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Artist’s impression of a neutron star. | Credit: ESA.
By developing a new theoretical link for how compact neutron stars, the remnants of massive stars that have gone supernova, can form, scientists have found a way to test the properties of nuclear physics under very extreme conditions.
Since the collapsed core a massive stara neutron star is a small but incredibly dense object packed up to three times the mass of our sun into a small volume. Models predict that neutron stars are about a dozen miles across, but their exact radius has always been uncertain.
“Measuring the material properties of a neutron star is really very difficult, and that’s because while we can measure the mass of a neutron star very precisely, it’s very difficult to measure its radius precisely,” Luciano Rezzolla, a professor of theoretical astrophysics at the University of Frankfurt, told Space.com.
Rezzolla and his Frankfurt colleague Christian Ecker made things a little clearer with their new study of the compactness of neutron stars.
There are several reasons why determining the radius of a neutron star is difficult. One obstacle is that all known neutron stars are very far away, but the main challenge lies in what physicists call the equation of state. This describes the density and pressure inside the neutron star, from which the radius and other properties can be accurately determined.
The problem is that the conditions inside a neutron star are so extreme that they push our understanding of nuclear physics to the limit. A spoonful of neutron star material can weigh billions of tons. Under such intense pressure, atoms are crushed and positively charged protons combine with negatively charged electrons to form an object full of neutrons.
However, exotic physics may prevail at the center of a neutron star: for example, there may be “strange” matter particles called hyperons, or perhaps even neutrons are mixed together and forced by the massive gravity quark the particles they are made of flow almost freely. However, there is no way to test this because scientists cannot replicate the conditions inside a neutron star in the laboratory Earth. It’s just too extreme.
Thus, rather than a single equation of state for neutron stars, there is a whole list of possible equations of state, one for each model that describes the possible conditions inside a neutron star.
To estimate how compact a neutron star can become, Rezzolla and Ecker considered tens of thousands of equations of state. But to keep things manageable, they only looked at the more massive neutron star in each case.
“A well-known result of general relativity is that there is a maximum allowed mass for every equation of state,” Rezzolla said. “Any mass greater than the maximum mass would cause a black hole. We know from observations that the maximum allowed mass should be between two and three solar masses.
Rezzolla and Ecker were surprised to learn that there is an upper limit to the compactness of a neutron star and that, based on this, the ratio between the mass of a neutron star and its radius is always less than 1/3.
This ratio can be determined using the so-called geometrized units, which are commonly used in physics. general relativity and allow mass to be expressed in terms of length rather than weight.
“As we put an upper bound on the compactness, we can put a lower bound on the radius,” Rezzolla said. “Once we’ve measured the mass of a neutron star, we can say that its radius should be three times its mass.
Rezzolla and Ecker also found that this relation holds for all equations of state, regardless of their maximum mass. This may seem surprising at first, as one would automatically think that the most massive neutron stars would be the most compact, as they would have stronger gravity trying to force them to contract. The exotic nuclear physics at work in neutron stars seems to override this and balance things out.
The connection derives in part from the principles of quantum chromodynamics, or QCD, which is the theory of how strong force binds particles called quarks together to form particles such as neutrons. The strong force is carried by particles called glue (the name comes from the fact that they bind quarks together), and QCD is the quantum field theory that governs them, giving them a quantum number whimsically called “color charge”.
Rezzolla and Ecker adapted certain standard QCD assumptions to derive the compactness relation, which they describe as QCD leaving an “imprint” on the internal structure of neutron stars. This means that if it is ever possible to accurately measure the radius of a neutron star, any deviation from this relation would be a strong indication that something is wrong with our understanding of QCD.
“If we were to see a violation of this result, such as a neutron star with a compactness greater than 1/3, it would mean that there is something wrong with the QCD assumptions we use,” Rezzolla said.
It may not be long before we can accurately observe the radius of a neutron star before this connection and QCD can be tested. Rezzolla describes the outlook as “optimistic” and cites the NICER (Neutron star Interior Composition Explorer) experiment. International Space Stationalso measurements from gravitational wave events, some of which involve the merger of a black hole with a neutron star. So far, in only one case, GW 170817, have two neutron stars merged.
“If we could see more events like GW 170817, we could put much tighter constraints on the radii of possible neutron stars,” Rezzolla said.
Rezzolla and Ecker’s research is published in the Preprint Paper Repository arXiv.