Hybrid neutron stars among mass gap objects are excluded by twin stars at 1.4,M

The gist: Mass-gap hybrid stars are excluded as candidates for observed mass-gap compact objects by twin star constraints at 1.4 M⊙, according to Bayesian analysis using a generic hybrid equation of state and mass–radius constraints.

Introduction and Context

Multi-messenger astrophysics provides unprecedented insights into the internal composition of neutron stars (NSs) and properties of strongly interacting matter at extreme conditions (Koehn et al. 2025; Ascenzi et al. 2024). Gravitational wave detections from merger events have led to the detection of objects in the mass gap 2.5 ≤ M/M⊙ ≤ 5, recent examples being: GW170817 Abbott et al. (2017) with a total mass of 2.74+0.04 −0.01 M⊙, GW190814 Abbott et al. (2020) where the lighter component was an object with 2.59+0.08 − - -, and GW230529 Abac et al. (2024) with a mass of 2.5 − 4.5 M⊙ (1). The nature of these objects is unclear: are they necessarily black holes or could they be stable neutron stars? Since the mass of purely hadronic neutron stars is limited to about 2.1 M⊙ (Yamamoto et al. 2016) because of the EoS softening due to the appearance of heavier baryons such as hyperons and nuclear resonances above 2-3 saturation densities, only hybrid neutron stars could be candidates for nonblack-hole mass-gap objects (1). The question arises: Could the hybrid stars reaching the mass gap be from a third family branch (Gerlach 1968) (1).

Hybrid Equation of State and Modeling

In this letter, we shall exploit a generic form of hybrid EoS which has proven to be suitable for studies of the kind we undertake here (2). The nuclear matter phase is described in a relativistic density functional of the Walecka type (Walecka+qPauli) for the pressure PH(n) and the energy density εH(n), which has an additional repulsive term from quark Pauli blocking between nucleons that is implemented as a density-dependent shift of the nucleon chemical potentials (Blaschke et al. 2020) (2). The quark matter phase is assumed to have a constant sound speed squared (c2s = dP/dε), which appears to be a good approximation for color superconducting quark matter, where for reasonable parametrizations the range of 0.4 < c2s < 0.6 has been obtained by Contrera et al. (2022) (2). A first-order deconfinement transition is defined by its onset at the density nonset with the corresponding values of Pc = PH(nonset) and εc = εH(nonset) with a jump in energy density ∆ε = εQ(Pc)−εH(Pc), so that the resulting EoS obtains the generic form Alford et al. (2013) (2).

Mass-Radius Diagrams and Twin Stars

The mass–radius diagram shows representative examples for TOV solutions are shown in Fig. 1 together with modern mass–radius constraints from multi-messenger astronomy (2). All curves except one show the mass-twin property: there are two different star configurations with exactly the same gravitational mass, but with different radii (2). One of them lies at the maximum mass configuration of the hadronic branch (red solid line) while the more compact twin star appears on the so-called ”third family” branch of hybrid stars, which is disconnected from the hadronic one by an unstable branch (2). Following these examples, one may hypothesize that the two pulsars PSR J0437-4715 Miller et al. (2026) and PSR J0614-3329 Mauviard et al. (2025) could be examples of twin stars, but the present level of accuracy for NICER mass and radius measurements does not yet allow a firm conclusion in that respect (1).

Seidov Diagrams and Mass Gap Exclusion

In Fig. 2 we show the Seidov diagrams, i.e. density jump in units of the onset density versus onset density for the hybrid EoS (2), for three cases of squared sound speed: c2s = 0.50 (upper panel), 0.75 (middle panel), 1.00 (lower panel) (2). The black line denotes the modified Seidov instability criterion (3) as a necessary condition for the existence of third family hybrid stars and blue lines indicate maximum masses of 2.0, 2.5 and 3.0 M⊙, where that for 2.5 M⊙ is the border to the mass gap region (2). From these diagrams, one can read off, that mass gap objects (Mmax ≥ 2.5 M⊙) can be hybrid stars as they populate the lower left corner of all three Seidov diagrams (2). However, in order to find cases of third-family objects among the high-mass hybrid stars, the density jump at the deconfinement transition has to exceed the value determined by the modified Seidov criterion, which is shown by the black line in Fig. 2 (2). For typical color superconducting quark matter models (Contrera et al. 2022), c2s = 0.5, one can find mass-gap objects for all onset densities below 2.5 n0 (2). But third family members among them are just a marginal case at the left border of the Seidov diagram, for nonset = n0 and ∆n = 0.6 n0 (2).

