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A canonical neutron star with a quarkyonic core leaves a distinct fingerprint in its mass–radius slope and central sound speed, and future radius measurements can find it.

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Quarkyonic equations of state pass current neutron-star constraints, and the mass–radius slope versus central sound-speed plane may observationally identify stars with a quarkyonic core.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection Solid Bayesian test of the quarkyonic EoS, but the claimed clean hadronic/quarkyonic separation is not established because both populations come from the same model. the 2 major comments →

arxiv 2510.23405 v3 pith:PXJKMFLV submitted 2025-10-27 nucl-th astro-ph.HEgr-qc

Observable Signatures of a Quarkyonic Phase in Neutron Stars

Probit J Kalita , Tuhin Malik , Tianqi Zhao , Bharat Kumar , James M. Lattimer This is my paper
classification nucl-th astro-ph.HEgr-qc PACS 26.60.Kp97.60.Jd
keywords quarkyonic matterneutron starsequation of statemass–radius relationsound speedBayesian inferencephase transitiondense matter
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether a neutron star's observable mass–radius curve can reveal a quarkyonic phase in its core. It shows that a quarkyonic equation-of-state model, constrained by all current multimessenger observations, can satisfy every existing bound while still allowing a quarkyonic core. The key result is a two-observable fingerprint: canonical-mass stars with quarkyonic cores cluster at high central sound speed (c_s^2 ≳ 0.4) and positive dR/dM, cleanly separated from purely nucleonic stars in the same model family. If a real star is found in that region, the authors argue it would be strong evidence for a quarkyonic or similar crossover transition. The diagnostic is testable with next-generation radius measurements.

Core claim

The paper claims that quarkyonic matter, a conjectured state where nucleons occupy a thin shell near the Fermi surface while quarks fill the deeper Fermi sea, can form the core of neutron stars while still passing all current astrophysical constraints. Its central discovery is a clean separation in the plane of the mass–radius slope dR/dM at a fixed mass versus the central sound speed squared c_s^2: canonical 1.4 solar-mass stars with a quarkyonic core have high central sound speed (c_s^2 ≳ 0.4) and a positive slope, while purely nucleonic stars have lower sound speed and negative or small slope. Observing a neutron star in the quarkyonic region would therefore provide strong evidence for a

What carries the argument

Quarkyonic matter: dense matter in which nucleons are color-singlet quasiparticles confined to a thin shell near the Fermi surface, while quarks fill deeper momentum states and dominate the bulk thermodynamics while remaining globally confined. The argument is carried by the slope of the mass–radius relation, dR/dM, evaluated at a fixed stellar mass (especially 1.4 solar masses), plotted against the central sound speed squared c_s^2. The transition density ρ_t controls when the sound speed rises sharply; when the central density exceeds ρ_t, the core stiffens, producing a positive dR/dM and high c_s^2. Bayesian inference over seven model parameters, constrained by pulsar timing, gravitationa

Load-bearing premise

The 'hadronic' population in the comparison is generated from the same quarkyonic equation-of-state family with the transition density above the central density, and the paper assumes this subset represents all purely nucleonic equations of state; if conventional nucleonic equations of state also give high central sound speed and positive dR/dM at canonical mass, the claimed clean separation and strong evidence for a quarkyonic core collapse.

What would settle it

Measure the mass–radius slope at 1.4 solar masses using two precise radius measurements of pulsars with different masses, and infer the central sound speed from the same stars (via asteroseismology or equation-of-state reconstruction). If a star with central c_s^2 ≳ 0.4 shows a negative dR/dM, or if a purely nucleonic equation of state with strong vector repulsion is demonstrated to occupy the region (dR/dM > 0, c_s^2 > 0.4), the claimed separation fails. A precise determination that a 1.4 solar-mass neutron star has radius below about 11.5 km would also conflict with the quarkyonic models' pr

