At the core of a cosmic mystery: What’s inside a neutron star?

A sugar cube of neutron star matter weighs a staggering one billion tons. It’s no wonder neutron stars are considered compact astrophysical objects. Under these extraordinary conditions, the laws of nuclear physics remain a mystery. In a recent submission to Physical Review D, we used a large scale statistical study to try to understand the exotic states of matter that can appear inside neutron stars.

Neutron stars are formed from the violent battle between gravitational and nuclear forces that takes place when a main-sequence star, like our Sun, has converted all of its light elements into heavier elements that cannot be fused together. As the star begins to collapse under its own weight, a reaction called beta decay kicks in, causing protons and electrons to combine to form neutrons. Forbidden to occupy more than one state by the Pauli exclusion principle, these neutrons are forced into increasingly higher energies. For some heavy stars, this phenomenon generates just enough outward pressure to prevent a full gravitational collapse, giving rise to a new stable object: the neutron star. In this transformation, a once-expansive stellar object condenses to about 20 kilometers in diameter—an entire star compressed into a city-sized celestial marble.

We know that the production of neutrons halts the gravitational collapse. We do not know what kind of matter makes up the inner core of the star once it has settled into a state of chemical and dynamical equilibrium. The conditions in the core of a neutron star cannot be replicated in experiments, meaning neutron stars are the only “laboratory” where we can study the properties of nuclear matter at such extreme densities. Understanding what happens under these conditions is currently one of the biggest priorities in nuclear physics.

Because we cannot directly send probes into neutron stars, we largely rely on theoretical models. These models agree that the atmosphere and crust are made up of nuclei, like the matter we observe on Earth. The more exotic physics begins in the core. About half a kilometer into the star, we run into the outer core. There, models agree that we would  largely find neutrons, with a small fraction of protons mixed in (about a 20:1 ratio). The agreement between models stops at the inner core, where many theories predict a phase transition. The predictions for phase transition include a range of exotic physics, such as particles containing strange quarks called hyperons, heavy resonances (think of a proton or neutron with extra mass), and even free quarks and gluons.

In our paper, we isolated the thermodynamic signatures associated with a transition from a phase of matter which contains some mixture of neutrons and protons to something else, like the exotic states mentioned above. We identified that these phase transitions result in bumps, kinks, and plateaus in how the speed of sound changes from the surface to the inner core, i.e., the speed of sound as a function of density.

We used the Illinois Campus Cluster at the National Center for Supercomputing Applications to generate over one million guesses for what the speed of sound looks like in the core of a neutron star. For each of these separate hypotheses, we calculated the macroscopic properties of a neutron star population. By comparing these macroscopic predictions to real observations of neutron stars, we were able to associate a statistical weight with each individual hypothesis.

When we investigated whether observations of neutron stars supported the assumption that exotic matter is produced in the core, we found no statistically significant difference between guesses where no phase transition was assumed (meaning that the entire star is made up of neutrons and protons) and guesses where some form of transition to exotic matter was present. However, when we isolated scenarios where exotic matter was present, we found a particular form that was given a higher weight: a speed of sound that presents a peak at around twice the density of nuclei. This type of function is seen in models that assume the core of neutron stars is made up of free or partially free quarks and gluons, as well as in models that predict the production of hyperons. None of these states have been observed in nature before.

In our work, we developed a completely new framework for studying phase transitions in neutron stars. Through this effort, we established a connection between nuclear physics phenomena and the speed of sound inside one of the densest objects in the universe. We saw preliminary hints, though inconclusive, that suggest neutron stars could be hiding undiscovered states of matter in their cores. We are currently working on including new observables from gravitational wave measurements of neutron star mergers and heavy-ion collision experiments in our analysis. These new observations could definitively confirm, or rule out, the existence of an entirely new state of matter.