Intermediate-Mass Black Holes

Intermediate-mass black holes (IMBHs) are candidate black holes between ordinary stellar remnants and the massive objects that dominate galactic nuclei. The class is scientifically useful because it probes both the upper reach of stellar dynamics and possible seed pathways, but it is not defined by a sharp physical threshold. Evidence is heterogeneous: some gravitational-wave components enter the lower part of the range, while many electromagnetic or dynamical candidates remain degenerate with stellar populations, accretion geometry, or source confusion.

Intermediate-mass candidate population

Property	Working statement
Object class	Astrophysical class
Physical status	Candidate population with object-by-object evidence of unequal strength
Operational range	Commonly $10^2$–$10^5M_\odot$; boundaries vary by method and context
Proposed channels	Runaway stellar collisions, repeated compact-remnant mergers, direct gas collapse, accretion growth, and stripped galactic nuclei
Search environments	Dense clusters, dwarf-galaxy nuclei, off-nuclear accretors, tidal disruptions, and gravitational-wave sources
Central inference problem	Distinguish a point mass from cluster dynamics or an accreting source from beaming and super-Eddington alternatives
Evidence cutoff	20 August 2026

An individual black hole with a posterior centered in the operational interval would establish that object, not automatically a distinct population or a single origin. Conversely, failure to detect an accreting source does not imply that a cluster lacks a dormant central object.

Formation hypotheses and useful limits

In a young, compact cluster, mass segregation can concentrate massive stars before they leave the main sequence. If core collapse outpaces stellar evolution, gravitational focusing and resonant encounters can drive repeated collisions. Winds, hydrodynamic mass loss, rejuvenation, rotation, pair instability, and binary heating then determine whether the merger product leaves an intermediate-mass remnant. The detailed clock and its uncertainties are developed in Runaway Stellar Collisions and Dense Clusters.

Direct cluster calculations demonstrate the channel in sufficiently compact initial conditions, while also exposing its dependence on stellar evolution and retained merger mass (Portegies Zwart et al. 2004, complete article, printed pp. 724–726).

After stellar remnants form, repeated black-hole mergers offer another route, but gravitational recoil competes with retention. Low escape speeds make hierarchical growth difficult; nuclear clusters and sufficiently massive globular clusters are more favorable. Direct gas collapse and rapid accretion connect the upper IMBH range to massive-seed scenarios reviewed by Inayoshi, Visbal, and Haiman 2020, §§ 3.1 and 5.1–5.2. A stripped nucleus can leave a compact stellar system around a once-nuclear black hole, blurring an origin-based boundary.

Two limits prevent category errors. In the single-remnant limit, standard stellar-collapse calculations set the reachable mass and any pair-instability depletion. In the galactic-nucleus limit, a black hole can be called “massive” even below $10^5M_\odot$ because occupation and host context, rather than mass alone, define the question. An IMBH classification should report both mass evidence and environment.

What the observables constrain

Resolved stellar or gas dynamics test whether velocities rise toward a central point. The characteristic scale is

$$M(<r)\sim \frac{r\,v^2}{G},$$

but converting line-of-sight velocities and projected radii into a central mass requires a distribution function, anisotropy, tracer density, binaries, stellar remnants, mass segregation, distance, and instrumental point-spread function. Casares and Jonker 2014, §§ 5–5.2 reviews how these dynamical mass measurements differ from accretion-based candidate estimates. A dark remnant cluster can mimic a point mass over a limited radial range. Robust evidence demands that the black hole improve a forward fit and that extended-mass alternatives be tested under comparable flexibility.

Accretion candidates supply luminosities, spectra, timing, nebular energetics, or radio/X-ray correlations. Luminosity gives a mass only through assumptions about distance, beaming, bolometric correction, radiative efficiency, and Eddington ratio. Super-Eddington stellar binaries can resemble sub-Eddington IMBHs. Quasi-periodic frequencies do not scale uniquely with inverse mass unless a specific mode and accretion state are established. The resulting evidence hierarchy—from secure dynamical masses to model-dependent accretion candidates—is reviewed by Greene, Strader, and Ho 2020, §§ 3–6.

Gravitational waves constrain redshifted masses through waveform phase and merger–ringdown structure. The LIGO Scientific and Virgo Collaborations 2020, Table I, for example, inferred an intermediate-mass merger remnant under its stated waveform models. Source-frame mass additionally uses luminosity distance and cosmology; mass ratio, spin, higher modes, and waveform systematics can be correlated. A component in the intermediate range is strong evidence for that event under the stated waveform model, but the formation channel still requires population and environment information. See Masses, Mass Ratios, and Pair-Instability Structure for that inference chain.

Population and selection effects

Cluster searches preferentially target nearby, dense, luminous systems with adequate angular resolution. Yet the sphere of influence shrinks with mass and distance, and the most crowded centers are often the hardest to model. Accretion searches select active objects and are sensitive to duty cycle, obscuration, host star formation, and multiwavelength follow-up. Gravitational-wave selection rises rapidly with mass over part of the detector band and then changes as the signal shortens.

Occupation fraction must therefore be separated from detection fraction. A hierarchical analysis should include nondetections, sensitivity variations, candidate contamination, and the host distribution. Combining candidate mass posteriors without their selection functions exaggerates abundance and can manufacture a class boundary.

Present limits

The conservative statement is that compact objects can reach at least the lower intermediate range and that several systems remain credible candidates at higher masses. It is not yet established that IMBHs form a smoothly occupied, abundant population across $10^2$–$10^5M_\odot$, nor that any one proposed channel dominates. A decisive case would resolve Keplerian motion well inside the influence radius, or obtain an equivalently discriminating waveform, while excluding extended mass, source confusion, and calibration alternatives.

References

• Casares, Jorge, and Peter G. Jonker. “Mass Measurements of Stellar and Intermediate-Mass Black Holes.” Space Science Reviews 183 (2014): 223–252. arXiv.
• Greene, Jenny E., Jay Strader, and Luis C. Ho. “Intermediate-Mass Black Holes.” Annual Review of Astronomy and Astrophysics 58 (2020): 257–312. DOI.
• Inayoshi, Kohei, Eli Visbal, and Zoltán Haiman. “The Assembly of the First Massive Black Holes.” Annual Review of Astronomy and Astrophysics 58 (2020): 27–97. DOI.
• LIGO Scientific Collaboration and Virgo Collaboration. “GW190521: A Binary Black Hole Merger with a Total Mass of $150M_\odot$.” Physical Review Letters 125 (2020): 101102. DOI.
• Portegies Zwart, Simon F., Holger Baumgardt, Piet Hut, Jun Makino, and Stephen L. W. McMillan. “The Formation of Massive Black Holes through Collision Runaway in Dense Young Star Clusters.” Nature 428 (2004): 724–726. DOI.