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

TL;DR

This paper models the expected detection rates of intermediate and supermassive black hole mergers for upcoming space-based gravitational wave detectors LISA and LGWA, highlighting their complementary sensitivities and potential for constraining black hole formation.

Contribution

It introduces a semi-analytical model with light seeding to estimate merger rates for LISA and LGWA, including optimistic and pessimistic scenarios based on dynamical friction timescales.

Findings

LGWA and LISA can detect over 15 IMBH mergers per year in optimistic scenarios.

Detection rates for SMBHs are slightly lower than for IMBHs.

Most mergers below redshift 4 are detectable, with some beyond redshift 8.

Abstract

With the upcoming space- and Moon-based gravitational-wave detectors, LISA and LGWA respectively, a new era of GW astronomy will begin with the possibility of detections of the mergers of intermediate-mass black holes (IMBHs) and supermassive black holes (SMBHs). We generate populations of synthetic black hole (BH) binaries with masses ranging from the intermediate ($10^3-10^5 M_\odot$) to the supermassive regime ($>10^5 M_\odot$), formed from the dynamical processes of merging halos and their residing galaxies, assuming that each galaxy is initially seeded with a single black hole at its centre. The aim is to estimate the rate of these BH mergers which could be detected by LISA and LGWA. Using PINOCCHIO cosmological simulation and a semi-analytical model based on GAEA, we construct a population of merging BHs by implementing a "light" seeding scheme and calculating the merging timescales using the Chandrasekhar prescription. We provide upper and lower limits of dynamical friction timescale by varying the mass of the infalling object to create "pessimistic" and "optimistic" merger rates respectively. We find that for our synthetic population of MBHs, both LGWA and LISA are able to detect more than $15$ binary IMBH mergers per year in the optimistic case, while in the pessimistic case less than $\sim5$ detections would be possible considering the entire lifetime of the detectors. For SMBHs, the rates are slightly lower in both cases. Most mergers below $z\approx4$ are detected in the optimistic case, although mergers beyond $z=8$ are also detectable at a lower rate. We find that LGWA is better suited for high-SNR IMBH detections 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.