The Mass Function of Neutron Stars from Core-Collapse Supernova Simulations

Deep in the heart of massive stars, a final, violent drama plays out. When a star much heavier than our Sun runs out of fuel, its core collapses under its own weight, triggering a supernova explosion that can outshine an entire galaxy. In the aftermath, the core often survives as a neutron star, an object so dense that a single teaspoon of its material would weigh as much as a mountain. For decades, astronomers have tried to understand the birth of these cosmic remnants. They have measured the masses of neutron stars found in binary systems, where two stars orbit each other, but the reasons behind the specific distribution of these weights have remained elusive. Is there a standard weight for a newborn neutron star, or do they are born with a wide variety of masses? And how does the chaotic process of a star's death determine whether it becomes a neutron star or collapses completely into a black hole?

A new study by a team of researchers brings together the most advanced computer simulations of these stellar explosions with the latest observations of neutron stars to answer these questions. By mapping the internal structure of the dying star to the weight of the remnant it leaves behind, the team has constructed a theoretical picture of how neutron stars are born. Their work suggests that the variety of masses we see today is not just a result of stars gaining weight later in life, but is written into the very moment of their creation. The findings offer a coherent explanation for why most neutron stars cluster around a specific weight, while a smaller group stretches toward much heavier masses, and they provide a new estimate for how often massive stars fail to become neutron stars at all, collapsing instead into black holes.

The researchers began by looking at the intricate relationship between a massive star's initial size and the structure of its core just before it explodes. They used sophisticated three-dimensional computer models that simulate the complex physics of a supernova, tracking how the star's core behaves in the final moments of its life. These simulations revealed a clear pattern: the internal "compactness" of the star's core—a measure of how tightly packed the matter is at a specific point inside—directly determines the mass of the neutron star that forms. A less compact core tends to leave behind a lighter neutron star, while a more compact core results in a heavier one. This connection allowed the team to take the known distribution of massive stars in the universe and predict the distribution of neutron star masses at the moment of their birth.

When they compared this theoretical birth distribution with the actual masses of neutron stars observed in the sky, a discrepancy appeared. The simulations predicted that the most common newborn neutron stars should be slightly lighter than the average observed mass, with a secondary group of heavier stars. However, the observed data showed a peak at a slightly higher weight. The researchers realized that this difference could be explained by two main factors: the neutron stars gaining mass after they are born, and the way they are born affecting whether they stay in a binary system.

Neutron stars in binary systems often pull material from their companion stars, a process called accretion, which adds weight to the neutron star over time. The team applied corrections to the observed data to estimate what the masses would have been at birth, stripping away the weight gained from these companions. This adjustment shifted the observed peak down to align much more closely with the theoretical prediction. Furthermore, the study highlighted the role of "kicks" given to neutron stars at birth. Just as a rocket is propelled forward by its exhaust, a neutron star receives a sudden push in the opposite direction of the explosion. The simulations suggest that heavier neutron stars receive stronger kicks on average. These powerful kicks can break the gravitational bond holding the binary system together, ejecting the heavier neutron stars into the void where they are harder to find. This selective removal means that the binary systems we observe are biased toward lighter neutron stars that received gentler kicks and stayed in orbit.

By combining the effects of black hole formation, mass accretion, and these birth kicks, the team created a refined model that matches the observed data remarkably well. Their model suggests that the universe produces a broad spectrum of neutron star masses at birth, ranging from about 1.2 to 2.0 times the mass of our Sun. The most common birth mass is around 1.35 times the mass of the Sun, which explains the prominent peak seen in observations. The heavier tail of the distribution, extending up to 2.0 solar masses, is a natural result of the varying structures of the progenitor stars, rather than just the result of later accretion.

The study also provided a new estimate for the fraction of massive stars that end their lives as black holes instead of neutron stars. By analyzing which types of stars in their simulations failed to produce a neutron star, the researchers calculated that approximately 21 percent of massive stars in the relevant mass range collapse directly into black holes. This number is not a simple rule based on the star's initial size; rather, it depends on the complex, non-linear structure of the star's core, meaning that stars of similar sizes can have very different fates.

This work represents a significant step forward in connecting the theory of how stars die with the reality of what we observe. It moves beyond the old idea that all neutron stars are born with nearly the same mass, replacing it with a dynamic picture where the initial structure of the star dictates a wide range of outcomes. The agreement between the complex simulations and the observed data suggests that our understanding of supernova explosions is maturing. While there are still uncertainties, such as the precise influence of the star's chemical composition or the details of binary interactions, the study demonstrates that modern supernova theory can now explain the population of compact objects we see in the sky. It opens a new era where the birth of these extreme objects can be traced back to the specific conditions of the stars that created them, turning a collection of measurements into a coherent story of stellar death and rebirth.