Bayesian approach study of hybrid neutron stars

Deep in the cosmos, far beyond the reach of our telescopes, lie some of the most extreme objects in the universe: neutron stars. These are the collapsed cores of massive stars that have died, compressed into spheres only about twenty kilometers wide but containing more mass than our entire sun. Inside them, gravity squeezes matter so tightly that atoms themselves are crushed, leaving behind a dense soup of protons and neutrons. For decades, physicists have wondered if this pressure goes even further, forcing the protons and neutrons to break apart into their own fundamental building blocks: quarks. If this happens, the star's core would transform into a new state of matter, creating what scientists call a "hybrid star"—a celestial body with a core of free-floating quarks surrounded by a shell of normal nuclear matter. Determining whether these exotic cores exist is one of the great challenges in modern astrophysics, as it would reveal how matter behaves under conditions that cannot be recreated in any laboratory on Earth.

To solve this puzzle, a team of researchers turned to a powerful statistical method known as Bayesian analysis. Instead of guessing which model of matter might be correct, they used this approach to test several different theories against real-world data collected by advanced instruments. They focused on measurements of neutron star masses and sizes, gathered from gravitational wave detectors that listen to the ripples in space-time caused by colliding stars, and from X-ray telescopes that time the pulses of light from spinning stars. The researchers built computer models of these stars, creating two distinct layers for each one: an outer shell made of normal nuclear matter and a central core made of deconfined quark matter. They tested three different ways to describe the outer shell, each based on slightly different assumptions about how particles interact, and paired them with a model for the quark core that included specific parameters for how the quarks push against each other and how they are confined.

The team then ran their models through a rigorous process of elimination. They asked their computer simulations to find the specific settings for the quark core that would allow the resulting hybrid stars to match the observed masses and sizes of real neutron stars. Crucially, they also checked if these stars would remain stable and if the transition from normal matter to quark matter happened at a density that makes physical sense. The results pointed to a very specific outcome. The most successful model, which combined a particular description of the outer shell with a specific set of rules for the quark core, suggested that a phase transition to quark matter could occur at densities less than twice the density of normal atomic nuclei. This finding implies that hybrid stars with large quark cores are a possible configuration consistent with the data, although the statistical evidence favoring this specific model over alternatives remains inconclusive.

However, the study also highlighted significant challenges for other possibilities. When the researchers tested models that included strange particles called hyperons in the outer shell, or when they used different mathematical descriptions for the nuclear matter, the resulting stars often failed to match the observed data or violated known physical limits. In particular, many of the alternative models, including those with hyperons, predicted stars that were either too soft or too stiff, or they suggested that the transition to quark matter would happen at densities so high that the stars would collapse before reaching the necessary mass. The analysis showed that while the hyperonic models were not entirely ruled out as a theoretical possibility, they violated specific constraints derived from perturbative Quantum Chromodynamics (pQCD). Only a narrow range of parameters for the quark core could produce a star that is both stable and consistent with the precise measurements from recent astronomical observations, though even the best-fitting model showed some tension with theoretical limits.

The researchers found that the best-fitting model predicts a transition to quark matter occurring at a density around 1.9 times the normal density of nuclear matter. At this point, the core of the star would begin to change its nature, creating a large region of quark matter inside. The study indicates that these hybrid stars would have a radius of about 12 kilometers and could support masses up to roughly 2.1 times that of our sun. These values align with the heaviest neutron stars we have observed, such as the one known as PSR J0740+6620, which weighs in at over two solar masses, though the study notes that the best-fitting model still violates specific pQCD constraints in certain diagrams. The findings suggest that the interior of these massive stars is likely a complex mix of phases, where the extreme pressure forces a fundamental change in the nature of matter itself.

While the study provides a clearer picture of the hidden interiors of the universe's densest objects, it also highlights the limits of our current knowledge. The researchers noted that the exact moment when the transition occurs depends heavily on the specific model used for the outer shell of the star. Some models suggested the transition happens earlier, while others pushed it to higher densities, but only one combination satisfied the majority of constraints from astronomical data, even though it still violated specific pQCD constraints in certain diagrams. The team also examined how the shape of the star changes when it is pulled by the gravity of a companion star, a property known as tidal deformability. Their results showed that the most successful models produce stars that deform in a way consistent with the gravitational waves detected from the collision of two neutron stars in 2017.

Ultimately, this work offers a clearer picture of the hidden interiors of the universe's densest objects. By combining precise astronomical measurements with sophisticated statistical tools, the researchers have narrowed down the possibilities for what lies at the heart of a neutron star. They have shown that a large quark core is a plausible feature of these cosmic giants, provided the laws governing the transition between normal matter and quark matter follow a specific path, even if the statistical evidence for this specific scenario is not yet definitive. This does not prove that every neutron star has a quark core, but it demonstrates that such a configuration is compatible with much of what we currently know about the universe. As new data arrives from more sensitive instruments, these models will be tested further, potentially revealing the true nature of matter at the very edge of existence.