Hungarian physicists have drawn a cosmic boundary line: 2.2 to 2.3 solar masses. Cross it, and a dying star doesn't become a neutron star—it collapses into a black hole instead.
For nearly a century, scientists have puzzled over where neutron stars end and black holes begin. These are objects so extreme that a teaspoon of neutron star material would weigh billions of tons, yet we can only study them from afar, through gravitational waves and X-rays. Now researchers at HUN-REN Wigner Research Center for Physics in Hungary have used a combination of telescope observations and gravitational wave data to answer one of physics' most enduring questions.
The challenge is that we cannot collect a sample of neutron star material to study in a laboratory. Instead, physicists rely on theoretical models called the Equation of State—essentially rulebooks describing how matter behaves under impossible pressures. The Hungarian team used two competing models with different assumptions. The SFHo model describes neutron stars made of "softer," more compressible nuclear matter with flexibility built in. The DD2 model, by contrast, portrays the material as tougher and more resistant to compression.
To ensure their models obeyed the laws of physics—particularly that the speed of sound inside neutron stars could never exceed the speed of light—the researchers incorporated constraints from advanced quantum physics calculations. They then tested their predictions against real observational data from two key sources. The NICER telescope observed hot spots on spinning pulsars and provided precise measurements that tightened the models further. More crucially, data from GW170817, the first-ever detection of two colliding neutron stars in 2017, gave scientists new information about how "squishy" or deformable the material actually is.
When Gábor Kasza and colleagues updated their models with this gravitational wave data, something remarkable happened: both the SFHo and DD2 models converged on nearly identical results. The maximum mass before collapse sits between 2.2 and 2.3 solar masses, with neutron stars having a radius around 12 kilometers.
This finding resolves a decades-old puzzle but also exposes a mystery. Several observed objects don't fit neatly into either category—they're too massive to be neutron stars by the new criteria, yet haven't been confirmed as black holes. One such object, GW190814, weighs 2.59 solar masses. If it were a neutron star, it would violate the DD2 model's constraints based on the GW170817 merger data. The research strongly suggests GW190814 and a similar object called HESS J1731-347 are actually black holes, not neutron stars caught in a size gap.
The Hungarian team's work also provides a definitive answer to the Tolman-Oppenheimer-Volkoff equations, the original theoretical framework for understanding neutron stars that physicists have relied on since 1939. By combining multiple independent sources of astronomical data with sophisticated physics modeling, they've illuminated one of the universe's most extreme transformations: the moment when stellar collapse becomes irreversible and the universe's most enigmatic objects are born.