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A neutron star with central sound speed squared above about 0.4 and a positive mass–radius slope at canonical mass would be strong evidence for a quarkyonic or quarkyonic-like phase in its core.
  • The signature is directly testable: two precise radius measurements at different masses (for example around 1.4 and 2.0 solar masses) can estimate dR/dM, and the central sound speed can be inferred from asteroseismology or equation-of-state reconstruction.
  • The radius difference R_2.0 - R_1.4 correlates strongly with dR/dM, so it can serve as a proxy and reduces the required accuracy in individual radius measurements.
  • Among single observables, the central sound speed shows a bimodal distribution and is the best discriminator between hadronic and quarkyonic compositions; radius alone is not sufficient because the radius distributions overlap.
  • Tightening the maximum neutron-star mass limit shifts the inferred quarkyonic transition density to higher values, so future high-mass pulsar discoveries will sharpen the predictions of the model family.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The separation in the dR/dM–c_s^2 plane likely reflects a general stiffening mechanism, not a unique quarkyonic signature: any crossover to a phase with a rapid rise in sound speed might populate a similar region, so the diagnostic could be a probe of exotic cores more broadly than the paper claims.
  • The paper's 'hadronic' comparison population is drawn from the same equation-of-state family with transition density above the central density; if fully independent nucleonic equations of state with strong vector repulsion also yield c_s^2 > 0.4 and positive dR/dM at 1.4 solar masses, the clean separation and the 'strong evidence' conclusion would weaken.
  • A natural extension is to compute the same diagnostic plane for hybrid stars with first-order quark transitions or hyperonic equations of state; the paper only contrasts with one class of NJL hybrid models, and overlap or separation in those cases would determine whether the signature is specific to quarkyonic matter.
  • Because the radius distributions overlap, future detections will need to combine slope and sound-speed information; this raises the practical requirement for reliable asteroseismological or machine-learning-based sound-speed inference rather than a single radius measurement.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper performs a Bayesian inference on the Zhao–Lattimer quarkyonic equation-of-state (EoS) model, using NICER mass–radius measurements, GW170817 tidal deformability, and χEFT pure-neutron-matter constraints as likelihoods (Eqs. 1–5). The authors find that quarkyonic EoSs can satisfy all current constraints, and they examine whether canonical (1.4 M_sun) neutron stars contain a quarkyonic core by comparing the transition density ρ_t with the central density. They propose a novel observational signature: plotting the slope dR/dM at fixed mass against the central sound speed c_s^2 (Figs. 3–4) separates 'hadronic' stars (green) from 'quarkyonic' stars (magenta). They conclude that a star with central c_s^2 ≳ 0.4 and positive dR/dM at 1.4 M_sun would be strong evidence for a quarkyonic or similar crossover phase.

Significance. If the claimed separation were robust, the dR/dM–c_s^2 plane would be a valuable, directly testable observable connection to dense-matter microphysics. The Bayesian framework is standard and the posterior distributions appear internally consistent; the paper also provides a well-defined model prediction. However, the central claim of uniqueness—that the magenta region is populated only by quarkyonic or crossover-type EoSs—is not supported by the analysis as presented, because the 'hadronic' comparison is not an independent nucleonic EoS ensemble. The paper's significance therefore rests on a single model family, and the proposed 'strong evidence' claim requires additional validation against conventional nucleonic EoSs.

major comments (2)
  1. [Results, Figs. 3-4] The 'hadronic' population is not an independent set of purely nucleonic EoSs; it is the subset of the same seven-parameter quarkyonic model with ρ_t above the central density of the 1.4 M_sun star. The statement that 'hadronic NSs' have c_s^2 between 0.2 and 0.4 is a property of this subset, not of all nucleonic EoSs. Conventional nucleonic models with strong vector repulsion can produce central c_s^2 > 0.4 at canonical mass while remaining purely hadronic. Without adding a posterior sample of independent nucleonic EoSs subjected to the same observational constraints, the claimed 'distinct regions' and the abstract's 'strong evidence' for a quarkyonic phase do not follow. The authors should either include such a comparison or restate the conclusion as consistency of the quarkyonic model with observations, not evidence for quarkyonic matter.
  2. [Fig. 3 and accompanying text] The paper states that mapping the c_s^2–dR/dM space results in 'distinct regions' and that a star in the magenta region would be evidence. However, the 95-percentile lines in Fig. 3 are population bounds, and the two posterior populations overlap in their tails. For a single star with finite measurement uncertainties, one needs the probability that a true quarkyonic star falls in the green region and vice versa. The paper does not provide a confusion matrix or quantify the separation as a function of measurement precision, so the proposed test is not yet a well-defined observational discriminator. This should be quantified with e.g. false-positive/false-negative rates for representative measurement uncertainties.
minor comments (3)
  1. [Abstract/Results] The abstract says 'c_s^2 ~ 0.4' while the text uses 'c_s^2 ≳ 0.4'; please make the threshold notation consistent.
  2. [Table I] The parameter 'γ1 term in interaction potential' is not defined in the letter; readers should be referred explicitly to the relevant equation in Ref. [13] or given a brief functional form.
  3. [Fig. 5 caption] The caption mentions Set α, β, γ distributions but does not define the line styles; please specify in the caption or text.

