Black holes span an almost absurd range of masses, from a few times the mass of our Sun to tens of billions of times heavier. The lightest known black holes weigh roughly three to five solar masses, while the heaviest confirmed supermassive black holes tip the scales above 10 billion solar masses. Between those extremes lies an uneven landscape with populated zones, forbidden gaps, and an elusive middle category that astronomers have spent decades trying to pin down.
Stellar-Mass Black Holes
The most common black holes form when massive stars exhaust their nuclear fuel and collapse. These stellar-mass black holes range from roughly 3 solar masses up to perhaps 50 or 60 solar masses, depending on the original star’s composition and how much material it shed during its lifetime. Below about 3 solar masses, a collapsing core is more likely to become a neutron star, held up by the pressure of densely packed neutrons. Above that threshold, gravity wins, and the remnant compresses into a black hole.
At the upper end, stellar-mass black holes bump against a limit set by the physics of the stars that make them. Very massive stellar cores become so hot late in their lives that photons in the core start converting into pairs of matter and antimatter particles. This robs the core of the radiation pressure holding it up, triggering violent pulsations that eject large amounts of material. The result is that the heaviest black holes born directly from individual stellar collapse are thought to top out somewhere between roughly 40 and 65 solar masses, depending on nuclear reaction rates, rotation, and metallicity.
The Pair-Instability Gap
Above that upper limit of stellar-mass black holes sits a predicted “mass gap” where black holes should not form from ordinary stellar evolution. Stars with cores heavy enough to exceed this boundary do not collapse quietly. Instead, they are completely destroyed in pair-instability supernovae, leaving nothing behind. Previous theoretical work placed the lower boundary of this gap around 50 solar masses and the upper boundary near 130 solar masses, but those numbers have been shifting.
One study found that the lower edge of the gap sits near 45 solar masses and is remarkably stable regardless of changes to metallicity, internal mixing, or wind-driven mass loss. However, varying a single nuclear reaction rate within its measured uncertainty could push that edge anywhere between 40 and 56 solar masses.1The Astrophysical Journal. Mind the Gap: The Location of the Lower Edge of the Pair-instability Supernova Black Hole Mass Gap Other work accounting for additional factors like rapid rotation and accretion after black hole birth suggests the lower boundary could rise to around 64 to 70 solar masses, while the upper boundary might reach as high as 161 solar masses.2arXiv. The Pair-Instability Mass Gap for Black Holes
This gap matters because gravitational wave observatories have detected merging black holes with individual masses that seem to sit inside the predicted forbidden zone. Those detections have pushed theorists to reexamine every assumption going into the models. The boundaries are less certain than textbooks sometimes imply, and the gap itself may be narrower or wider than originally thought.
Intermediate-Mass Black Holes
Between the stellar-mass range and the millions-of-solar-masses regime of supermassive black holes sits a category that has long frustrated astronomers. Intermediate-mass black holes, roughly 100 to 100,000 solar masses, are theoretically expected but extremely hard to find. They do not form from ordinary single-star collapse, and they are not massive enough to dominate the centers of large galaxies in obvious ways.
The best candidates have turned up in dense stellar environments. In 47 Tucanae, one of the Milky Way’s densest globular clusters, pulsar dynamics provided evidence for a central black hole with a mass of about 2,300 solar masses. The black hole is not actively feeding on surrounding gas, which helps explain why it went undetected for so long in electromagnetic surveys.3PubMed. An intermediate-mass black hole in the centre of the globular cluster 47 Tucanae More recently, fast-moving stars in ω Centauri, the Milky Way’s most massive globular cluster, provided strong evidence for another intermediate-mass black hole. This object and similar candidates in ultracompact galaxies appear to follow the same scaling relationships that link supermassive black holes to their host environments, suggesting that intermediate-mass black holes are not fundamentally different beasts but rather the low-mass end of a continuous spectrum.4The Astrophysical Journal Letters. Black Hole Scaling Relations in the Dwarf-galaxy Regime with Gaia-Sausage/Enceladus and ωCentauri
Why so few confirmed cases? Intermediate-mass black holes are too small to be easily detected by their gravitational influence on surrounding stars unless they sit in very dense clusters. And if they are not actively consuming gas, they produce little or no detectable light. Gravitational wave detectors may eventually catch mergers involving these objects, which would provide clean mass measurements. For now, the intermediate-mass category remains the least populated part of the black hole census.
