Black hole merger rates for LISA and LGWA from semi-analytical modelling of light seeds

¹ INAF – Osservatorio Astronomico di Brera Via Brera 20 I-20121 Milano, Italy
² Department of Physics, Informatics & Mathematics, University of Modena & Reggio Emilia Via G. Campi 213/A 41125 Modena, Italy
³ INAF – Istituto di Astrofisica e Planetologia Spaziali (IAPS) Via Fosso del Cavaliere Roma I-133, Italy
⁴ Dipartimento di Fisica e Astronomia ‘Augusto Righi’, Università degli Studi di Bologna Via Gobetti 93/2 I-40129 Bologna, Italy
⁵ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna Via Gobetti 93/3 I-40129 Bologna, Italy
⁶ INFN, Sezione di Milano-Bicocca Piazza della Scienza 3 I-20126 Milano, Italy
⁷ Como Lake centre for AstroPhysics (CLAP), DiSAT, Università dell’Insubria Via Valleggio 11 22100 Como, Italy
⁸ Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Roma Via Frascati 33 00077 Monte Porzio Catone, Italy
⁹ Dipartimento di Fisica, Sezione di Astronomia, Università degli Studi di Trieste Via G.B. Tiepolo 11 I-34131 Trieste, Italy
¹⁰ INAF – Osservatorio Astronomico di Trieste Via G.B. Tiepolo 11 I-34131 Trieste, Italy
¹¹ INFN, Sezione di Trieste Via Valerio 2 34127 Trieste TS, Italy
¹² IFPU, Institute for Fundamental Physics of the Universe Via Beirut 2 34151 Trieste, Italy
¹³ Department of Space, Earth & Environment, Chalmers University of Technology SE-412 96 Gothenburg, Sweden
¹⁴ Department of Astronomy, University of Virginia Charlottesville VA 22904-4235, USA
¹⁵ Dipartimento di Matematica e Fisica, Università Roma Tre Via della Vasca Navale 84 I-00146 Roma, Italy
¹⁶ Gran Sasso Science Institute (GSSI) I-67100 L’Aquila, Italy
¹⁷ INFN, Laboratori Nazionali del Gran Sasso I-67100 Assergi, Italy
¹⁸ Dipartimento di Fisica, Università di Roma Tor Vergata Via della Ricerca Scientifica I-00133 Roma, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 12 August 2025
Accepted: 1 December 2025

Abstract

Context. With the upcoming space- and Moon-based gravitational-wave detectors, LISA and LGWA, a new era of gravitational-wave (GW) astronomy begins, with the possibility of detecting mergers of intermediate-mass black holes (IMBHs) and supermassive black holes (SMBHs).

Aims. We generated populations of synthetic black hole (BH) binaries with masses ranging from the intermediate (10³ − 10⁵ M_⊙) to the supermassive regime (> 10⁵ M_⊙), formed through the dynamical processes of merging haloes and their host galaxies, assuming that each galaxy is initially seeded with a single black hole at its centre. We aimed to estimate the rate of these BH mergers that could be detected by LISA and LGWA.

Methods. Using the PINOCCHIO cosmological simulation and a semi-analytical model based on the GAlaxy Evolution and Assembly (GAEA) framework, we constructed a population of merging BHs by implementing a ‘light’ seeding scheme and calculated the merging timescales using the Chandrasekhar prescription. We calculated upper and lower limits of the dynamical friction timescale by varying the mass of the infalling object to create ‘pessimistic’ and ‘optimistic’ merger rates.

Results. For our synthetic population of BHs, both LGWA and LISA detect more than 15 binary IMBH mergers per year in the optimistic case, while in the pessimistic case fewer than approximately five detections would be expected over the entire lifetime of the detectors. For SMBHs, the rates are slightly lower in both cases. Most mergers below z ≈ 4 are detected in the optimistic case, although mergers beyond z = 8 are also detectable at a lower rate.

Conclusions. We find that LGWA is better suited for detections of IMBH with a high signal-to-noise ratio at higher redshift, while LISA is more sensitive to massive SMBHs. Joint observations will probe the full BH mass spectrum and constrain BH formation and seeding models.