Circularity Check

0 steps flagged

No significant circularity: the predicted dR/dM and central sound-speed signatures are computed from posterior TOV solutions, not fitted to the signature itself.

full rationale

The derivation is self-contained given the assumed quarkyonic EoS model. The seven parameters (Table I) are constrained by a likelihood built from chiEFT, GW170817 tidal data, and NICER mass/radius data; the signatures (dR/dM and central c_s^2) are computed afterwards from TOV solutions and do not appear in the likelihood. The hadronic-vs-quarkyonic split is defined physically by whether the quarkyonic transition density rho_t exceeds the central density of the 1.4 M_sun solution, not by the plotted signature. Thus the separation in Figs. 3-4 is a genuine conditional prediction of the model, not a fit to the signature. The self-citation [13] supplies the model construction and is not invoked as a uniqueness proof or as a way to forbid alternative EoSs. The reader's concern that the 'hadronic' comparison set is drawn from the same quarkyonic family is a robustness/external-validity limitation, not a circularity: the paper's central claim is conditional on the model family, and no equation or fitted parameter is equivalent by construction to the predicted signature.

Axiom & Free-Parameter Ledger

7 free parameters · 5 axioms · 0 invented entities

The central claim rests on the seven fitted EoS parameters and on the prior quarkyonic model of Ref. [13]. No new particles or forces are introduced. The empirical content beyond the priors comes from NICER, GW170817, and χEFT.

free parameters (7)
  • Quarkyonic transition density ρ_t = 0.405 fm^{-3} (Set β median)
    Flat prior [0.18,0.8] fm^{-3}; constrained by all data; determines whether a 1.4 M_sun star has a quarkyonic core.
  • QCD scale parameter Λ_QCD = 933.8 MeV (Set β median)
    Flat prior [10,2000] MeV; weakly constrained by data.
  • Symmetry energy at saturation J = 32.10 MeV (Set β median)
    Gaussian prior 32.5±2.5 MeV; posterior stays near prior.
  • Symmetry energy slope L = 53.25 MeV (Set β median)
    Flat prior [20,100] MeV; constrained by NICER and χEFT data.
  • Incompressibility K = 229.5 MeV (Set β median)
    Gaussian prior 230±40 MeV; posterior stays near prior.
  • Binding energy BE/A = 16.00 MeV (Set β median)
    Gaussian prior 16±0.2 MeV; posterior stays near prior.
  • Interaction potential exponent γ1 = 1.77 (Set β median)
    Flat prior [0.5,5.0]; constrained by data.
axioms (5)
  • domain assumption The Zhao–Lattimer quarkyonic EoS model (Ref. [13]) is a valid description of cold dense NS matter.
    The EoS family and its parameters are taken from prior work by two of the authors; no independent derivation is given here. All signatures inherit this model's structure.
  • standard math TOV equations and the Hinderer tidal formalism map EoS → M(R) and M(Λ).
    Standard general-relativistic stellar structure; used to compute observables in Fig. 2.
  • domain assumption The likelihood factorizes over the independent data sets (Eq. 1).
    Assumes NICER, GW170817, and χEFT are statistically independent; any covariance would change posteriors.
  • domain assumption A canonical NS is classified as quarkyonic iff its central density exceeds the fitted ρ_t.
    This defines the green/magenta separation in Figs. 3, 4, and 7; the separation is a property of this classification rule.
  • domain assumption The posterior sample after causality and Mmax ≥ 1.97 M_sun cuts is representative of all allowed quarkyonic EoSs.
    The inference explores the 7-D parameter space with nested sampling, but convergence and prior boundaries are not independently verified here.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Observable Signatures of a Quarkyonic Phase in Neutron Stars." pith.science (2026). https://pith.science/paper/PXJKMFLV