Supermassive Black Holes
At the centers of most large galaxies sit black holes that dwarf their stellar-mass cousins by factors of millions or billions. The supermassive black hole at the center of the Milky Way, Sagittarius A*, has a mass of about 4 million solar masses. Astronomers pinned down that number by tracking the orbits of individual stars whipping around the galactic center at thousands of kilometers per second.5Monthly Notices of the Royal Astronomical Society. Stellar orbits near Sagittarius A* That work eventually earned a Nobel Prize and remains one of the most direct black hole mass measurements ever made.
Sagittarius A* is modest by supermassive standards. The black hole at the center of the giant elliptical galaxy M87, famously imaged by the Event Horizon Telescope in 2019, weighs roughly 6.5 billion solar masses. The EHT collaboration determined this by measuring the angular size of the black hole’s “shadow,” the dark silhouette cast against the glowing ring of surrounding material, and combining it with the known distance to M87.6The Astrophysical Journal Letters. First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole A handful of other confirmed supermassive black holes are thought to exceed 10 billion solar masses, sitting in the largest elliptical galaxies in the universe.
That spread alone is striking. Within the supermassive category, masses range across more than three orders of magnitude, from a million to tens of billions of solar masses. Understanding why some galaxies harbor relatively restrained central black holes while others grow to such extreme masses has become one of the central questions in modern astrophysics.
How Astronomers Weigh Something They Cannot See
Black holes emit no light of their own, so every mass measurement is indirect. The approach depends on the type of black hole and its environment.
- Stellar orbits: For nearby supermassive black holes like Sagittarius A*, astronomers track the paths of individual stars over years or decades. The speed and shape of those orbits reveal the mass of the invisible object they are orbiting. This is conceptually the same method used to weigh the Sun from the Earth’s orbit, just applied to far more extreme conditions.
- Gas dynamics: In many galaxies, disks of gas orbit the central black hole. Measuring how fast that gas rotates at different distances, using Doppler shifts in spectral lines, lets astronomers calculate the enclosed mass.
- Reverberation mapping: For actively feeding black holes in distant galaxies, astronomers monitor fluctuations in the light from the hot accretion disk. Those fluctuations echo off clouds of gas orbiting farther out, and the time delay between the original flash and the echo reveals the size of the orbiting region. Combined with the speed of the orbiting gas, that gives the black hole’s mass.7The Astrophysical Journal. Black Hole–Galaxy Scaling Relationships for Active Galactic Nuclei with Reverberation Masses
- Shadow imaging: For the two black holes imaged by the Event Horizon Telescope, the angular diameter of the shadow can be converted directly into a mass if the distance is known, as was done with M87.6The Astrophysical Journal Letters. First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
- Gravitational waves: When two black holes spiral together and merge, the gravitational wave signal encodes the masses of both objects with high precision. This has been transformative for measuring stellar-mass black holes, many of which sit in regions of space where no electromagnetic observation would have found them.
Each method has its own biases and blind spots. Stellar orbit tracking only works for nearby objects where individual stars can be resolved. Reverberation mapping requires an actively accreting black hole. Gravitational waves only catch merging systems. Combining multiple methods has been essential for building a reliable census of black hole masses across the full range.
How Black Holes Grow to Billions of Solar Masses
The existence of billion-solar-mass black holes in the early universe poses a genuine puzzle. Quasars powered by such enormous black holes have been found when the universe was less than a billion years old. Growing a black hole that massive in so little time strains conventional models of accretion, which assume a natural speed limit.
