Scientists at University of Stavanger and Goethe University Frankfurt have identified a new way to probe the interior of neutron stars using gravitational waves from their collisions.
By analyzing the "long ringdown" phase – a pure-tone signal emitted by the post-merger remnant – they have found a strong correlation between the signal’s properties and the equation of state of neutron-star matter. The results were recently published in Nature Communications.
Neutron stars, with a mass greater than that of the entire solar system confined within a nearly perfect sphere just a dozen kilometers in diameter, are among the most fascinating astrophysical objects known. Yet, the extreme conditions in their interiors make their composition and structure highly uncertain.
The collision of two neutron stars, such as the one observed in 2017, provides a unique opportunity to uncover these mysteries. As binary neutron stars inspiral for millions of years, they emit gravitational waves, but the most intense emission occurs at and just milliseconds after the moment of merging. The post-merger remnant – a massive, rapidly rotating object formed by the collision – emits gravitational waves in a strong but narrow frequency range. This signal holds crucial information about the so-called "equation of state" of nuclear matter, which describes how matter behaves at extreme densities and pressures.
Researches at the University of Stavanger and at Goethe University in Frankfurt have now discovered that although the amplitude of the post-merger gravitational-wave signal diminishes over time, it becomes increasingly "pure"—tending toward a single tone, much like a giant tuning fork resonating after being struck. They have termed this phase the "long ringdown" and identified strong connection between its unique characteristics and the properties of the densest regions in neutron-star cores.
Just as tuning forks made of different materials produce distinct pure tones, remnants governed by different equations of state will ring down at different frequencies. Detecting this signal could therefore reveal the composition of neutron stars.
"With this new understanding of the relationship between gravitational-wave emission and the properties of neutron star cores, we are now equipped to study the exotic phases of matter that may exist under these extreme conditions. It will be incredibly exciting to test various theoretical ideas about matter at the highest densities found in the universe," explains Assoc. Prof. Aleksi Kurkela.
Through advanced general-relativistic simulations of merging neutron stars with carefully constructed equations of state, the researchers have demonstrated that analyzing the long ringdown can significantly reduce uncertainties in the equation of state at very high densities – where no direct constraints are currently available. This finding paves the way for a better understanding of dense neutron star matter, especially as new events are observed in the future.
While current gravitational-wave detectors have not yet observed the post-merger signal, scientists are optimistic that the next-generation detectors, such as the Einstein Telescope expected to become operational in Europe within the next decade, will make this long-awaited detection possible. When that happens, the long ringdown will serve as a powerful tool to probe the enigmatic interiors of neutron stars and reveal the secrets of matter at its most extreme.