@misc{pith2026251023405,
  author       = {Pith},
  title        = {Pith review of: Observable Signatures of a Quarkyonic Phase in Neutron Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PXJKMFLV}},
  note         = {Machine review of arXiv:2510.23405}
}
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read the original abstract

Quarkyonic matter in \(\beta\)-equilibrium is a potential description of cold dense matter in neutron stars (NSs), that introduces non-interacting quarks alongside nucleons and leptons in NS cores. In this paper, we impose observational and theoretical constraints on the model to perform Bayesian inference on it, and find that it is possible to have quarkyonic matter equations of state that satisfy all current astrophysical observations, thereby reinforcing the argument for its use alongside traditional ones. To differentiate between NSs where a quarkyonic phase does and does not appear in the core, we identify some novel signatures based on the mass-radius relation. Focusing on canonical (\(1.4\ \mathrm{M_\odot}\)) NSs, we find the populations of NSs with and without quarkyonic cores show separability on the basis of the slope and curvatures of the mass-radius curve, the central sound speed of the star, and the radius difference between two NSs of \(2\ \mathrm{M_\odot}\) and \(1.4\ \mathrm{M_\odot}\). Our results indicate that observing a neutron star with these signatures matching the values for quarkyonic core NSs would provide a strong evidence for the existence of a quarkyonic phase or a similar crossover transition in its core.

Figures

Figures reproduced from arXiv: 2510.23405 by Bharat Kumar, James M. Lattimer, Probit J Kalita, Tianqi Zhao, Tuhin Malik.

Figure 1
Figure 1. Figure 1: FIG. 1. Correlation corner-plot of the seven parameters con [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. 1-dimensional posteriors at 90% confidence interval of, (a) pressure on energy density grid, (b) radius on mass grid, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Slope of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Probability distributions of the log-likelihoods of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Corner-plot showing correlations between NS and nuclear matter properties for the three result sets. The off-diagonal [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Histograms of d [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

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Reference graph

Works this paper leans on

51 extracted references · 2 linked inside Pith · cited by 1 Pith paper

  1. [1]

    P. B. Demorest, T. Pennucci, S. M. Ransom, M. S. E. Roberts, and J. W. T. Hessels, Nature467, 1081 (2010)

    2010

  2. [2]

    Antoniadis et al., Science340, 6131 (2013)

    J. Antoniadis et al., Science340, 6131 (2013)

    2013

  3. [3]

    Abbott et al., Phys

    B. Abbott et al., Phys. Rev. Lett.121, 161101 (2018)

    2018

  4. [4]

    Drischler, S

    C. Drischler, S. Han, J. M. Lattimer, M. Prakash, S. Reddy, and T. Zhao, Phys. Rev. C103, 045808

  5. [5]

    I. Tews, J. Carlson, S. Gandolfi, and S. Reddy, Astrophys. J.860, 149 (2018)

    2018

  6. [6]

    McLerran and S

    L. McLerran and S. Reddy, Phys. Rev. Lett.122, 122701 (2019)

    2019

  7. [7]

    Brandes, W

    L. Brandes, W. Weise, and N. Kaiser, Physical Review D 107, 014011 (2023)

    2023

  8. [8]

    Biswas and S

    B. Biswas and S. Rosswog, Physical Review D112, 023045 (2025)

    2025

  9. [9]

    McLerran and R

    L. McLerran and R. D. Pisarski, Nucl. Phys. A796, 83 (2007)

    2007

  10. [10]

