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

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 (10 3 − 10 5 M ⊙ ) to the supermassive regime (> 10 5 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.