Bayesian Analysis and Constraints

In order to take into account these M-R constraints depicted in Fig. 1, we apply the Bayesian analysis scheme described in Ayriyan et al. (2025), but with the quark matter EoS parameters (nonset, ∆n) instead of the Lagrangian model parameters for the coupling strengths in the vector meson and diquark interaction channels (ηV, ηD) of that model approach (2). The other solutions with high posterior probability correspond to onset masses with twin star solutions around 1.4 M⊙, but for these sequences maximum masses just reach beyond 2 M⊙ and cannot reach the mass gap region (2). This latter solution class could support the speculation that PSR J0614-3329 and PSR J0437-4715 (possibly including PSR J0030+0451) could be mass twin stars, see Fig. 1 (2).

Conclusion and Implications

In this letter we have shown that for a generic twoparametric hybrid neutron star EoS in dependence on the onset density and density jump at the deconfinement transition there exist parameter sets for which the maximum mass is in the mass gap region, Mmax > 2.5 M⊙ (5). These sequences belong to an early onset of deconfinement at Monset ≲ 0.7 M⊙ with onset densities 1.0 ≤ nonset/n0 ≤ 1.2 (5). Should, however, the conjecture be confirmed that the pulsars PSR J0614-3329 and PSR J0437-4715 are mass twin stars at 1.4 M⊙, then the maximum mass for such a hybrid EoS shall be limited to Mmax < 2.2 M⊙ so that the detected mass gap objects cannot be hybrid neutron stars but rather must be black holes (5).

Acknowledgments and Data Availability

This research is part of the project No. 2011/43/P/ST2/03319 co-funded by the National Science Centre and the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement no. 945339 (5). The numerical data supporting the results and figures presented in this work, including the equation-of-state, mass–radius, and Bayesian inference tables, are publicly available on Zenodo (Ayriyan et al. 2026b) (5).

References

Abac A G et al. 2024 Astrophys J Lett. 970 L34 doi:10.3847/2041-8213/ad5beb (6)

Abbott B P et al. 2017 Phys Rev Lett. 119 161101 doi:doi:https://doi.org/PhysRevLett.119.161(6)

Abbott B P et al. 2020 Astrophys J Lett. 896 L44 doi:doi:https://doi.org/10.3847/2041-8213/ab960f (6)

Alford M G & Han S 2016 Eur Phys J A 52 62 doi:doi:https://doi.org/10.1140/epja/i2016-16062-9 (3)

Alford M G Han S & Prakash M 2013 Phys Rev D 88 083013 doi:doi:https://doi.org/PhysRevD.88.

1. Use Bayesian inference schemes described by Ayriyan et al. (2025) to constrain hybrid EoS parameters, specifically applying the Bayesian analysis scheme described in Ayriyan et al. (2025), but with the quark matter EoS parameters (nonset, ∆n) instead of the Lagrangian model parameters. This allows the system to find solutions where mass gap objects are below the Seidov line and thus cannot be members of a third family branch based on observed M-R constraints.

2. Implement a predictive capability for eccentric MSP orbits by modeling an accretion-induced phase transition from a hadronic to a hybrid mass twin star, which can explain these orbits when this transition is accompanied with a gravitational mass defect ∆M/M⊙ ≈ 0.01 which induces a kick to the pulsar.

3. Develop an algorithm capable of assessing the plausibility of low onset densities for deconfinement by referencing arguments from the occupation of fermionic phase space in cold, degenerate (quarkyonic) matter, specifically noting that "due to quark exchange effects among nucleons (quark Pauli blocking, see Blaschke et al. (2020)) just above the nuclear saturation density for nT = 0.17 fm−3 = 1.13 n0 a transformation of nuclear matter to quarkyonic matter sets in."

4. Create a classifier to distinguish between compact objects based on Seidov diagram positions, identifying that mass gap objects (Mmax ≥ 2.5 M⊙) can be hybrid stars as they populate the lower left corner of all three Seidov diagrams, and further distinguishing them from third-family members by checking if they fall below the Seidov line.

5. Integrate constraints derived from mass-twin solutions, noting that if confirmed, [mass-twin stars] would rule out hybrid stars as candidates for observed mass-gap compact objects, to refine the model space and rule out certain parameter sets.

We investigate the question whether compact objects in the so-called mass gap (2.5 < M/M < 5.0) can be neutron stars or hybrid stars. Using a generic hybrid star equation of state with a first-order deconfinement transition, we map the allowed parameter space in a Seidov-type diagram and confront it with modern mass-radius constraints. We find that mass-gap hybrid stars require an extremely early onset of deconfinement and very stiff quark matter. The Bayesian analysis, however, favors equations of state with deconfinement at typical neutron-star masses around 1.4,M with mass-twin stars that, if confirmed, would rule out hybrid stars as candidates for observed mass-gap compact objects.