Exploring intermediate and massive black-hole binaries with the Einstein Telescope

We discuss the capability of a third-generation ground-based detector such as the Einstein Telescope (ET) to enhance our astrophysical knowledge through detections of gravitational waves emitted by binaries including intermediate-mass and massive black holes. The design target for such instruments calls for improved sensitivity at low frequencies, specifically in the ~ 1-10 Hz range. This will allow the detection of gravitational waves generated in binary systems containing black holes of intermediate mass, ~ 100-1000 solar masses. We primarily discuss two different source types – mergers between two intermediate mass black holes (IMBHs) of comparable mass, and intermediate-mass-ratio inspirals (IMRIs) of smaller compact objects with mass ~ 1-10 solar masses into IMBHs. IMBHs may form via two channels: (i) in dark matter halos at high redshift through direct collapse or the collapse of very massive metal-poor Population III stars, or (ii) via runaway stellar collisions in globular clusters. In this paper, we will discuss both formation channels, and both classes of merger in each case. We review existing rate estimates where these exist in the literature, and provide some new calculations for the approximate numbers of events that will be seen by a detector like the Einstein Telescope. These results indicate that the ET may see a few to a few thousand comparable-mass IMBH mergers and as many as several hundred IMRI events per year. These observations will significantly enhance our understanding of galactic black-hole growth, of the existence and properties of IMBHs and of the astrophysics of globular clusters. We finish our review with a discussion of some more speculative sources of gravitational waves for the ET, including hypermassive white dwarfs and eccentric stellar-mass compact-object binaries.

💡 Research Summary

The paper evaluates how the third‑generation ground‑based gravitational‑wave detector known as the Einstein Telescope (ET) will transform our understanding of intermediate‑mass black holes (IMBHs) and massive black‑hole binaries. Current second‑generation detectors (LIGO, Virgo, KAGRA) are limited in low‑frequency sensitivity; they can only observe stellar‑mass mergers whose signals reside above ~10 Hz. ET’s design goal is to improve strain sensitivity by roughly an order of magnitude and, crucially, to push the detector’s noise floor down to the 1–10 Hz band. This low‑frequency window is where the inspiral and merger of binaries containing black holes of 100–1000 M⊙ emit most of their power, allowing the signal to be tracked for hundreds of seconds rather than a few seconds. The longer observation time dramatically raises the signal‑to‑noise ratio (SNR) and enables precise measurement of masses, spins, and sky location even at cosmological distances.

The authors discuss two principal formation pathways for IMBHs. The first is a “high‑redshift direct‑collapse” channel: metal‑poor Population III stars or massive gas clouds in early dark‑matter halos collapse directly into black holes of 10⁴–10⁵ M⊙, which may subsequently fragment or accrete to produce the 10²–10³ M⊙ IMBHs of interest. This scenario predicts a population of IMBHs already present at redshifts z ≈ 10–20, potentially serving as seeds for the supermassive black holes observed in quasars. The second channel involves runaway stellar collisions in dense globular clusters. In the cores of such clusters, massive stars can merge repeatedly, forming a very massive star (≈10³ M⊙) that quickly collapses into an IMBH. Observational hints such as ultra‑luminous X‑ray sources and dynamical studies of cluster cores lend support to this pathway.

Two classes of gravitational‑wave sources are examined. (1) Comparable‑mass IMBH–IMBH mergers, where the mass ratio is close to unity. Their waveforms are relatively simple, dominated by a long inspiral in the ET low‑frequency band, a rapid merger, and a ringdown. Rate estimates from the literature place the volumetric merger rate at 0.1–10 Gpc⁻³ yr⁻¹. Given ET’s horizon distance of several gigaparsecs (a detection volume of ≈30 Gpc³), the authors calculate that ET could observe anywhere from a few dozen to a few thousand such events per year, depending on the true astrophysical rate. (2) Intermediate‑mass‑ratio inspirals (IMRIs), in which a stellar‑mass compact object (1–10 M⊙) spirals into an IMBH. These systems retain significant orbital eccentricity and can exhibit complex waveforms with both high‑frequency (near the small object’s orbital frequency) and low‑frequency (overall inspiral) components. IMRIs are expected to arise from dynamical interactions in globular clusters or from capture processes in galactic nuclei. Published rate estimates range from 0.5 to 5 Gpc⁻³ yr⁻¹. ET’s sensitivity would allow detection of IMRIs out to redshift z ≈ 5, translating into several hundred observable events per year.

The scientific payoff of these detections is multi‑fold. First, a statistically robust sample of IMBH masses and spins will discriminate between the direct‑collapse and cluster‑collision formation channels, because each predicts a distinct mass distribution and spin‑alignment pattern. Second, IMRI observations will probe the dynamical environment of dense stellar systems: the measured eccentricities, inclination angles, and spin precession will reveal the rate of close encounters, the presence of a surrounding gas disc, and the efficiency of mass segregation. Third, high‑redshift IMBH–IMBH mergers will serve as “standard sirens” for cosmology and as tracers of early‑universe structure formation, offering insight into metal enrichment, star‑formation efficiency, and the growth of dark‑matter halos. Finally, the authors discuss more speculative sources that could become accessible with ET’s low‑frequency reach, such as hyper‑massive white dwarfs on the brink of collapse and highly eccentric stellar‑mass binaries that produce repeated bursts of gravitational radiation.

The paper concludes by outlining future work needed to fully exploit ET’s capabilities: improving numerical relativity waveforms for high‑mass‑ratio, high‑spin, and eccentric systems; refining population‑synthesis models for IMBH formation in both cosmological and cluster contexts; and integrating multi‑messenger observations (X‑ray, radio, optical) to cross‑validate rate estimates. In sum, the Einstein Telescope’s low‑frequency sensitivity will open a new observational window on intermediate‑mass black holes, enabling a transformative leap in our understanding of black‑hole demographics, galaxy evolution, and the dynamical processes governing dense stellar systems.