Research Highlight: Peering inside the core of a neutron star using gravitational waves

Neutron stars are some of the densest objects in the universe, and as such, the conditions at the cores of these extreme objects are impossible to reproduce on Earth. However, we can use data from the Laser Interferometer Gravitational Wave Observatory (LIGO) and the Virgo gravitational wave detector to gain insights into the physics of neutron stars.

Given the known masses and radii of neutron stars, we can estimate the maximum densities reached within their cores. These estimates indicate that the core of a neutron star is many times denser than a nucleus, the densest object measured on Earth. Inside the core, nuclei dissolve into their nucleon (proton and neutron) components, heavier versions of nucleons (hyperons) can appear, and all these particles can melt into quarks—their constituent building blocks.

In these conditions, both the composition and the interactions of particles remain mysterious. This mystery stems from the fact that we are unable to reproduce such extreme densities in a laboratory, as well as the fact that the strong force between nucleons, hyperons, and quarks—unlike any other force—comprises both attractive and repulsive components. 

All of this complexity is codified in the “equation of state,” which describes the relationship between thermodynamical properties of matter (like pressure versus density). This equation determines the mass and radius of a neutron star, as well as its other observable properties. There are very few ways to observationally determine the equation of state, and therefore peek into the cores of neutron stars. All of them have limitations.

In our paper recently published in Physical Review Letters, we demonstrate a new way to determine the equation of state that describes neutron star cores by using data extracted from LIGO and Virgo detections of the gravitational waves produced by neutron star mergers. 

Many neutron stars are found in binary systems. If their orbits are close, they can merge in a catastrophic phenomenon that emits enormous amounts of light, neutrinos, and gravitational waves. These gravitational waves encode the neutron stars’ tidal deformability, a measure of how much the stars deform before merging, which is associated with how big they are. Furthermore, a relation between the tidal deformability of both stars, the so-called binary Love relation, is used by the LIGO/Virgo collaboration to determine the original radii of the merged neutron stars. 

In our paper, we provide new insight into the physics behind the binary Love relation in two ways. First, we show how the slope of the binary Love relation is sensitive to sudden increases and decreases in pressure, and thus encodes information about the equation of state in a regime corresponding to the outer core of neutron stars. We show that these sudden changes in pressure are correlated with gradual changes in particle composition or interactions.

Second, we show that steep phase transitions, usually associated with the sudden deconfinement of quarks in the inner core of neutron stars, dramatically change the shape of the curve in the binary Love relation. The newly found curve structures were named "hill", “drop”, and “swoosh” because of their shapes (and to keep in line with the ski language inspired by the term “slope”). Allowing the equation of state to present curve structures can change, for example, the extraction of neutron-star radii performed by the LIGO/Virgo collaboration. 

Future measurements of gravitational waves produced by neutron star mergers detected in the fourth and fifth LIGO observing runs could reveal the slope of the binary Love relations and, consequently, reveal details about neutron star cores. Detecting the hill, drop, and swoosh will be more challenging, but still possible in future LIGO observing runs.

This work is published in Phys. Rev. Lett., April 28, 2022.