The Laser Interferometer Space Antenna (LISA) will discover and study intermediate‑mass black holes (≈10²–10⁵ M☉) embedded in dwarf galaxies or dense star clusters. It does so by detecting gravitational waves from a small compact object—such as a stellar‑mass black hole, neutron star or white dwarf—spiralling into the larger black hole. The inspiral signal can be recognised even when the system is far from its final plunge.

A comprehensive mapping of the LISA‑detectable parameter space shows that the survey depth depends strongly on the primary mass. For a black hole of 10⁴ M☉, LISA can detect such binaries out to a redshift of about 5, while for a 10³ M☉ primary the reach is roughly z≈0.1. If the companion is a white dwarf, its tidal disruption may occur before the plunge, but LISA’s horizon still matches or exceeds that of many electromagnetic surveys.

The authors quantify the observability using the sensitivity time‑volume, ℭ(θ). For more massive primaries (10⁵ M☉) ℭ(θ) can reach 10³ Gpc³ yr, whereas for lighter primaries (10³ M☉) it drops to as little as 10⁻⁴ Gpc³ yr. The analysis also introduces the no‑plunge bonus, ζ(θ), which captures the contribution of systems that survive the full mission lifetime without forming a final merger. For most of the parameter space examined, ζ(θ) is close to one, but it rises dramatically for light binaries, showing that the majority of detectable events will be long‑lived, pre‑plunge sources.

Because the intrinsic merger rate of compact‑object‑to‑intermediate‑mass‑black‑hole systems is highly uncertain—spanning from 10⁻³ to 10² Gpc⁻³ yr⁻¹—predicted detection counts are also broad, ranging from a handful to roughly a thousand events over a one‑year mission. This range underscores the need for targeted observations to constrain the population.

Finally, the study excludes the final plunge, merger and ringdown phases from its waveform modelling, which limits sensitivity estimates to only the inspiral part of the signal.