    Hidaka, L

    Y. Hidaka, L. D. McLerran, and R. D. Pisarski, Nucl. Phys. A808, 117 (2008)

    2008

  11. [11]

    Fujimoto, T

    Y. Fujimoto, T. Kojo, and L. D. McLerran, Phys. Rev. Lett.132, 112701 (2024)

    2024

  12. [12]

    Fujimoto, T

    Y. Fujimoto, T. Kojo, and L. McLerran, Quarkyonic mat- ter pieces together the hyperon puzzle (2024)

    2024

  13. [13]

    Zhao and J

    T. Zhao and J. M. Lattimer, Phys. Rev. D102, 023021 (2020)

    2020

  14. [14]

    Ferreira and C

    M. Ferreira and C. Providˆ encia, Physical Review D112, 083058 (2025)

    2025

  15. [15]

    Bauswein, A

    A. Bauswein, A. Nikolaidis, G. Lioutas, H. Kochankovski, P. Char, C. Mondal, M. Oertel, L. Tolos, N. Chamel, and S. Goriely, Stellar properties indicating the presence of hyperons in neutron stars (2025)

    2025

  16. [16]

    Cartaxo, C

    J. Cartaxo, C. Huang, T. Malik, S. Sourav, W.-L. Yuan, T. Zhou, X. Liu, and C. Providˆ encia, A Complete Sur- 7 2.24+0.155 −0.122 2.14+0.094 −0.079 2.08+0.042 −0.045 11 12 13 14 15 R1.4 13.23+0.619 −0.665 12.37+0.569 −0.457 12.18+0.609 −0.429 400 800 1200Λ 1.4 663.06+242.182 −190.924 426.82+122.669 −87.704 372.91+106.917 −66.727 0.2 0.4 0.6 0.8 1.0 c2 s,c...

    2025

  17. [17]

    S. K. Greif, G. Raaijmakers, K. Hebeler, A. Schwenk, and A. L. Watts, Mon. Not. Roy. Astron. Soc.485, 5363 (2019)

    2019

  18. [18]

    Raaijmakers et al., Astrophys

    G. Raaijmakers et al., Astrophys. J. Lett.893, L21 (2020)

    2020

  19. [19]

    Raaijmakers et al., Astrophys

    G. Raaijmakers et al., Astrophys. J. Lett.887, L22 (2019)

    2019

  20. [20]

    Raaijmakers, S

    G. Raaijmakers, S. K. Greif, K. Hebeler, T. Hinderer, S. Nissanke, A. Schwenk, T. E. Riley, A. L. Watts, J. M. 8 TABLE II. Median and 2σconfidence limits for neutron star and nuclear matter properties from the three constrained sets. SetαSetβSetγ 2σCI2σCI2σCI Quantity Median Min Max Median Min Max Median Min Max ρt (fm−3) 0.345 0.198 0.774 0.405 0.240 0.7...

    2021

  21. [21]

    Buchner, JOSS6, 3001 (2021)

    J. Buchner, JOSS6, 3001 (2021)

    2021

  22. [22]

    T. E. Riley et al., Astrophys. J. Lett.887, L21 (2019)

    2019

  23. [23]

    T. E. Riley et al., Astrophys. J. Lett.918, L27 (2021)

    2021

  24. [24]

    Huth et al., Nature606, 276 (2022)

    S. Huth et al., Nature606, 276 (2022)

    2022

  25. [25]

    Choudhury et al., Astrophys

    D. Choudhury et al., Astrophys. J. Lett.971, L20 (2024)

    2024

  26. [26]

    Mauviard et al., A NICER view of the 1.4 solar-mass edge-on pulsar PSR J0614–3329 (2025)

    L. Mauviard et al., A NICER view of the 1.4 solar-mass edge-on pulsar PSR J0614–3329 (2025)

    2025

  27. [27]

    Fan, M.-Z

    Y.-Z. Fan, M.-Z. Han, J.-L. Jiang, D.-S. Shao, and S.-P. Tang, Phys. Rev. D109, 043052 (2024)

    2024

  28. [28]

