The more accurately the metal-dependent star formation rate is modeled, the larger the predicted excess of binary black hole mergers

¹ SISSA, Via Bonomea 365, I–34136 Trieste, Italy
² National Institute for Nuclear Physics – INFN, Sezione di Trieste, I–34127 Trieste, Italy
³ Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Roma, Via Frascati 33, I–00040 Monteporzio Catone, Italy
⁴ Institut für Theoretische Astrophysik, ZAH, Universität Heidelberg, Albert-Ueberle-Straße 2, D–69120 Heidelberg, Germany
⁵ Physics and Astronomy Department Galileo Galilei, University of Padova, Vicolo dell’Osservatorio 3, I–35122 Padova, Italy
⁶ INFN – Padova, Via Marzolo 8, I–35131 Padova, Italy
⁷ Gran Sasso Science Institute, Via F. Crispi 7, I-67100 L’Aquila, Italy
⁸ INFN, Laboratori Nazionali del Gran Sasso, I–67100 Assergi, Italy
⁹ Universidad Andres Bello, Facultad de Ciencias Exactas, Departamento de Fisica y Astronomia, Instituto de Astrofisica, Fernandez Concha 700, Las Condes, Santiago RM, Chile
¹⁰ Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain
¹¹ Institute for Fundamental Physics of the Universe – IFPU, Via Beirut 2, I–34014 Trieste, Italy
¹² Istituto di Radioastronomia – INAF/IRA, Via Piero Gobetti 101, I–40129 Bologna, Italy

^⋆ Corresponding authors: cecilia.sgalletta@sissa.it, mapelli@uni-heidelberg.de

Received: 25 October 2024
Accepted: 4 April 2025

Abstract

As the number of gravitational wave detections grows, the merger rate of binary black holes (BBHs) can help us to constrain their formation, the properties of their progenitors, and their birth environment. Here, we aim to address the impact of the metal-dependent star formation rate (SFR) on the BBH merger rate. To this end, we have developed a fully data-driven approach to model the metal-dependent SFR and coupled it to BBH evolution. We have adopted the most up-to-date scaling relations, based on recent observational results, and we have studied how the BBH merger rate density varies over a wide grid of galaxy and binary evolution parameters. Our results show that including a realistic metal-dependent SFR evolution yields a value of the merger rate density that is too high compared to the one inferred from gravitational wave data. Moreover, variations in the SFR in low-mass galaxies (M_* ≲ 10⁸ M_⊙) do not contribute more than a factor ∼2 to the overall merger rate density at redshift z = 0. These results suggest that the discrepancy between the BBH merger rate density inferred from data and theoretical models is not caused by approximations in the treatment of the metal-dependent SFR, but rather stems from stellar evolution models and/or BBH formation channels.