Astrophysical Black-Hole Classes

Black-hole mass is measured continuously, whereas names such as stellar-mass, intermediate-mass, and supermassive are operational categories. Their numerical boundaries vary with the question being asked, and a mass interval by itself does not determine a formation channel. This directory therefore treats each class as a population hypothesis: it asks how its members can form, which observables identify them, how selection reshapes the observed sample, and how secure the population statement is.

Reading black-hole populations

The four pages occupy different evidential positions.

Population page	Useful working range	Present observational status	Defining issue
Stellar-Mass Black Holes	From a few to hundreds of solar masses, depending on metallicity, stellar physics, and merger history	Established through binary dynamics, accretion, microlensing candidates, and gravitational waves	Recover an intrinsic remnant population from several differently selected samples
Intermediate-Mass Black Holes	Commonly $10^2$–$10^5M_\odot$	Heterogeneous candidates; existence and abundance as a distinct population remain active questions	Exclude stellar-cluster, accretion, distance, and source-confusion alternatives
Massive and Supermassive Black Holes	Roughly $10^5$–$10^{11}M_\odot$, with a conventional lower boundary	Established in galactic nuclei by dynamics and accretion; demographics are selection dependent	Connect seeds, growth, mergers, and host galaxies without mistaking correlation for causation
Primordial Black Holes	Potentially many orders of magnitude; set by early-Universe formation physics	Hypothetical population; no population-level detection is established	Combine model-dependent constraints consistently and find a discriminant from astrophysical origins

The ranges overlap in both theory and observation. A product of repeated stellar mergers can enter the intermediate range; a stripped galactic nucleus can masquerade as a massive cluster; an early massive seed can grow until its initial mass is almost unrecoverable. The stellar-remnant and early-seed sides of this overlap are reviewed by Mapelli 2021 and Inayoshi, Visbal, and Haiman 2020, respectively. The correct class label therefore follows a stated operational rule, not an assumption about ancestry.

From an observable to a population

Most instruments do not measure black-hole mass, spin, or formation channel directly. They measure radial velocities and periods, photon counts and spectra, angular positions and proper motions, lensing light curves, or detector strain. A forward model maps physical parameters into those data. A likelihood then combines the measurement model with calibration and background uncertainty, while priors encode information such as distance, inclination, host properties, or a population distribution.

This distinction is especially important for the binary mass function. Period $P$, donor radial-velocity amplitude $K_2$, and eccentricity $e$ determine a robust combination,

$$f(M)=\frac{PK_2^3}{2\pi G}(1-e^2)^{3/2},$$

but the black-hole mass additionally requires inclination and donor-mass information; Casares and Jonker 2014, §§2–2.1 reviews that distinction and its main binary-systematics. Likewise, a gravitational-wave chirp mass is tightly constrained in the detector frame, but component masses, source-frame conversion, and population structure involve waveform, distance, cosmology, and selection assumptions. A plotted mass histogram is therefore never the final population inference.

Selection, occupation, and absence

Each discovery channel favors a different subset. X-ray binaries require mass transfer and can miss detached or persistently faint systems. Dynamical searches need adequate angular resolution and tracer density. Flux-limited active-galaxy surveys favor efficiently accreting objects and are affected by obscuration. Gravitational-wave searches weight masses, spins, redshift, and orientation through detector sensitivity. Microlensing favors particular lens masses, distances, and relative motions. These selection functions must be folded into a population model rather than appended as a verbal caveat.

An occupation fraction is also different from an active fraction. A galaxy or cluster can host a dormant black hole that produces no selected accretion signature. Conversely, a bright source can be detected over a large volume and dominate a catalog despite a short duty cycle. Nondetection constrains a population only after the search completeness and the predicted observable distribution are specified.

Controlled comparisons

Useful comparisons hold the inference machinery fixed while changing one physical hypothesis. Compare two stellar-remnant prescriptions through the same survey selection; test an intermediate-mass candidate with and without a central point mass under the same stellar anisotropy model; infer a massive-black-hole mass function with alternative obscuration corrections; fold the same extended primordial mass function through several constraints rather than intersecting monochromatic exclusion curves by eye. Green and Kavanagh 2021, §§6–7 shows how primordial-black-hole conclusions change with the mass function and the astrophysical assumptions behind individual constraints.

The pages are current through 20 August 2026 for mutable evidence. That date does not freeze the categories. A new catalog, calibration, formation calculation, or decisive counterexample should change the relevant posterior and possibly the useful boundary, while the observable-to-inference logic remains the same.

References

• Casares, Jorge, and Peter G. Jonker. “Mass Measurements of Stellar and Intermediate-Mass Black Holes.” Space Science Reviews 183 (2014): 223–252. arXiv.
• Green, Anne M., and Bradley J. Kavanagh. “Primordial Black Holes as a Dark Matter Candidate.” Journal of Physics G 48 (2021): 043001. 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.
• Mapelli, Michela. “Formation Channels of Single and Binary Stellar-Mass Black Holes.” In Handbook of Gravitational Wave Astronomy. Springer, 2021. arXiv.