On the dynamical accessibility of twin stars

Deep in the cosmos, where gravity crushes matter to densities far beyond anything found on Earth, neutron stars stand as nature's ultimate laboratories. These city-sized remnants of exploded stars are so dense that a single teaspoon of their material would weigh billions of tons. For decades, physicists have wondered what happens to the matter inside when it is squeezed even harder. Standard theory suggests that under such extreme pressure, the protons and neutrons that make up the star might dissolve into a soup of their constituent parts, known as quarks. If this happens, the star could undergo a dramatic transformation, shrinking into a new, even denser type of object. Theoretical models predict that these "hybrid" stars, containing a core of quark matter surrounded by normal nuclear matter, could exist alongside ordinary neutron stars. In fact, some models suggest that for a specific amount of mass, two different stable stars could exist: a larger, puffier neutron star and a smaller, more compact hybrid star. These pairs are known as "twin stars."

The existence of these twin stars would revolutionize our understanding of the fundamental forces that hold matter together. However, a crucial question has remained unanswered: even if these twin stars are theoretically possible, can they actually form in the real universe? Just because a stable configuration exists on a map of possibilities does not mean a star can travel the road to get there. A new study by researchers at the University of Arizona investigates this exact problem, using powerful computer simulations to watch how these stars behave when they are pushed to their limits. They found that while the denser twin stars are energetically favored, the path to reaching them is blocked by the very heat generated during the journey.

To understand the researchers' approach, one must first grasp the concept of gravitational binding energy. In simple terms, this is a measure of how tightly a star holds itself together. The more tightly bound a star is, the more energy would be required to pull it apart. Theoretical calculations show that for a given amount of matter, the compact twin star is more tightly bound than its larger neutron star counterpart. In the cold, quiet world of equilibrium physics, this suggests that the twin star is the preferred destination; nature should naturally want to settle into the most tightly bound state available. Previous studies had shown that if you start with an unstable star, it tends to collapse into the less dense neutron star branch rather than the denser twin star branch, which was puzzling given the energy hierarchy.

The researchers set out to solve this puzzle by running detailed simulations of stellar evolution. They modeled several scenarios, including the collapse of unstable white dwarf stars and the perturbation of existing stable stars, to see where they would end up. Crucially, they did not just look at the final state; they watched the entire process unfold, paying close attention to what happens to the heat inside the star. When a star is compressed or shaken, the friction and shock waves generated during the movement create immense amounts of thermal energy. This heat creates pressure, which acts like an invisible cushion pushing outward against gravity.

The simulations revealed a decisive factor: the fate of the star depends entirely on how quickly this generated heat can escape. In the absence of rapid cooling, the thermal pressure builds up and acts as a brake. As the star tries to collapse into the denser twin star configuration, the heat generated by the compression pushes back, causing the star to bounce back and expand. It settles instead into the less dense, larger neutron star state. The star essentially gets stuck in a "hot" state that prevents it from reaching the "cold," tightly bound twin star configuration, even though the twin star is the energetically preferred destination.

However, the story changes if the star can cool down quickly. The researchers introduced a mechanism to simulate rapid cooling, effectively removing the thermal energy as fast as it was generated. When this happened, the thermal cushion disappeared. Without the outward push of heat, gravity was free to continue its work, compressing the star all the way down to the denser twin star branch. The simulations showed that for a twin star to form through these violent dynamical processes, the cooling must happen on a timescale comparable to, or faster than, the time it takes for the star to collapse and bounce.

This finding has profound implications for what we might actually observe in the universe. The researchers calculated that the heat generated during such a collapse would take a very long time to dissipate naturally—likely thousands of times longer than the rapid collapse itself. In the real universe, where cooling happens slowly through the emission of neutrinos and light, the thermal pressure would almost certainly prevent the formation of twin stars via these specific channels. The simulations suggest that while twin stars might exist in theory, the universe is likely to favor the formation of ordinary neutron stars because the heat generated during their birth acts as a barrier to the denser state.

The study does not rule out the existence of twin stars entirely, but it places a strict condition on their formation. It suggests that for a twin star to form, the process must involve a way to remove heat almost instantly, a condition that is unlikely to be met by standard astrophysical processes like the collapse of a white dwarf or the shaking of a neutron star. The researchers conclude that the mere existence of a more tightly bound equilibrium state is not enough to guarantee that nature will find it. The path matters just as much as the destination. If the journey generates too much heat that cannot be shed quickly enough, the star will never reach the twin star branch, regardless of how much more stable it might be. This work provides a unified explanation for why previous simulations consistently produced neutron stars instead of twin stars, highlighting that the dynamics of heat and cooling are just as important as the static laws of gravity in determining the fate of the densest objects in the cosmos.