Ultra-compact twin stars with hybrid equations of state from bosonic dark matter

Deep in the heart of the universe, where gravity is so intense that it crushes matter into a state denser than any material on Earth, lie the remnants of dead stars. These are neutron stars, the cosmic corpses of massive suns that have collapsed under their own weight. While we understand the outer layers of these objects, their cores remain a profound mystery. The pressure inside is so extreme that it might force protons and neutrons to dissolve into a soup of their constituent parts, known as quark matter. At the same time, the universe is filled with invisible dark matter, a substance that does not emit light but exerts gravity. For decades, scientists have wondered what happens if these two cosmic puzzles collide: what if a neutron star is not just made of ordinary matter, but also contains a significant amount of dark matter trapped within its core?

A team of researchers at Goethe University in Frankfurt has taken a fresh look at this possibility, combining the physics of quark matter with the physics of dark matter to see how they reshape the life of a neutron star. They focused on a specific scenario where the transition from normal matter to quark matter is sudden and violent, rather than gradual. In the world of single-fluid stars, such a sudden jump usually creates a gap in stability, meaning that stars with certain masses simply cannot exist. However, the researchers found that adding a second fluid of dark matter changes the rules entirely. By simulating these hybrid stars, they discovered that dark matter can act as a stabilizing agent, smoothing out the gaps and allowing for new types of stars that were previously thought impossible.

The study reveals that when dark matter is present, it can alter the structure of a neutron star in two very different ways, creating two distinct families of ultra-compact objects. In one scenario, the dark matter forms a dense core hidden deep inside the star, surrounded by a shell of normal matter. In the other, the dark matter forms a vast, diffuse halo that envelops the entire star, extending far beyond the visible surface of the normal matter. Remarkably, both types of stars can be incredibly small and heavy, packing so much mass into such a small space that they approach the limits of what physics allows. The researchers found that these ultra-compact stars can have a compactness value of at least one-third, a threshold where the star is so dense that light can orbit it, a feature usually associated with black holes.

What makes this discovery particularly striking is how dark matter changes the relationship between a star's mass and its size. In a standard neutron star, if you add more mass, the star shrinks. But with dark matter involved, the researchers found that the star's visible size can shrink dramatically while its total mass remains high, or conversely, the star can maintain a similar visible size while carrying a vastly different amount of dark matter. This leads to a phenomenon the authors call "ultimate twins." These are pairs of stars that look identical to our telescopes—having the same mass and the same visible radius—but are fundamentally different inside. One might be a pure hybrid star with a quark core, while its twin is a hybrid star with a massive dark matter halo. To an observer measuring only the star's size and weight, they would appear to be the same object, yet their internal composition and their response to gravitational forces would be completely different.

The researchers also looked at how these stars would behave if they were to collide or be pulled by the gravity of a companion star. They found that the presence of dark matter leaves a clear fingerprint in the form of gravitational waves. The "ultimate twins" they identified would produce different signals when they interact with other stars, even though they look the same in visible light. Furthermore, the study examined the light escaping from the surface of these stars. Because gravity bends light, the light from a very dense star is stretched, or redshifted, as it travels to us. The team found that the two types of ultra-compact stars produce very different redshifts. The stars with a dark matter core show a high redshift, similar to what we expect from the densest normal stars. In contrast, the stars with a dark matter halo show a surprisingly low redshift, despite being just as compact. This counterintuitive result happens because much of the star's mass in the halo version is located outside the surface where the light is emitted, so the light does not have to climb out of as deep a gravitational well as one might expect.

These findings suggest that the universe may be hiding a zoo of exotic stars that we have not yet identified. The researchers propose that future telescopes, which will be able to measure the size and mass of neutron stars with much greater precision than current instruments, could spot these anomalies. If a telescope detects a star that is incredibly small and heavy, or if gravitational wave detectors hear a signal that doesn't match the star's visible size, it could be the first evidence of dark matter living inside a neutron star. The study does not claim to have found these stars yet, but it provides a detailed map of where to look and what to expect. It shows that the interplay between the sudden transition to quark matter and the presence of dark matter creates a rich landscape of possibilities, turning the neutron star into a laboratory where the laws of gravity and particle physics are tested in the most extreme conditions imaginable.

The work also clarifies a long-standing question about the stability of these stars. In previous models, a sudden change from normal matter to quark matter was thought to create an unstable region where stars could not exist. The researchers found that the addition of dark matter removes this instability. Instead of a gap in the sequence of possible stars, the presence of dark matter creates a continuous path, allowing stars to transition smoothly from one state to another without collapsing. This means that the "twin stars" predicted by earlier theories might not be as rare or as distinct as once thought; they could be part of a continuous family of stars that simply carry different amounts of dark matter. The study concludes that the search for dark matter may not require looking at the empty spaces between galaxies, but rather at the densest, most compact objects in the universe, where the invisible and the visible are locked together in a gravitational embrace.