Black holes that should not exist

Every so often, a long-predicted feature in astronomy finally comes into view.

The story of black holes is often told through the idea of a stellar graveyard. Massive stars live fast, die violently, and leave behind compact remnants: neutron stars, black holes, or sometimes nothing at all. If you line up those remnants by mass, theory says the graveyard should not be evenly filled. There should be missing rows, places where stars are so unstable at the end of their lives that they tear themselves apart instead of leaving a black hole behind.

For years, gravitational-wave astronomers have been trying to map that graveyard. Each new LIGO, Virgo, and KAGRA catalogue has added more black holes to the picture, but the predicted empty region has remained frustratingly hard to pin down.

Now, a new set of results has researchers excited. A team led by Hui Tong, a PhD student at Monash University and the ARC Centre of Excellence for Gravitational Wave Discovery, OzGrav, has found the strongest evidence to date that nature really does avoid forming black holes in a particular mass range. The study, published in the journal Nature, uses the latest gravitational-wave catalogue, GWTC-4, to identify a clear gap in the black hole mass distribution between roughly 45 and 116 times the mass of the Sun (solar masses).

“We find the lower edge of the gap at around 44 solar masses,” says Tong. “Statistically, the data strongly prefer the existence of a gap over a smooth, continuous mass distribution.”

Stars are held together by a delicate balance. Gravity pulls everything inward, while pressure from light and hot gas pushes outward. This is known as hydrostatic equilibrium. For most of a star’s life, those two forces keep each other in check.

But in very massive stars, things can go wrong in a dramatic way. These stars are predominantly held up by the pressure from light (radiation pressure). When the core becomes hot enough, this creates the right conditions for some photons to become energetic enough to spontaneously convert into particles: pairs of electrons and positrons. As a result of this pair production avalanche, fewer photons means less pressure, so gravity gains the upper hand and the core contracts.

The contraction heats the core even more. This ignites oxygen, and sometimes silicon, explosively. For the right range of core masses, this results in a thermonuclear runaway reaction and is powerful enough to blow the entire star apart. No neutron star. No black hole. Nothing.

For black hole astronomy, the consequence is striking. It would mean that the ordinary stellar-mass progenitor stars in a particular mass range of 40 - 130 solar masses should struggle to make black holes. Stars below the pair-instability regime can still leave black holes. Stars far above it may collapse more directly. But stars in the middle can destroy themselves before they ever get the chance.

That missing region is what astronomers call the pair-instability gap.

So why has this gap been so difficult to find so far? The answer, it turned out, was a matter of where people had been looking. “The idea sounds almost obvious in hindsight,” says Tong. “Every merger has two black holes. Most studies focused on the heavier one, so we asked what happens if you look at the lighter companion instead.”

And there it was: a much cleaner, statistically robust gap in the range of secondary masses of black holes.

The reason it appears more clearly in the secondary mass distribution is due to hierarchical mergers. Most black holes are first-generation black holes, meaning they formed from the collapse of a massive star. These black holes should obey the rules set by pair instability. But in dense star cluster environments, such as globular clusters or the discs around active galactic nuclei (AGN), black holes can merge, remain in the same environment, and then merge again. The product of a previous merger is a second-generation black hole. These black holes can fall directly within the pair-instability gap. Such second-generation black holes are typically more massive than first-generation black holes and are therefore more likely to populate the pair-instability mass gap in the primary mass distribution.

The result also reaches far beyond black holes. It touches one of the long-standing uncertainties in nuclear astrophysics: how quickly carbon turns into oxygen inside stars.

After a massive star has burned hydrogen into helium, it begins fusing helium into heavier elements. One of the most important reactions in this phase is ¹²C(α, γ)¹⁶O, where a carbon nucleus captures a helium nucleus, also called an alpha particle, and becomes oxygen. This reaction helps set the final balance of carbon and oxygen in the core.

That balance matters because it changes how the star evolves in its final stages. A different carbon-to-oxygen ratio changes the core’s structure, how it burns later in life, and where the star crosses into the pair-instability regime. The location of the black hole mass gap is partly controlled by nuclear physics happening deep inside massive stars.

The difficulty is that this reaction is notoriously hard to measure in the laboratory at the energies relevant for stars. Nuclear physicists often describe it using a quantity called the astrophysical S-factor, which is a convenient way of quoting the reaction strength after accounting for the difficulty of getting charged nuclei close enough to fuse.

By measuring where the pair-instability gap appears in gravitational-wave data, and then comparing that measurement with stellar models, the team can infer a value for this S-factor: around 152 to 450 keV barns, at 300 keV.

Ultimately, this means that black holes merging billions of light-years away are being used as a probe of the nuclear reactions that once powered the hearts of massive stars.

There are alternative explanations to test as well. It is still possible that some combination of binary stellar evolution effects could imitate a pair-instability gap without pair instability being the true cause.

“The evidence for a pair-instability gap is becoming increasingly compelling, but it is not yet definitive proof,” says Tong. “What we’re seeing is very consistent with pair instability, but future data will tell us whether that interpretation really holds up.”

The good news is that the catalogue of black holes is still growing. Features that are only marginal today may become clear with more detections, and features that look convincing now will be tested against much larger datasets. Future measurements of spin orientations should be especially useful, because they can help determine whether the most massive black hole binaries are indeed coming from dynamical environments such as globular clusters and AGN discs, where hierarchical mergers are expected to occur.

For now, though, gravitational-wave astronomy finally has a clear view of the forbidden zone in the black hole graveyard. Massive stars can destroy themselves so completely that they leave no black hole behind. After years of searching, we are finally seeing the inferred imprint of that missing population.