Intermediate-Mass Binary Black Hole Mergers

• Intermediate-mass binary black hole mergers are coalescences involving components with masses between 10² and 10⁶ solar masses, bridging the gap between stellar-mass and massive black holes.
• They form via diverse channels such as hierarchical mergers in dense star clusters, nuclear star clusters, AGN disks, and globular cluster collisions, each imprinting distinctive gravitational waveform signatures.
• Next-generation detectors will enhance sensitivity and precision, enabling detailed parameter estimation, environmental diagnostics, and empirical differentiation among formation channels.

Searching arXiv for papers on intermediate-mass binary black hole mergers and related channels. Intermediate-mass binary black hole mergers occupy the regime between the stellar-mass binaries now routinely observed by LIGO–Virgo–KAGRA and the massive black hole binaries targeted by LISA. In current usage, the term covers coalescences in which at least one component lies in the intermediate-mass black hole (IMBH) range $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$, but the observational literature also includes heavy systems in the $100\!-\!450\,M_\odot$ total-mass interval and binaries that produce an IMBH remnant, such as GW190521 with source-frame component masses $85^{+21}_{-14}\,M_\odot$ and $66^{+17}_{-18}\,M_\odot$ and a final remnant of $142^{+28}_{-16}\,M_\odot$ (Reali et al., 2024, Collaboration et al., 2012, Anagnostou et al., 2020).

1. Definition, mass scales, and observational scope

The standard mass scale adopted for IMBHs is $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$, while ground-based interferometers are sensitive mainly to the lower end of that interval, from a few tens up to a few thousand solar masses (Reali et al., 2024). Within this broader category, the literature distinguishes at least three overlapping observational classes: comparable-mass IMBH binaries, IMBH–stellar-mass systems in the intermediate mass-ratio inspiral range $10^{-4}\lesssim q\lesssim 0.1$, and heavy binaries whose components occupy or approach the pair-instability gap and whose merger remnant is itself an IMBH (Cheung et al., 1 Jul 2025, Anagnostou et al., 2020).

GW190521 sharpened this taxonomy because its component masses lie well inside the “upper black-hole mass gap,” for which first-generation black holes formed by ordinary single-star evolution at low metallicity are expected to have a maximum mass of order $45\text{–}60\,M_\odot$, with a quoted lower edge near $\sim 50^{+4}_{-8}\,M_\odot$ (Anagnostou et al., 2020). This made hierarchical assembly a central interpretive theme for intermediate-mass mergers. A plausible implication is that the empirical category “intermediate-mass binary black hole merger” now includes both binaries containing an IMBH and binaries whose observed masses require repeated merger growth across the pair-instability gap.

Search strategies have reflected this mixed observational scope. Initial LIGO–Virgo targeted non-spinning mergers with total mass $100\!-\!450\,M_\odot$ and mass ratios from $100\!-\!450\,M_\odot$0 to $100\!-\!450\,M_\odot$1 (Collaboration et al., 2012), while more recent LVK searches have explicitly targeted IMRIs with detector-frame masses $100\!-\!450\,M_\odot$2, $100\!-\!450\,M_\odot$3, and $100\!-\!450\,M_\odot$4 (Cheung et al., 1 Jul 2025). This observational spread is one reason the subject links stellar-dynamical, stellar-evolutionary, and relativistic-binary populations rather than a single sharply bounded mass class.

2. Formation channels across dense stellar and gaseous environments

A major channel is hierarchical growth in dense stellar systems. In direct $100\!-\!450\,M_\odot$5-body globular-cluster simulations with \texttt{NBODY6-gpu}, one black hole in a representative $100\!-\!450\,M_\odot$6 cluster undergoes a chain of seven BH–BH mergers within $100\!-\!450\,M_\odot$7 Gyr and reaches $100\!-\!450\,M_\odot$8, while the broader suite of 58 simulations supports an order-of-magnitude cluster-level probability $100\!-\!450\,M_\odot$9 for IMBH formation through hierarchical mergers over a Hubble time in a median-mass globular cluster if gravitational recoil is neglected (Anagnostou et al., 2020). In this picture, first-generation black holes with $85^{+21}_{-14}\,M_\odot$0 mass-segregate into the core, dynamically assemble binaries, and then build second- and higher-generation remnants through repeated merger cycles.

