Noronha-Hostler group leverages data from astrophysics and nuclear physics to understand the strongest force of nature.

Scientists at the University of Illinois Urbana-Champaign, the University of Washington, and Kent University in Ohio have confirmed that a mysterious class of astronomical objects that fall within the “mass gap” of astronomical observations could indeed be ultradense neutron stars.

Very few known astrophysical objects have a mass between that of the largest observed neutron star and the smallest detected black hole. Scientists use thermodynamic relations known as the equation of state to model the physical properties of this ultradense matter. An equation of state is a mathematical representation of the relationships between the pressure and energy density.

In the equation of state for a traditional neutron star, the speed of sound increases smoothly with the star’s density; higher speeds of sound are observed at higher densities. However, in the depths of ultradense neutron stars, the rules seem to change.

Illinois Physics graduate student Nanxi Yao is the lead author on the new research. She explains, “Within the set of these ultradense objects, the neutron star equation of state demonstrates a sudden rise that approaches the speed of light and a steep decline—a ‘bump’—in the speed of sound as a function of density.”

The team’s results are published as an Editor’s Choice article in Physical Review C.

The new findings build on prior research by Illinois Physics Professors Nico Yunes, Jacquelyn Noronha-Hostler, and colleagues at Kent State University. That research mathematically demonstrated the presence of a “bump” near the core of a neutron star of equivalent mass to one of these mysterious observed objects. One possible explanation is that at the extreme densities around the core of a neutron star, the fundamental forces that hold together a particle like a proton or neutron are overcome.

Protons and neutrons are themselves made up of particles called quarks. “It’s possible that the densities reached in ultradense neutron stars are so large that quarks become free, which would mean that the core of a neutron star is actually composed of unbound quarks,” says Agnieszka Sorensen, a former postdoc at the University of Washington now a professor at Michigan State, and a member of the research team.

Unbound quarks are extremely challenging to study experimentally. In fact, the only place on Earth where unbound quarks are observed is in the extreme environments produced by heavy-ion collisions in particle accelerator laboratories. Interestingly, in the current research, Noronha-Hostler, Yao, and collaborators found that the previously proposed bump in the speed-of-sound profile from the neutron star equation of state is consistent with experimental data from heavy-ion collisions. The capacity to translate neutron star equation of state data to be compatible with heavy-ion collision data provides further evidence that unidentified mass-gap objects could be heavy neutron stars.

“Now is an exciting time to connect heavy-ion data to astrophysical observations of neutron star mergers,” says Noronha-Hostler. “There is so much activity going on both in laboratories and through observations. We have new heavy-ion data coming in from Brookhaven National Laboratory, smaller error bars for the neutron star radii from NICER, and hopefully new gravitational wave measurements of binary neutron star mergers will be detected by LIGO/Virgo/KAGRA in the ongoing observational run 4.”

The team’s work yields new insight into a recent astrophysical observation dubbed GW190814. When two massive objects in space spiral towards a collision, energy is carried away from the system by gravitational waves. Measurements of these gravitational waves provide information about the extreme astrophysical phenomena from which they originated. GW190814 denotes the measurement of a gravitational wave signal from just such a collision. One of the involved objects is a black hole, but scientists can’t be sure whether the other object is an ultradense neutron star or a very light black hole, because its mass falls within the mass gap of astronomical observations—the range of 2.3 to 5 solar masses, wherein very few astrophysical objects have been observed.

Back in 2022, Noronha-Hostler and Yunes proposed a neutron star equation of state with a bump in the speed of sound compatible with the physics of a neutron star having a mass around 2.6 times the mass of the Sun. However, another group argued that neutron star equations of states that support such heavy neutron stars are in tension with heavy-ion collision data. To demonstrate that this mysterious object could be a neutron star, it was necessary to compare apples and oranges—that is, to reconcile the gravitational-wave data with heavy-ion collision data.

Thus, Noronha-Hostler and collaborators set about finding a way to systematically compare an equation of state with a large bump in the speed of sound against heavy-ion collision data while satisfying constraints from astronomical observations. The comparison posed a technical challenge: heavy-ion collisions and neutron stars exist at widely different extremes of matter. Heavy-ion collisions produce temperatures in excess of 4 trillion kelvin—orders of magnitude greater than the temperature of a neutron star. Furthermore, while heavy-ion collisions use approximately even numbers of neutrons and protons, neutron stars are by nature imbalanced, having many more neutrons than protons.

Notes Yao, “In the past, researchers have used heavy-ion collision data to describe neutron-star nuclear physics. We are one of the first groups to translate the neutron star equation of state to be compatible with heavy-ion collision data.”

Such a translation is valuable because heavy-ion collisions can be simulated. Once the team converted the heavy neutron-star equation of state to a zero-temperature equation of state having an even ratio of neutrons to protons, they were able to test their new equation by putting it into the computer simulation SMASH (Simulating Many Accelerated Strongly-interacting Hadrons). This program was run on the Illinois Campus Cluster, which is operated by the Illinois Campus Cluster Program and the National Center for Supercomputing Applications.

Yao notes, “There were many technical challenges in developing a method to compare the exceptionally different systems of neutron stars and heavy-ion collisions. Now that we have delineated this method, we will be able to use data from one system to constrain the other.”

Obstacles remain. “The next step for this work is to run a full Bayesian analysis using constraints from both heavy-ion collision data and astrophysical observations,” explains Noronha-Hostler. “However, this presents significant challenges due to the runtime of heavy-ion collision simulations and nailing down the systematics in the theoretical uncertainty.”

Still, the team’s methods have far-reaching implications for both astrophysics and nuclear physics. Says Noronha-Hostler, “Making these connections will help us to better understand the strongest force of nature in the densest environments known to humanity.”

This work was supported by the National Science Foundation under Grant Nos. OAC-2103680, PHY1748621, and NP3M PHY-2116686. Additional support came from the U.S. Department of Energy under Grant Nos. DESC0023861 and DE-FG02-00ER41132, and from the Fulbright Scholar Program. The conclusions presented are those of the scientists and not necessarily those of the funding agencies.