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Quarkyonic Neutron Stars as Candidates for the GW230529 Mass-Gap Object

This paper proposes that the heavier component of the GW230529 gravitational-wave event, which falls within the mass gap, could plausibly be a massive quarkyonic neutron star rather than a low-mass black hole, as quarkyonic equations of state predict stable configurations in the $2.5$- $4.5\,M_\odot$ range with radii of approximately $13$-$15$ km.

Original authors: Jeet Amrit Pattnaik, S. K. Patra

Published 2026-02-20

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CC BY 4.0

Original authors: Jeet Amrit Pattnaik, S. K. Patra

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant cosmic construction site. For decades, astronomers have been trying to figure out what the "bricks" of the universe are made of, especially inside the most extreme buildings of all: Neutron Stars.

These stars are like cosmic diamonds the size of a city but with the mass of our entire Sun. They are so dense that a single teaspoon of their material would weigh a billion tons on Earth.

The Mystery: The "Missing Middle"

For a long time, astronomers thought they had a clear rule for how heavy these stars could get.

The Heavy Neutron Stars: The heaviest ones we knew of weighed about 2.3 times the mass of our Sun.
The Light Black Holes: The lightest black holes we knew of weighed about 5 times the mass of our Sun.

This left a weird "gap" in the middle, between 2.5 and 5 solar masses. It was like having a shelf where you could only put small boxes or giant crates, but nothing in between.

Then, in 2023, a new gravitational wave event called GW230529 happened. Two objects crashed into each other. One was a normal neutron star, but the other was a mystery object weighing between 2.5 and 4.5 times the Sun's mass.

This was the "Mass Gap" object. Was it a tiny black hole? Or was it a super-heavy neutron star that broke the rules?

The New Theory: The "Quarkyonic" Star

This paper proposes a new idea to solve the mystery. The authors suggest that this heavy object isn't a black hole at all. Instead, it might be a Quarkyonic Neutron Star.

To understand this, let's use an analogy:

The Crowd in a Stadium
Imagine a neutron star as a packed stadium.

Normal Neutron Stars: The seats are filled with "fans" (protons and neutrons) sitting in their assigned spots. They push against each other, but they stay in their seats. This creates a certain amount of pressure.
The Problem: If you try to pack too many fans in, the stadium walls (gravity) crush the whole thing into a black hole. The fans can't push back hard enough to stop the collapse.
The Quarkyonic Solution: Now, imagine that as the crowd gets denser, the fans start to realize they don't actually need to stay in their seats. They start to "melt" into a super-dense, energetic soup of their own parts (called quarks).
- In this "Quarkyonic" state, the fans aren't just sitting; they are vibrating and moving with incredible energy, creating a massive amount of extra pressure.
- Think of it like a spring. A normal spring is stiff, but a "quarkyonic spring" is like a super-spring made of steel and rubber combined. It pushes back much harder against gravity.

What the Paper Found

The authors used complex math (like a cosmic calculator) to model this "super-spring" behavior. They tested different scenarios to see if a star made of this "Quarkyonic" stuff could survive at the weight of the GW230529 mystery object.

Here is what they discovered:

It Works: When they added this "Quarkyonic" pressure, the stars could get much heavier without collapsing. They found stable stars weighing up to 2.95 times the Sun's mass.
The Size: Even though these stars are super heavy, they aren't tiny. They are still about 13 to 15 kilometers wide (roughly the size of a small city). This fits perfectly with what we expect from a neutron star, not a black hole (which would be smaller and invisible).
The Sweet Spot: The math shows that for this to happen, the transition from "normal fans" to "quarkyonic soup" needs to happen at a specific density inside the star. The paper found that if this transition happens early enough, the star can support the extra weight.

The Conclusion: A New Identity for GW230529

The authors conclude that the heavy object in the GW230529 event was likely not a black hole.

Instead, it was probably a Quarkyonic Neutron Star—a super-dense, super-stiff star that managed to hold its own against gravity by turning its internal matter into a high-pressure "quarkyonic" state.

In simple terms:
The universe didn't break the rules; we just didn't know about the "super-spring" inside the star yet. This "Quarkyonic" material acts like a hidden support beam, allowing a neutron star to grow much heavier than we thought possible, filling in that mysterious "Mass Gap" and proving that nature is even more creative than we imagined.

1. Problem Statement

The paper addresses the nature of the compact object detected in the gravitational wave event GW230529. The primary component of this merger is estimated to have a mass between 2.5 and 4.5 $M_\odot$ (solar masses) with 99% credibility. This mass range falls into the "mass gap" between the heaviest known neutron stars (NS) and the lightest known black holes (BH).

The Dilemma: Current observations suggest the lightest BH is $\sim 5 M_\odot$ , while the heaviest confirmed NS is $\sim 2.35 M_\odot$ . The GW230529 primary object is too massive to be a standard neutron star under many conventional equations of state (EOS) but too light to be a typical black hole.
The Question: Can a specific theoretical model of dense matter—Quarkyonic matter—support stable neutron star configurations within this 2.5–4.5 $M_\odot$ mass window without collapsing into a black hole?