Nuclear star clusters provide a related but deeper-potential variant. Semi-analytic Monte Carlo calculations for nuclear star clusters find IMBH-binary merger rates in the range $85^{+21}_{-14}\,M_\odot$1, depending on IMBH mass, metallicity, seed mass, and initial spin (Fragione et al., 2022). Direct $85^{+21}_{-14}\,M_\odot$2-body calculations in nucleated dwarf galaxies go further and show that comparable-mass IMBHs merge very efficiently once brought inside the dense nuclear region: binary coalescence times are typically a few hundred million years, hardening rates span $85^{+21}_{-14}\,M_\odot$3, and the stellar encounters that drive the binary originate predominantly from nuclear star clusters when the NSC-to-IMBH-binary mass ratio is greater than $85^{+21}_{-14}\,M_\odot$4 (Khan et al., 2021).

Other channels populate the same mass regime with different initial conditions. Collisions and mergers of massive globular clusters in a Milky-Way-like disc can pair pre-existing IMBHs; for a globular-cluster collision rate of $85^{+21}_{-14}\,M_\odot$5 per Gyr and an IMBH occupation fraction $85^{+21}_{-14}\,M_\odot$6, the expected number of IMBH–IMBH binaries formed per Milky-Way-like galaxy over a Hubble time is $85^{+21}_{-14}\,M_\odot$7 (Sedda et al., 2019). In very massive Population III binaries, IMBH-involving mergers depend sensitively on the common-envelope parameter $85^{+21}_{-14}\,M_\odot$8; the study finds that the Einstein Telescope has the potential to detect $85^{+21}_{-14}\,M_\odot$9 BBHs with IMBHs per year (Hijikawa et al., 2022). In dense young clusters with collisional runaways, a very massive star of mass $66^{+17}_{-18}\,M_\odot$0 collapses into an IMBH seed, and the subsequent IMBH–BH mergers are expected to be broadly detectable, with some sources observable in multiple bands (Purohit et al., 2024). In AGN disks, IMBBHs with total mass $66^{+17}_{-18}\,M_\odot$1 are treated as a distinct environmental population in which gas dynamical effects become directly measurable in the waveform (Roy et al., 13 Mar 2025).

3. Dynamical assembly, recoil, and distinctive waveform signatures

The recurrent dynamical ingredients are mass segregation, three-body binary formation, exchange interactions, binary hardening, and eventual gravitational-wave inspiral. In the globular-cluster hierarchical-merger picture, binaries form dynamically in the core, harden through binary–single and binary–binary encounters, and merge once GW emission dominates at small separation; the heaviest black hole is almost always retained in a binary through exchange bias, which reinforces hierarchical growth (Anagnostou et al., 2020). This same combination of Heggie’s law, exchange preference for the most massive component, and GW-driven inspiral underlies IMBH growth in several cluster channels.

Gravitational recoil is the principal brake on that hierarchy. In the seven-merger “Snowball” chain, post-processing with isotropic spin orientations shows that the second-generation remnant is ejected in $66^{+17}_{-18}\,M_\odot$2 of realizations after the first merger, only $66^{+17}_{-18}\,M_\odot$3 of chains reach length $66^{+17}_{-18}\,M_\odot$4 across the full sample with spin recoil included, $66^{+17}_{-18}\,M_\odot$5 reach $66^{+17}_{-18}\,M_\odot$6, $66^{+17}_{-18}\,M_\odot$7 reach $66^{+17}_{-18}\,M_\odot$8, and no $66^{+17}_{-18}\,M_\odot$9 chains are seen (Anagnostou et al., 2020). This establishes recoil and spin orientation as gatekeepers of intermediate-mass growth in globular clusters. A plausible implication is that environments with high escape speeds are not merely favorable but often necessary for long hierarchical chains.

Several channels predict substantial eccentricity. In nucleated dwarf galaxies, IMBH binaries attain high eccentricities $142^{+28}_{-16}\,M_\odot$0, and residual eccentricity may persist to the LISA regime (Khan et al., 2021). In AGN disks, the distinctive feature is not eccentricity but a measurable environmental phase correction from gas dynamical friction. The waveform phase acquires an additional term

$142^{+28}_{-16}\,M_\odot$1

which behaves as an effective $142^{+28}_{-16}\,M_\odot$2PN correction and is therefore strongest at low frequencies (Roy et al., 13 Mar 2025). For $142^{+28}_{-16}\,M_\odot$3, LISA can detect this imprint; for $142^{+28}_{-16}\,M_\odot$4, the density is measurable with order-unity fractional error, and for $142^{+28}_{-16}\,M_\odot$5 the constraint improves to a few percent (Roy et al., 13 Mar 2025). This provides a direct route to distinguishing AGN-disk IMBBHs from effectively vacuum channels.

