Mass of black holes: The State of the Art
In this small review we present the actual state the knowledge about weighting black holes. Black holes can be found in stellar binary systems in our Galaxy and in other nearby galaxies, in globular clusters, which we can see in our and nearby galaxies, and in centres of all well-developed galaxies. Range of values of their masses is wide and cover about ten orders of magnitude (not taking into account the hypothetic primordial black holes). Establishing the presence of black holes, and in particular the measurement of their mass is one on the key issues for many branches of astronomy, from stellar evolution to cosmology.
💡 Research Summary
The paper provides a concise yet comprehensive review of the current state of knowledge regarding black‑hole mass measurements across the full astrophysical spectrum, from stellar‑mass remnants in binary systems to the supermassive black holes (SMBHs) that dominate galactic nuclei. It begins by outlining the observational evidence for black holes in three principal environments: (1) stellar binaries within the Milky Way and nearby galaxies, where dynamical mass estimates are obtained from radial‑velocity curves of the companion star combined with orbital inclination constraints; (2) globular clusters and dwarf galaxy nuclei, where intermediate‑mass black holes (IMBHs) are sought through stellar velocity dispersions, X‑ray luminosities, and, more recently, gravitational‑wave detections; and (3) the centers of well‑developed galaxies, where SMBHs ranging from ∼10⁶ to 10¹⁰ M☉ are measured using a suite of techniques.
The review details the principal methodologies: (i) dynamical spectroscopy of X‑ray binaries, emphasizing the mass function, the need for accurate inclination angles, and the systematic uncertainties tied to companion‑star evolutionary models; (ii) stellar‑dynamical modeling of nuclear star clusters, which relies on high‑resolution near‑infrared imaging and sophisticated orbit‑superposition codes, yet suffers from degeneracies between anisotropy and mass distribution; (iii) gas‑dynamical modeling of rotating circumnuclear disks (e.g., megamaser disks, CO molecular rings), where assumptions about circular motion and disk thickness introduce notable error bars; (iv) reverberation mapping of active galactic nuclei, which measures time delays between continuum and broad‑line region variability to infer a characteristic radius, then applies a virial factor calibrated against other methods; and (v) direct imaging of event‑horizon scales with the Event Horizon Telescope, which has yielded mass and spin estimates for M87* and Sgr A*.
The authors also discuss the emerging role of gravitational‑wave astronomy. Detections by LIGO/Virgo/KAGRA of binary black‑hole mergers provide direct measurements of component masses and spins, extending the observable mass range into the “mass gap” (∼50–150 M☉) and offering the first robust evidence for black holes in the intermediate‑mass regime (e.g., GW190521). Future space‑based detectors such as LISA will be sensitive to mergers of 10⁴–10⁶ M☉ black holes, potentially filling the observational gap between stellar‑mass and supermassive populations.
A critical part of the review addresses sources of uncertainty and bias. Distance errors (even with Gaia parallaxes), inclination ambiguities, assumptions of Keplerian dynamics, and the choice of virial scaling factors can each introduce uncertainties of 20–50 %. Selection effects—such as the preferential detection of bright X‑ray binaries or luminous AGN—skew the inferred mass distribution, making it difficult to assess the true underlying population.
Finally, the paper looks ahead to upcoming facilities. Extremely Large Telescopes (ELT, TMT, GMT) will resolve stellar motions in galactic nuclei out to tens of megaparsecs, while JWST and the Roman Space Telescope will enable infrared reverberation mapping of dust‑obscured nuclei. The synergy between electromagnetic observations and next‑generation gravitational‑wave detectors promises a multi‑messenger approach that will dramatically improve mass measurements, reduce systematic errors, and allow a unified view of black‑hole demographics. This, in turn, will sharpen constraints on stellar evolution pathways, galaxy formation models, and cosmological scenarios that depend on the growth history of black holes.