That speed limit comes from the balance between gravity pulling material inward and the radiation produced by that infalling material pushing outward. There is a rate, called the Eddington limit, at which those two forces balance. Above that rate, radiation pressure should theoretically blow away the incoming fuel and choke off further growth. If a black hole could only accrete at this maximum rate, even starting from a heavy stellar-mass “seed,” it would struggle to reach billions of solar masses in under a billion years.
Simulations have shown, however, that periods of accretion exceeding the Eddington limit can be sustained for tens of millions of years at a stretch in the right conditions. These super-Eddington episodes allow a black hole to grow by up to three orders of magnitude, depending on how much energy it dumps back into its surroundings through jets and radiation.8Astronomy & Astrophysics. Sustained super-Eddington accretion in high-redshift quasars In other simulations, black holes growing in typical early-universe environments can sustain super-Eddington accretion during a brief but intense early phase. Once the black hole reaches a mass of roughly 10,000 to 100,000 solar masses, its own feedback becomes strong enough to self-regulate, slowing accretion to a more sedate pace.9The Astrophysical Journal Letters. How Fast Could Supermassive Black Holes Grow at the Epoch of Reionization?
A complementary picture emerges from models that follow a black hole from early cosmic times all the way through to more recent epochs. In one such simulation, a black hole growing at the Eddington limit from a redshift of 9 (about 500 million years after the Big Bang) eventually becomes massive enough by a redshift of around 5.5 that its feedback shuts down both its own growth and star formation in its host galaxy.10Monthly Notices of the Royal Astronomical Society. The effects of super-Eddington accretion and feedback on the growth of early supermassive black holes and galaxies The interplay between runaway early growth and eventual self-regulation helps explain why supermassive black holes end up in a surprisingly tight relationship with their host galaxies.
Why Black Hole Mass Tracks Galaxy Properties
One of the more surprising discoveries of the last few decades is that a supermassive black hole’s mass is tightly correlated with properties of the galaxy around it, even though the black hole is vanishingly tiny compared to the galaxy as a whole. The black hole at a typical galaxy’s center accounts for only about a thousandth of the galaxy’s total stellar mass, yet the two quantities track each other with remarkable consistency.
The best-known version of this relationship links black hole mass to the velocity dispersion of stars in the galaxy’s central bulge. Faster-moving stars in the bulge correspond to a heavier black hole, and the relationship follows a steep power law. One widely cited calibration, based on 49 measured black hole masses, found that the black hole mass scales with velocity dispersion raised to roughly the fourth power, with an intrinsic scatter of about 0.44 in the logarithm of mass for all galaxy types and a tighter scatter of about 0.31 for elliptical galaxies alone.11arXiv. The M-sigma and M-L Relations in Galactic Bulges and Determinations of their Intrinsic Scatter A separate formulation puts the relationship as roughly 300 million solar masses times the fourth power of the velocity dispersion normalized to 200 kilometers per second.12Monthly Notices of the Royal Astronomical Society. Ultramassive black holes and the three M–sigma relations
This correlation is not just a curiosity. It implies that the growth of a supermassive black hole and the formation of stars in the surrounding galaxy are connected by feedback loops, even though the black hole’s gravitational reach extends only a tiny fraction of the galaxy’s size. Energy and momentum from the black hole’s accretion, in the form of radiation, winds, and jets, push outward and regulate how much gas is available for star formation across the entire galaxy. The galaxy, in turn, controls the supply of gas funneled inward toward the black hole. The result is a kind of self-regulating partnership that keeps the two masses in proportion.
This scaling relation is also a practical tool. For galaxies too distant for direct black hole mass measurement, astronomers can estimate the central black hole’s mass simply by measuring the velocity dispersion of the bulge. It is less precise than direct methods, but it works across enormous cosmic distances.
