Analytical study of the merging rate of low-mass intermediate-mass black holes in preparation for the future Einstein Telescope

¹ Department of Chemical, Physical, Mathematical and Natural Sciences, University of Sassari, Via Vienna, 07100 Sassari, Italy
² Istituto Nazionale di Fisica Nucleare – Sezione di Cagliari, Monserrato, 09042 Cagliari, Italy
³ Department of Physics and Astronomy, University of Catania, Via S. Sofia, 95123 Catania, Italy
⁴ Istituto Nazionale di Fisica Nucleare – Laboratori Nazionali del Sud, Via S. Sofia, 95125 Catania, Italy
⁵ Dipartimento di Fisica, Università degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
⁶ Istituto Nazionale Fisica Nucleare – Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
⁷ Department of Physics, University of Naples Federico II, 80126 Naples, Italy
⁸ Istituto Nazionale di Fisica Nucleare – Sezione di Napoli, Via Cinthia, 80126 Napoli, Italy
⁹ Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 34136 Trieste, Italy

^⋆ Corresponding authors; nazanin.davari@inaf.it; iara.tosta.melo@dfa.unict.it

Received: 27 June 2024
Accepted: 26 October 2024

Abstract

Context. The detection of gravitational wave (GW) signals by Advanced LIGO, Virgo, and KAGRA interferometers opened a new chapter in our understanding of the formation of compact objects. In particular, the detection of GW190521 is observational confirmation of the existence of intermediate-mass black holes (IMBHs); yet more direct observations are needed to better understand the mechanisms behind their formation.

Aims. In this study, we explore the potential of the next-generation ground-based detector, the Einstein Telescope (ET), to advance our understanding of astrophysics through the detection of GWs emitted by IMBHs. To achieve this, the ET is designed to have improved sensitivity in the low-frequency range of approximately 2–10 Hz, enabling the detection of GWs originating from binary systems containing IMBHs with masses in the range of approximately 10²–10⁵ M_⊙.

Methods. We consider black holes (BHs) in the pair-instability form via the hierarchical merger model in galaxies, and approximate the number of events that could be observed by the ET.

Results. Our findings indicate that ET could detect a binary black hole (BBH) merger rate of around 2 × 10⁵ Gpc⁻³ yr⁻¹ for BH masses ranging from 10 to 200 M_⊙, with around 100 Gpc⁻³ yr⁻¹ of this rate specifically attributed to BHs in the 100–200 M_⊙ mass range, which we classify as low-mass IMBHs in this study. This suggests that ET could detect several dozen events similar to GW190521. The exact locations of these BBH mergers are not specified and we count our BH mergers across the entire universe up to a redshift of z ≈ 2.

Conclusions. Observations made with the ET are expected to significantly enhance our comprehension of galactic BH growth, and the existence and characteristics of low-mass IMBHs.