Incorporating neutron star physics into gravitational wave inference with physics-informed priors using normalizing flows

When two dense stellar remnants, such as neutron stars or black holes, spiral toward each other and collide, they send ripples through the fabric of space-time known as gravitational waves. Detectors on Earth capture these faint signals, allowing scientists to listen to the universe in a way that was impossible just a few decades ago. To understand what happened during a collision, researchers use a statistical method to work backward from the sound of the waves to the properties of the objects that made them. This process requires making educated guesses about what those objects might be like before the signal even arrives. Traditionally, scientists have used "agnostic" guesses, which assume no prior knowledge about the stars' masses or internal structures, treating every possibility as equally likely. However, this approach ignores a vast amount of existing knowledge about how matter behaves under extreme pressure and how neutron stars are distributed across the galaxy.

A new study proposes a smarter way to handle these guesses. The researchers developed a method to feed real-world physics directly into the analysis of gravitational wave signals. Instead of ignoring what we already know about the internal composition of neutron stars or the typical masses of these objects, they built a system that incorporates this information from the start. By using a type of artificial intelligence trained on the laws of nuclear physics and observations of known stars, they created a set of "physics-informed" expectations. When applied to real data from three specific cosmic collisions, this method not only helped confirm the nature of the colliding objects but also provided a much sharper picture of their properties than previous methods could achieve.

The core of this work lies in how scientists interpret the data from these collisions. When a gravitational wave signal is detected, it is a complex mixture of information about the masses of the objects, how they spin, and how their internal structures deform as they get close. To extract this information, researchers rely on Bayesian inference, a mathematical framework that updates the probability of a hypothesis as new evidence arrives. The starting point of this update is the "prior," which represents what scientists believe to be true before looking at the new data. For years, the standard practice has been to use uninformative priors that assume any mass or internal structure is possible, simply because it seemed safer to avoid bias. Yet, we already know a great deal about neutron stars. We know they are made of incredibly dense matter that follows specific rules of physics, and we have measured the masses of many neutron stars in our own galaxy. The new study argues that discarding this knowledge is a missed opportunity.

To fix this, the team created a flexible system that encodes our current understanding of neutron star physics directly into the analysis. They started by gathering constraints on the "equation of state," which is essentially a rulebook describing how matter behaves at the extreme densities found inside a neutron star. This rulebook is informed by nuclear theory experiments and observations of pulsars, which are rapidly spinning neutron stars. They also gathered data on how massive neutron stars typically are, drawing from radio observations of stars in our galaxy. Using this information, they generated millions of simulated scenarios of what a collision might look like if it involved objects that obeyed these physical laws.

These simulations were then used to train a machine learning model known as a normalizing flow. Think of this model as a highly efficient mapmaker that learns the shape of the most likely physical scenarios. Once trained, this model acts as a sophisticated filter. Instead of allowing the analysis to wander through every theoretically possible combination of mass and internal structure, it guides the search toward the regions where physics tells us the objects are most likely to exist. This allows the analysis to focus its attention on the most plausible explanations, making the results more precise and the conclusions more robust.

The researchers tested this new approach on three real gravitational wave events detected by observatories in the United States, Italy, and Japan. The first event, GW170817, was a collision between two neutron stars that was also seen by telescopes looking for light. The second, GW190425, was another neutron star collision, but with heavier components. The third, GW230529, was a collision between a neutron star and a black hole, an event that had previously been difficult to classify with certainty. In every case, the physics-informed method provided a clearer view of the universe than the traditional, unguided approach.

For the first event, GW170817, the new method confirmed that the colliding objects were indeed two neutron stars. More importantly, it allowed the researchers to distinguish between different theories about the internal stiffness of these stars. The data strongly favored a "soft" equation of state, meaning the matter inside the stars is relatively easy to compress. This conclusion matched what other studies had found by combining gravitational wave data with light observations, but the new method reached this conclusion using only the gravitational wave signal itself. It also provided a more precise measurement of how far away the collision occurred, pushing the estimated distance slightly further than previous analyses suggested.

The second event, GW190425, presented a puzzle because the colliding stars were much heavier than the typical neutron stars found in our galaxy. The traditional analysis struggled to pin down their exact nature. The physics-informed approach, however, clearly identified them as a binary neutron star system, despite their unusual mass. It also revealed that the two stars were likely not of equal weight, a detail that the older, unguided methods had missed. The analysis suggested a specific distance for this event that was significantly larger than what was previously thought, aligning better with the fact that the signal was relatively faint.

The third event, GW230529, involved a neutron star and a black hole. Because the signal was faint, it was difficult to tell exactly what the objects were or how they were spinning. The new method excelled here by narrowing down the possibilities. It decisively classified the event as a collision between a neutron star and a black hole, ruling out other possibilities with high confidence. Furthermore, by incorporating the physical constraints, the analysis provided a much tighter estimate of the mass ratio between the two objects. This, in turn, gave a clearer picture of the spin of the black hole, which had been uncertain before. The method also pushed the estimated distance of this event further away, consistent with the faintness of the signal.

A key finding across all three events was that the physics-informed priors consistently led to larger estimates of the distance to the collision. This happened because the new method constrained the masses of the objects more tightly. Since the signal we hear depends on both the mass and the distance, knowing the mass more precisely forces the distance calculation to adjust. In these cases, the adjustment meant the objects were further away than previously thought. This shift has real consequences for astronomers searching for the light that might accompany these collisions, as a more distant object would be fainter and harder to spot.

The study also demonstrated that this approach can act as a powerful tool for sorting out ambiguous events. In the case of GW230529, the method provided decisive evidence for the nature of the collision, something that was previously difficult to achieve with such a faint signal. The researchers showed that by using the laws of physics to guide the search, they could extract more information from the same data without needing to wait for louder signals or better detectors.

Looking forward, the researchers emphasize that their method is designed to be flexible. As our understanding of neutron stars improves, or as new types of observations become available, the system can be updated to include this new knowledge. It does not require a complete overhaul of the analysis process; instead, it simply updates the map the computer uses to navigate the data. This means that as we learn more about the dense matter inside stars, our ability to interpret the sounds of the universe will automatically improve. The work represents a shift from treating the data as a blank slate to treating it as a conversation with the known laws of nature, allowing us to hear the universe with greater clarity.