Primordial Black Holes and the Smallest Possible Masses
Every black hole discussed so far forms through astrophysical processes: collapsing stars, merging objects, or gas accretion in galaxy centers. But there is a theoretical category that does not require any star at all. Primordial black holes could have formed in the extreme density fluctuations of the very early universe, within the first fraction of a second after the Big Bang. Unlike their astrophysical cousins, these objects have no minimum mass set by stellar physics. They could, in principle, span a range from less than a gram to thousands of solar masses.
At the low-mass end, primordial black holes lighter than about 1015 grams (roughly the mass of a small asteroid) would have already evaporated through Hawking radiation over the age of the universe. Heavier ones could still be around today, and some researchers have proposed that they might account for some or all of the dark matter that pervades galaxies and galaxy clusters. Current observational constraints span the full mass range, and no confirmed detection has been made yet, but the search continues with gravitational wave observatories and other techniques.13La Rivista del Nuovo Cimento. Primordial black holes: constraints, potential evidence and prospects
The idea is appealing because it would solve two problems at once: explaining what dark matter is and providing the heavy “seed” black holes that some models need to explain how supermassive black holes got so big so quickly. If primordial black holes in the range of thousands of solar masses existed in the early universe, they could have served as starting points for the rapid accretion that eventually built the billion-solar-mass monsters seen in early quasars. The evidence for this scenario remains circumstantial, but it is an active area of research that connects particle physics, cosmology, and black hole astrophysics.
Mass, Size, and Density
An unintuitive feature of black holes is that more massive ones are actually less dense on average. The event horizon, the boundary beyond which nothing escapes, grows in direct proportion to the mass. Double the mass, double the radius. But volume grows as the cube of the radius, so the average density inside the event horizon drops steeply as mass increases.
A stellar-mass black hole of about 10 solar masses has an event horizon only about 30 kilometers across, giving it an average density far exceeding that of an atomic nucleus. A supermassive black hole of a billion solar masses has an event horizon roughly the size of the solar system, and its average internal density is actually less than that of water. You could, in a purely mathematical sense, fit a billion-solar-mass black hole inside a sphere with a lower density than a swimming pool. The mass is not packed into some impossibly small point in practical terms; at the event horizon boundary, conditions can be surprisingly gentle for the largest black holes. An astronaut falling through the event horizon of a sufficiently massive black hole would not feel any particular tidal forces at the moment of crossing.
This inverse relationship between mass and density explains why it is easier for nature to make very heavy black holes than you might expect. The larger the black hole, the lower the density threshold needed to form one. In the early universe, large regions of slightly-above-average density could have collapsed directly into massive black holes without needing the extreme compression that a stellar core collapse produces.
Gravitational Waves and the New Mass Census
Before gravitational wave detectors came online in 2015, the masses of stellar-mass black holes were estimated almost entirely from X-ray binary systems, where a black hole feeds on a companion star. That sample was small and biased toward black holes in close binary orbits. Gravitational wave detections have radically expanded the catalog. Dozens of merging black hole pairs have now been observed, with individual masses ranging from about 5 solar masses to over 80 solar masses.
Several of these detections produced post-merger black holes with masses squarely inside the predicted pair-instability gap, forcing a rethinking of where the gap boundaries actually lie. The most famous example, GW190521, involved two merging black holes with individual masses around 85 and 66 solar masses, producing a final black hole of roughly 142 solar masses. That final object also happens to be the first strong gravitational wave evidence for an intermediate-mass black hole, bridging the gap between the stellar and supermassive categories.
The growing catalog of gravitational wave events is beginning to reveal the shape of the black hole mass distribution: where masses cluster, where gaps exist, and how the distribution changes with cosmic time. Each new observing run adds more data points, and the picture that emerges will eventually constrain the physics of massive stellar evolution, binary interactions, and black hole formation channels in ways that electromagnetic observations alone could never achieve.