4. Searches with initial and current ground-based detectors

The first dedicated LIGO–Virgo search for IMBH mergers used a weakly modeled burst strategy on 2005–2007 data, targeting non-spinning systems with total mass $142^{+28}_{-16}\,M_\odot$6 and component mass ratios between $142^{+28}_{-16}\,M_\odot$7 and $142^{+28}_{-16}\,M_\odot$8 (Collaboration et al., 2012). No plausible signals were observed. The most stringent 90% confidence rate-density upper limit was obtained in the bin centered on $142^{+28}_{-16}\,M_\odot$9, where the limit is $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$0 per $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$1 per Myr for non-spinning sources (Collaboration et al., 2012). That search established the burst-based methodology for merger–ringdown-dominated signals but did not yet reach the theoretically favored astrophysical rate range.

Matched-filter searches improved this picture in O3. An optimized PyCBC search tailored to detector-frame total masses $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$2, stricter signal-noise discriminators, and a $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$3 Hz low-frequency cutoff improves the sensitive volume-time product over previous PyCBC-based searches by a factor of $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$4 to $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$5, depending on total binary mass, at an inverse false alarm rate of $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$6 years (Chandra et al., 2021). Applied to O3a data, it identifies no new significant IMBH binaries but confirms GW190521 with a false alarm rate of $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$7 in $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$8 years (Chandra et al., 2021). In parallel, the hierarchical-merger interpretation of GW190521 remains quantitatively plausible in optimistic recoil conditions: a no-recoil globular-cluster estimate yields a volumetric rate $10^2 M_\odot \lesssim M \lesssim 10^6 M_\odot$9, broadly consistent with the inferred GW190521-like rate $10^{-4}\lesssim q\lesssim 0.1$0, whereas isotropic spin recoil suppresses the predicted rate to $10^{-4}\lesssim q\lesssim 0.1$1 in the same median-mass cluster model (Anagnostou et al., 2020).

The dedicated O3 IMRI search extends the observational program to the highly asymmetric sector $10^{-4}\lesssim q\lesssim 0.1$2, using aligned-spin template banks built from SEOBNRv5HM and including higher modes for the first time (Cheung et al., 1 Jul 2025). The inclusion of higher modes increases the sensitivity volume by up to $10^{-4}\lesssim q\lesssim 0.1$3. No significant candidates with IFAR $10^{-4}\lesssim q\lesssim 0.1$4 year are found, and the resulting upper limits on the local IMRI merger rate lie between $10^{-4}\lesssim q\lesssim 0.1$5 and $10^{-4}\lesssim q\lesssim 0.1$6, depending on the component masses (Cheung et al., 1 Jul 2025). This places present LVK searches in a regime where sensitivity to the IMBH–stellar-mass corner is improving rapidly but still remains above many theoretical rate estimates.

5. Next-generation detectors, multiband observations, and parameter estimation

Forecasts for next-generation ground-based networks show that IMBBHs should become precision sources provided low-frequency sensitivity reaches a few hertz. For the CE40–CE20–ET network with $10^{-4}\lesssim q\lesssim 0.1$7 Hz, binaries with component masses $10^{-4}\lesssim q\lesssim 0.1$8 have mass errors $10^{-4}\lesssim q\lesssim 0.1$9 at $45\text{–}60\,M_\odot$0 and $45\text{–}60\,M_\odot$1 at $45\text{–}60\,M_\odot$2, while the source redshift can be measured with percent-level accuracy or better at $45\text{–}60\,M_\odot$3 (Reali et al., 2024). Lighter binaries with $45\text{–}60\,M_\odot$4 still admit $45\text{–}60\,M_\odot$5 redshift accuracy even at $45\text{–}60\,M_\odot$6, and binaries with $45\text{–}60\,M_\odot$7 can be localized within $45\text{–}60\,M_\odot$8 for $45\text{–}60\,M_\odot$9, with many comparable-mass systems localized within $\sim 50^{+4}_{-8}\,M_\odot$0 (Reali et al., 2024). The same study emphasizes that low-frequency sensitivity is crucial: raising $\sim 50^{+4}_{-8}\,M_\odot$1 from $\sim 50^{+4}_{-8}\,M_\odot$2 Hz to $\sim 50^{+4}_{-8}\,M_\odot$3 Hz drastically reduces detection horizons and parameter-estimation quality for $\sim 50^{+4}_{-8}\,M_\odot$4 binaries (Reali et al., 2024).

