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A recent presents a new model for quark star merger ejecta that could resolve whether these cosmic collisions generate ordinary matter or something different.

The existence of quark stars has puzzled astronomers for decades, since they were first theorized in the 1970s. These hypothetical objects, made of deconfined quark matter rather than normal nuclear matter, bear an uncanny resemblance to neutron stars.

Even with precise measurements from gravitational wave detectors and X-ray observations, quark stars fit within the same observational constraints as their nuclear counterparts, making them nearly impossible to distinguish.

When the binary neutron star merger GW170817 was detected in 2017, it produced a brilliant kilonova, an electromagnetic radiation powered by radioactive decay of heavy elements formed through r-process nucleosynthesis in the neutron-rich ejecta.

The key uncertainty is whether quark star mergers would produce the same neutron-rich environment and kilonova signature, or something entirely different.

"Usually, people think that quark star mergers would be similar to neutron star mergers, since after decompression one would obtain normal nuclear matter," said Zhiqiang Miao, a postdoctoral researcher at Tsung-Dao Lee Institute, Shanghai Jiao Tong University, and first author of the study.

"But is this really the case? For example, when a big rock is smashed, it does not turn into a gas of atoms, molecules, and plasma, but rather breaks into sand-like fragments."

The overlooked saturation effect

Previous studies suggested that quark nuggets (small droplets of quark matter ejected during mergers) would efficiently evaporate into individual nucleons (protons and neutrons), creating a neutron-rich environment capable of producing heavy elements.

These calculations, which used formalism originally developed for the early universe, failed to account for a critical physical process: saturation.

The system reaches saturation once quark nuggets and the ambient nucleon gas achieve equilibrium. Here, nucleons evaporate from the nuggets and are reabsorbed at the same rate, essentially ending net evaporation.

Where particles are constantly colliding in this dense environment, saturation might happen exceptionally fast, potentially much faster than the timescale on which the ejecta expands.

If saturation occurs quickly enough, it would dramatically suppress evaporation, meaning that many quark nuggets could survive rather than converting completely into nucleons. This would fundamentally change the composition of the ejecta and, consequently, whether r-process nucleosynthesis could occur.

Modeling ejecta evolution

To properly account for saturation and other overlooked effects, the team performed the first calculation of the non-equilibrium equation of state for decompressed quark matter at finite temperature.

Their model tracks three crucial physical processes as the ejecta expands and cools: quark nugget evaporation, nugget cooling, and weak interactions that convert neutrons to protons and vice versa.

"In fact, the main challenge is not the technical calculation of the non-equilibrium equation of state itself, but rather in constructing the right physical picture," said Miao. "Once such a picture is established, the calculations become relatively straightforward."

The evaporation and absorption rates both depend on temperature, making cooling calculations essential for understanding how the system evolves.

Weak interactions add another layer of complexity. Neutrons and protons behave very differently during reabsorption because protons are electrically charged and must overcome a Coulomb barrier of several MeV to re-enter the nuggets, while neutrons face no such obstacle.

"Because protons are charged, their absorption is strongly suppressed," Miao noted. "Therefore, weak interactions are also important, since they allow protons and neutrons in the environment to convert into each other, further shaping the composition of the ejecta."

At temperatures around 10 MeV, typical during ejecta expansion, neutrons are reabsorbed far more efficiently than protons. This asymmetry leads to a counterintuitive buildup of protons in the gas phase, particularly when nuggets are stable enough to resist evaporation.

The researchers applied their model to simulated quark star mergers, tracking how the ejecta evolves as it expands and cools, from initial densities around 10¹² g/cm³ down to temperatures of 1 MeV, where nucleosynthesis begins.

Three possible outcomes

The team's calculations revealed that quark star mergers don't have a single, predictable outcome. Instead, the fate of the ejecta depends critically on one parameter: the binding energy of quark matter, which is the energy required to release a neutron from bulk quark matter.

The researchers found that saturation occurs in 10^-11 seconds in the dense merger environment—orders of magnitude faster than the ejecta expansion timescale of 10^-3 seconds or longer. This rapid saturation dramatically suppresses evaporation, but the degree to which nuggets survive depends on the binding energy.

For binding energies below approximately 20–30 MeV, quark nuggets evaporate completely despite saturation effects. The resulting gas is neutron-rich, similar to neutron star merger ejecta, and can produce heavy elements through r-process nucleosynthesis. This scenario would generate red or blue kilonovae.

For binding energies above approximately 50 MeV, the outcome changes dramatically. Most of the mass remains locked in quark nuggets, with only a small fraction existing as gas, and that gas becomes extremely proton-rich.

"For relatively large binding energies of quark matter, the merger ejecta are composed mainly of massive quark nuggets plus a small fraction of nucleons, which is very different from the nucleon gas produced from neutron star mergers," Miao explained.

"Because the ejecta are dominated by nuggets, they cannot efficiently undergo nucleosynthesis to form heavy elements. As a result, they would not produce the kilonova emission that is powered by the decay of such heavy elements."

The team tested their model against realistic merger simulations, analyzing over 1,000 different fluid elements as they evolved post-merger. The results confirmed this three-outcome framework across different initial conditions and temperatures.

Conclusion

The findings offer a potential way to finally distinguish quark stars from neutron stars through kilonova observations.

"The implications of kilonova observations regarding quark stars consist of two complementary perspectives," explained Miao.

"On the one hand, the detection of a kilonova signal—if attributed to a quark star merger—can help constrain quark matter properties. On the other hand, the non-detection of kilonovae for sufficiently nearby 'neutron star' mergers could potentially serve as evidence supporting the existence of quark stars."

As future gravitational wave detectors discover more compact binary mergers, electromagnetic follow-up observations will be critical. The presence or absence of kilonovae from nearby mergers could finally resolve whether quark stars exist.

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