The physics of neutron stars are almost too fantastic to believe. Something the weight of two Suns compacted to a sphere the size of a city. Each teaspoon of its material would weigh billions of tons. If you’ve done any reading on the topic, you’ve heard these facts before. But despite the intense interest these extreme objects hold, we are still actively learning lots about them. One of the most pertinent outstanding questions is where is the line between becoming a neutron star and becoming a black hole when a star dies. A new paper by researchers at the HUN-REN Wigner Research Centre for Physics in Hungary describes what they believe to be a definitive answer to that question - between 2.2 and 2.3 solar masses.

Coming to that conclusion required a lot of calculations and assumptions though. The physics underlying neutron stars are governed by a rulebook called the Equation of State - basically a rulebook describing how matter acts under these absurd pressures. But since we can’t actively collect a sample of a neutron star to study, that rulebook is primarily defined by models. The authors used two with slightly different properties to develop their estimate.

First, SFHo defines a neutron star made up of “softer”, more compressible nuclear matter. These have some more flexibility in them, and therefore lack the rigidness of its stiffer counterpart. DD2 models neutron star material as tougher and more resistant. It is primarily designed for use in “larger” stars, but either model can be used for any size neutron star, at least in theory. However, in order to make sure that the speed of sound in this material wouldn’t exceed the speed of light (and therefore violate the laws of physics), the authors manually forced the models to respect the results of models that use perturbative Quantum Chromodynamics (pQCD).

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After developing their model, the authors tested their model against various data and signals from various telescopes. They compared it to results of hot spots on the surfaces of spinning pulsars from the Neutron Star Interior Composition ExploreR telescope (NICER), which constrained the models further. They then updated the models based on “squishiness” data from the gravitational wave detection of GW170817, the first known merger of two neutron stars.

It turns out, with the updates from those two data sources, both models converged on almost exactly the same number - somewhere in between 2.2 and 2.3 solar masses. However, it left open the question about the actual size of these behemoths. Their physical dimensions vary somewhat based on which starting model was chosen, but the general consensus is that their radius would be somewhere around 12 km.

That leaves a few strange objects in the lurch, though, as they are too big to qualify as neutron stars by this metric, but also don’t seem to be black holes either. For example, object GW190814 weighs in at 2.59 solar masses. If this object is assumed to be a neutron star, it would break the DD2 model entirely, since the material supporting that size would not be able to be deformable enough to still meet the requirements set out by the data collected during the GW170817 merger.

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The results strongly imply that GW190814, as well as a fellow “size gap” object HESS J1731-347, are in fact black holes rather than neutron stars. They also supply a definitive answer to the Tolman-Oppenheimer-Volkoff (TOV) equations that were originally used to describe neutron stars back in 1939. With a definitive weight, and good estimates on the physical size, this new paper provides plenty of insight into the inner workings of some of the universe’s strange objects - even if we never get to physically see those inner workings ourselves.

Learn More:

Gábor Kasza & György Wolf - Maximal mass of neutron stars constrained by neutron star observations

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