Space-based observations add both reach and environmental diagnostics. In AGN disks, a single LISA observation of a source with total mass $\sim 50^{+4}_{-8}\,M_\odot$5, mass ratio $\sim 50^{+4}_{-8}\,M_\odot$6, and luminosity distance $\sim 50^{+4}_{-8}\,M_\odot$7 Gpc is sufficient to associate the merger with an AGN disk of density $\sim 50^{+4}_{-8}\,M_\odot$8, because the density can be estimated with an error bar $\sim 50^{+4}_{-8}\,M_\odot$9; joint LISA+ET analyses improve density constraints by a factor $100\!-\!450\,M_\odot$0, and for a $100\!-\!450\,M_\odot$1, $100\!-\!450\,M_\odot$2 system the minimum fractional density error reaches $100\!-\!450\,M_\odot$3 in the examined mass–density range (Roy et al., 13 Mar 2025). More generally, nuclear-star-cluster models predict that a few merger events per year should be detectable with LISA, DECIGO, ET, and LIGO for IMBHs with masses $100\!-\!450\,M_\odot$4, and a few tens of merger events per year with DECIGO, ET, and LIGO only (Fragione et al., 2022). The collisional-runaway cluster models likewise find that most IMBH–BH merger signals could be detected, with some of them being multi-band sources (Purohit et al., 2024).

These capabilities imply that future catalogs will not merely enlarge the sample; they will separate channels observationally. Mass-gap occupancy, redshift evolution, sky localization, residual eccentricity in the mHz band, higher-mode content in IMRIs, and direct environmental phasing in AGN disks all become measurable diagnostics once IMBBHs are seen across LISA, ET, CE, DECIGO, and improved ground-based networks (Reali et al., 2024, Roy et al., 13 Mar 2025).

6. Theoretical uncertainties, host dependence, and population-level implications

The principal uncertainty across channels is retention. In globular clusters, recoil treatment, natal-kick prescriptions, the absence or inclusion of primordial binaries, and the lack of post-Newtonian terms in the direct $100\!-\!450\,M_\odot$5-body equations all affect whether hierarchical chains survive long enough to cross the pair-instability gap (Anagnostou et al., 2020). In Population III binaries, the maximum primary BH mass and the survival of IMBH-involving mergers to low redshift depend strongly on the common-envelope parameter $100\!-\!450\,M_\odot$6; for $100\!-\!450\,M_\odot$7, all IMBH-involving mergers have merged by $100\!-\!450\,M_\odot$8, while the Einstein Telescope may detect $100\!-\!450\,M_\odot$9 such systems per year across the allowed model set (Hijikawa et al., 2022). In AGN-disk systems, omitting environmental effects in waveform models biases the chirp mass, mass ratio, and arrival time, which directly affects multiband analyses (Roy et al., 13 Mar 2025).

Host structure also controls whether IMBH binaries merge efficiently at all. Nucleated dwarf galaxies produce very efficient pairing and coalescence on timescales of a few hundred million years (Khan et al., 2021), whereas in non-nucleated dwarf galaxies the direct $100\!-\!450\,M_\odot$00-body simulations reported in the lowest-density regime find that none of the IMBHs in the simulation suite merge within a Hubble time (Khan et al., 2024). This suggests that the presence or absence of a dense nuclear star cluster is a first-order discriminator between efficient and stalled IMBH assembly in dwarfs.

Intermediate-mass black holes also feed back on the broader black-hole merger ecosystem. In the MOCCA survey, the number of stellar-mass BBH mergers from a globular cluster follows the expected scaling with initial mass and density unless the present-day IMBH mass is more massive than $100\!-\!450\,M_\odot$01 or exceeds about $100\!-\!450\,M_\odot$02 per cent of the cluster’s initial total mass; in such cases, binary-black-hole formation and subsequent merger events are significantly reduced, and the under-population of BBHs can reach a factor of $100\!-\!450\,M_\odot$03 depending on the clusters’ initial distributions (Hong et al., 2020). A plausible implication is that a mature IMBH population can suppress one observational channel while enhancing another: fewer ordinary cluster BBH mergers, but more IMBH–BH or IMBH-seeded hierarchical events.

Taken together, the current literature presents intermediate-mass binary black hole mergers as a heterogeneous but physically connected population. Dense stellar systems build them through repeated exchange and hardening, gaseous disks imprint environmental phase shifts, dwarf nuclei can merge them efficiently or not at all depending on nuclear structure, and next-generation detectors will measure masses, redshifts, localizations, and in some cases environmental parameters precisely enough to separate these channels empirically (Anagnostou et al., 2020, Reali et al., 2024, Fragione et al., 2022).