2. Methodology

The authors employ a thermodynamically consistent, smooth crossover framework to model the Equation of State (EOS) of dense matter, rather than a sharp first-order phase transition (Maxwell or Gibbs construction).

Theoretical Framework:
- Quarkyonic Matter: Based on the model by McLerran and Reddy, extended by Zhao and Lattimer. This model posits that at high densities, baryonic degrees of freedom (nucleons) coexist with deconfined quarks, leading to a gradual crossover rather than a sudden phase change.
- Relativistic Mean Field (RMF): The hadronic sector is described using two specific parameterizations: IOPB-I and G3.
- Interpolation Scheme: Following Masuda et al. and Han et al., the pressure $P(n)$ is interpolated between the purely hadronic sector ( $P_{had}$ ) and the quarkyonic-inspired sector ( $P_{qk}$ ) using a smooth switching function involving a hyperbolic tangent ( $\tanh$ ).
- Thermodynamic Consistency: The energy density $\varepsilon(n)$ is reconstructed to satisfy the thermodynamic identity $P = n^2 \frac{\partial}{\partial n}(\frac{\varepsilon}{n})$ . This introduces an additional term $\Delta\varepsilon(n)$ to ensure the EOS remains physically valid during the crossover.
Key Parameters:
- Transition Density ( $n_t$ ): The central density where quarkyonic effects begin to dominate. Values tested: $0.3, 0.4, 0.5 \text{ fm}^{-3}$ .
- Confinement Scale ( $\Lambda_{cs}$ ): Controls the onset and strength of quark contributions. Values tested: $800$ and $1400 \text{ MeV}$ .
- Crossover Width ( $\Gamma$ ): Controls the smoothness of the transition.
Calculation:
- The authors solve the Tolman-Oppenheimer-Volkoff (TOV) equations for non-spinning, isolated neutron stars using the constructed EOSs.
- They compute Mass ( $M$ ), Radius ( $R$ ), Compactness ( $C = M/R$ ), and Dimensionless Tidal Deformability ( $\Lambda$ ).

3. Key Contributions

Smooth Crossover Implementation: The paper rigorously applies a smooth crossover model to the GW230529 problem, avoiding the unphysical discontinuities often associated with sharp hybrid star models.
Systematic Parameter Analysis: It systematically explores the impact of different nuclear force parameterizations (IOPB-I vs. G3), transition densities, and confinement scales on the maximum mass and radius.
Re-evaluation of Stiffness Hierarchy: The study reveals a non-intuitive finding: a "softer" baseline hadronic model (G3) combined with a high confinement scale can produce a stiffer total EOS at high densities than a "stiffer" baseline model (IOPB-I) with a lower confinement scale. This is due to the fractional stiffening potential of the quarkyonic sector.

4. Results

Maximum Mass ( $M_{max}$ ):
- The models successfully produce stable configurations exceeding $2.5 M_\odot$ .
- The stiffest model, (G3, $n_t=0.3, \Lambda_{cs}=1400$ ), yields a maximum mass of 2.95 $M_\odot$ with a radius of 15.16 km.
- The (G3, $n_t=0.3, \Lambda_{cs}=800$ ) model reaches 2.75 $M_\odot$ .
- Models with higher transition densities ( $n_t = 0.5 \text{ fm}^{-3}$ ) fail to reach the mass gap, with $M_{max} < 2.5 M_\odot$ .
Mass-Radius (M-R) Relations:
- Five of the tested sequences intersect the GW230529 mass window (2.5–4.5 $M_\odot$ ).
- For stars in this high-mass range, the predicted radii fall between 13 and 15 km.
- The curves show no turning points or instabilities up to the maximum mass, indicating stable configurations.
Tidal Deformability ( $\Lambda$ ):
- The canonical tidal deformability ( $\Lambda_{1.4}$ ) varies significantly across models (ranging from ~448 to ~1210), showing no strict correlation with the maximum mass in this specific quarkyonic framework.
Crossover Behavior:
- The transition is smooth; there are no abrupt plateaus in the $P(\varepsilon)$ curve.
- The "inversion" of stiffness (where G3-based models outperform IOPB-I at high densities) demonstrates that the quarkyonic contribution depends heavily on the balance between nucleonic and quark pressures at the transition density.

5. Significance and Conclusion

Resolution of the Mass Gap: The study provides a viable theoretical explanation for the GW230529 primary object. It suggests that the object could be a massive quarkyonic neutron star rather than a low-mass black hole.
Physical Implications: The results imply that matter at supranuclear densities can sustain stars significantly heavier than the traditional $2.2-2.3 M_\odot$ limit if quarkyonic degrees of freedom provide sufficient pressure support via a smooth crossover.
Constraints on EOS: The findings constrain the transition density ( $n_t$ ) to be relatively low ( $\sim 0.3 - 0.4 \text{ fm}^{-3}$ ) for such massive objects to exist. If the transition occurs at higher densities ( $n_t = 0.5 \text{ fm}^{-3}$ ), the stars collapse before reaching the mass gap.
Future Outlook: The work supports the hypothesis that the "mass gap" may not be empty but populated by exotic compact objects governed by quarkyonic dynamics, offering a new target for multi-messenger astronomy to distinguish between massive neutron stars and low-mass black holes.