100 L’Aquila, Italy
⁶ INFN, Laboratori Nazionali del Gran Sasso, 67100 Assergi, Italy
⁷ INAF – Osservatorio Astronomico d’Abruzzo, Teramo, Italy
⁸ Instituto de Astrofisica, Facultad de Ciencias Exactas, Universidad Andres Bello, Fernandez Concha 700, Santiago, Chile

Received: 18 January 2024
Accepted: 22 April 2024

Abstract

Hierarchical black hole (BH) mergers are one of the most straightforward mechanisms producing BHs inside and above the pair-instability mass gap. We investigated the impact of globular cluster (GC) evolution on hierarchical mergers, accounting for the uncertainties related to BH mass pairing functions on the predicted primary BH mass, mass ratio, and spin distribution. We find that the evolution of the host GC quenches the hierarchical BH assembly at the third generation, mainly due to cluster expansion powered by a central BH subsystem. Hierarchical mergers match the primary BH mass distribution from GW events for m₁ > 50 M_⊙ regardless of the assumed BH pairing function. At lower masses, however, different pairing functions lead to dramatically different predictions on the primary BH mass merger-rate density. We find that the primary BH mass distribution evolves with redshift, with a larger contribution from mergers with m₁ ≥ 30 M_⊙ for z ≥ 2. Finally, we calculate the mixing fraction of binary black holes (BBHs) from GCs and isolated binary systems. Our predictions are very sensitive to the spins, which favor a large fraction (> 0.6) of BBHs born in GCs in order to reproduce misaligned spin observations.