Neutron stars are among the most fascinating and enigmatic objects in the universe. Formed from the collapsed core of massive stars that have exploded in a supernova, neutron stars are incredibly dense, with a mass comparable to that of the Sun but packed into a sphere with a radius of only about 10 kilometers—just slightly more than the height of Mount Everest. These stellar remnants are composed primarily of neutrons, held together by incredibly strong forces, and their density can be several times greater than that of atomic nuclei.
Due to these extreme conditions, neutron stars present a unique and challenging opportunity for physicists to test the limits of existing theories and explore new realms of science. As one of the densest objects in the universe, the study of neutron stars requires innovative approaches, and recent advancements have helped us uncover new information about their internal properties. One such breakthrough comes from the use of lattice quantum chromodynamics (QCD), a computational approach that allows scientists to probe the behavior of matter under extreme conditions, shedding light on the behavior of matter inside these stars.
Understanding the Challenges of Studying Neutron Stars
Studying neutron stars is inherently difficult. One of the main challenges arises from their incredibly small size—despite their immense mass, neutron stars are often too small to be observed directly through telescopes. Even the closest known neutron star to Earth is located about 400 light-years away, making it impossible to observe it in detail through traditional optical methods. Additionally, the extreme density of neutron stars makes it nearly impossible to replicate similar conditions in laboratory experiments on Earth. Their matter is about a quadrillion times denser than water, and no laboratory can produce substances with comparable density or size.
Furthermore, the interior of neutron stars is governed by quantum chromodynamics (QCD), the theory of the strong nuclear force, which is responsible for the interactions between quarks and gluons, the fundamental constituents of matter. The interactions described by QCD are notoriously complex, particularly in the dense environment of a neutron star, where particles are tightly packed together. The equations that govern these interactions are so complicated that traditional mathematical techniques are inadequate for solving them in such extreme conditions. This is where new approaches, such as lattice QCD, come into play.
Lattice QCD: A New Approach to Understanding Neutron Stars
In recent years, researchers have turned to lattice QCD, a computational technique that divides space and time into a discrete grid, allowing scientists to simulate particle interactions under extreme conditions. This method involves calculating the behavior of particles at specific points on the grid and using computational power to simulate the dynamics of particle interactions across the entire system. While lattice QCD has been successful in a variety of contexts, simulating neutron stars with it is still a highly complex task, requiring significant computational resources.
To address these challenges, Ryan Abbott, a physicist at the Massachusetts Institute of Technology (MIT), and his colleagues employed a refined approach that involved using isospin—another quantum property that differentiates protons from neutrons. Isospin is a quantum number that can be used to simplify the simulations of neutron star matter by treating protons and neutrons as different states of the same particle with opposite isospin values. This approach allowed the team to simulate the behavior of nuclear matter at densities similar to those found in neutron stars, without the need to directly calculate all the intricate details of the QCD interactions at every point in the star.
The research team ran their simulations using a network of supercomputers, dedicating thousands of GPU hours to the task. Abbott estimates that the project required several million GPU hours in total, with the simulations producing a range of new results that have deepened our understanding of neutron star interiors. Their work is significant because it represents the first time that the continuum limit—the idealized scenario where the discrete lattice spacing vanishes—has been reached in simulations involving isospin nuclear matter.
New Findings: Speed of Sound and Neutron Star Equations of State
One of the most important outcomes of the team’s research is the establishment of new constraints on the behavior of matter inside neutron stars. In particular, the researchers discovered a new maximum limit for the speed of sound within a neutron star’s interior. Prior to this work, it had been theorized that the speed of sound in strongly interacting QCD matter could not exceed c/√3, where c is the speed of light. However, the MIT team’s results showed that the speed of sound could exceed this threshold, with their simulations indicating that the maximum speed could be as high as ¾ c.
This discovery has significant implications for the study of neutron stars and their internal structure. The speed of sound inside a neutron star is an important factor that influences its overall stability and the relationship between temperature, pressure, and density in these extreme environments. By obtaining a more accurate value for the speed of sound, the researchers have provided a more complete equation of state (EoS) for isospin-dense matter at zero temperature, offering a clearer picture of the behavior of neutron star matter under different conditions.
The equation of state for a neutron star is analogous to the phase diagram of substances like water, where different phases (solid, liquid, gas) are defined by relationships between temperature, pressure, and other properties. In the case of neutron stars, the EoS helps determine how the star’s properties change as its density and temperature fluctuate. By refining the EoS, scientists can better understand the structure and evolution of neutron stars, including how their mass and radius are related.
Implications for Neutron Star Growth and Future Research
Another important consequence of the new findings is that neutron stars may be able to grow more massive than previously thought. The previous assumption that there was a limit to the mass of a neutron star—known as the Tolman–Oppenheimer–Volkoff (TOV) limit—was based on earlier models of the EoS. However, the new results suggest that neutron stars could potentially exceed the TOV limit, which could lead to new insights into the formation and behavior of more massive stars and even the possibility of neutron stars turning into black holes under certain conditions.
The work by Abbott and his team opens up new avenues for further computational studies of neutron stars. In the future, more refined calculations could explore other properties of neutron star matter, such as conductivity, viscosity, and thermal properties, which could help interpret astronomical observations of neutron stars. Additionally, these simulations could lead to more accurate predictions of neutron star behavior, providing new insights into astrophysical phenomena such as gravitational waves and the interaction between neutron stars and other objects like black holes.
Conclusion
The study of neutron stars has long been a challenging and rewarding field of astrophysics. The extreme conditions present inside these stars—where matter is compressed to densities far beyond what we can replicate on Earth—have made it difficult to study their properties directly. However, the use of lattice quantum chromodynamics has provided new insights into the internal structure of neutron stars, offering a more accurate understanding of how pressure, temperature, and density interact within these dense stellar remnants.
The results from Abbott and his colleagues are a significant step forward in our understanding of neutron stars and their behavior under extreme conditions. Their discovery of a higher maximum speed of sound inside neutron stars, as well as their refinement of the equation of state for isospin-dense matter, opens new possibilities for future research. As computational techniques continue to advance, the hope is that these models will lead to even more detailed and accurate descriptions of neutron stars, allowing us to unravel some of the most profound mysteries of the universe.
Reference: Ryan Abbott et al, QCD Constraints on Isospin-Dense Matter and the Nuclear Equation of State, Physical Review Letters (2025). DOI: 10.1103/PhysRevLett.134.011903