    Shao, S.-P

    D.-S. Shao, S.-P. Tang, X. Sheng, J.-L. Jiang, Y.-Z. Wang, Z.-P. Jin, Y.-Z. Fan, and D.-M. Wei, Phys. Rev. D101, 063029 (2020)

    2020

  29. [29]

    R. C. Tolman, Phys. Rev.55, 364 (1939)

    1939

  30. [30]

    J. R. Oppenheimer and G. M. Volkoff, Phys. Rev.55, 374 (1939)

    1939

  31. [31]

    Hinderer, Astrophys

    T. Hinderer, Astrophys. J.677, 1216 (2008)

    2008

  32. [32]

    Hinderer, B

    T. Hinderer, B. D. Lackey, R. N. Lang, and J. S. Read, Phys. Rev. D81, 123016 (2010)

    2010

  33. [33]

    Annala, T

    E. Annala, T. Gorda, A. Kurkela, J. N¨ attil¨ a, and A. Vuorinen, arXiv:1903.09121 [astro-ph.HE]16, 907 (2020)

    Pith/arXiv arXiv 1903

  34. [34]

    Altiparmak, C

    S. Altiparmak, C. Ecker, and L. Rezzolla, Astrophys. J. Lett.939, L34 (2022)

    2022

  35. [35]

    LIGO-P1800115-v12: GW170817: Measurements of Neutron Star Radii and Equation of State

  36. [36]

    Abbott et al., Phys

    B. Abbott et al., Phys. Rev. X9, 011001 (2019)

    2019

  37. [37]

    Tang, Y.-J

    S.-P. Tang, Y.-J. Huang, and Y.-Z. Fan, Physical Review D112, 083009 (2025)

    2025

  38. [38]

    Albino, T

    M. Albino, T. Malik, M. Ferreira, and C. Providˆ encia, A Bayesian Inference of Hybrid Stars with Large Quark Cores (2025)

    2025

  39. [39]

    B. S. Sathyaprakash, B. F. Schutz, and C. Van Den Broeck, Class. Quantum Grav.27, 215006 (2010)

    2010

  40. [40]

    Sathyaprakash et al., Class

    B. Sathyaprakash et al., Class. Quantum Grav.29, 124013 (2012)

    2012

  41. [41]

    Begnoni, S

    A. Begnoni, S. Anselmi, M. Pieroni, A. Renzi, and A. Ric- ciardone, Detectability and Parameter Estimation for Einstein Telescope Configurations with GWJulia (2025). 9

    2025

  42. [42]

    Maggiore et al., J

    M. Maggiore et al., J. Cosmol. Astropart. Phys.2020 (03), 050

    2020

  43. [43]

    Baibhav, E

    V. Baibhav, E. Berti, and V. Cardoso, Phys. Rev. D101, 084053 (2020)

    2020

  44. [44]

    Zhang, Y

    C. Zhang, Y. Gong, B. Wang, and C. Zhang, Phys. Rev. D103, 104066 (2021)

    2021

  45. [45]

    J. I. Thorpe, S. T. McWilliams, B. J. Kelly, R. P. Fahey, K. Arnaud, and J. G. Baker, Class. Quantum Grav.26, 094026 (2009)

    2009

  46. [46]

    B laut, Phys

    A. B laut, Phys. Rev. D83, 083006 (2011)

    2011

  47. [47]

    Jaikumar, A

    P. Jaikumar, A. Semposki, M. Prakash, and C. Con- stantinou, Phys. Rev. D103, 123009 (2021)

    2021

  48. [48]

    Han, S.-P

    M.-Z. Han, S.-P. Tang, and Y.-Z. Fan, Astrophys. J.950, 77 (2023)

    2023

  49. [49]

    S. M. A. Imam, T. Malik, C. Providˆ encia, and B. K. Agrawal, Physical Review D109, 103025 (2024)

    2024

  50. [50]

    Malik, V

    T. Malik, V. Dexheimer, and C. Providˆ encia, Phys. Rev. D110, 043042 (2024), arXiv:2404.07936 [nucl-th]

    Pith/arXiv arXiv 2024

  51. [51]

    Li and W.-J

    B.-A. Li and W.-J. Xie, Phys. Rev. C104, 034610

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.