Pith. sign in

REVIEW 1 major objections 1 minor 89 references

Unified QMF equation of state for neutron star matter: Static and dynamic properties

T0 review · 1 major / 1 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A quark-level equation of state predicts heavier crust clusters, a higher maximum mass, and a longer direct-Urca cooling delay than the equivalent hadronic model.

desk verdict A careful, systematic QMF-vs-RMF EoS comparison with real new results, but the headline claim of longer QMF dUrca relaxation is plausible rather than proven because local dUrca emissivity and pairing gaps are not computed consistently. read the letter →

arxiv 2505.00539 v2 pith:VTWZMTON submitted 2025-05-01 nucl-th astro-ph.HE

Zhonghao Tu , Xiangdong Sun , Shuochong Han , Zhiqiang Miao , Ang Li This is my paper · ORCID
classification nucl-thastro-ph.HE
keywords neutronstarequationofstatequarkmean-fieldmodelunifiedEoScoolingdirectUrcaprocessr-modeinstabilitysymmetryenergyslopeWigner-Seitzcell
verification ladder T0 review T1 audit T2 compute T3 formal

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 constructs unified neutron-star equations of state from the quark mean-field (QMF) model, calibrated to three values of the symmetry-energy slope ($L_0 = 40, 60, 80$ MeV), and compares them with hadronic relativistic mean-field (RMF) models fitted to the same saturation properties. It seeks to show that the quark-level description changes the coherent picture of neutron-star structure: the QMF crust contains heavier nuclear clusters and larger Wigner-Seitz cells, the maximum mass is higher by about $0.13\,M_\odot$, and when the direct Urca process is open the star cools through a smaller rapid-cooling core with a longer thermal relaxation time. The paper also claims that both QMF and RMF reproduce the observed crustal cooling of the transient KS 1731-260, and that a larger $L_0$ widens the r-mode instability window while a larger stellar mass narrows it. The value of this claim is that static and dynamical neutron-star observables are traced back to one internally consistent microscopic input.

What carries the argument

The central object is the in-medium nucleon mass $M_N^*$ of the quark mean-field model, obtained by solving the Dirac equation for constituent quarks confined by a harmonic-oscillator potential in the presence of $\sigma$, $\omega$, and $\rho$ meson fields, then adding center-of-mass, pion-cloud, and one-gluon-exchange corrections. This density-dependent mass controls the proton fraction, the direct Urca threshold, neutrino emissivities, and the viscous damping that sets the r-mode window. The crust is built in the same framework by solving coupled Klein-Gordon and Poisson equations in Wigner-Seitz cells under the Thomas-Fermi approximation, with five pasta geometries, and the core is joined to it at the crust-core transition density. The paper also supplies power-law parameterizations $\log_{10}\xi = 12.9285\,L_0^{0.0767}$ and $\log_{10}\eta = 17.5192\,L_0^{-0.0028}$ for the bulk and shear viscosities at saturation density.

What would settle it

Recompute the proton $^1S_0$ and neutron $^3P_2$ critical temperatures from the Landau effective masses and proton fractions of the QMF and RMF unified EoSs and rerun the thermal evolution; if the QMF star no longer shows a longer direct-Urca relaxation time than the RMF star at the same $L_0=80$ MeV, the paper's central cooling distinction fails.

Watch

Extended reading notes

Core claim

The central claim is that the QMF model, because its in-medium nucleon effective mass $M_N^*$ approaches roughly $0.5M_N$ at high density instead of declining monotonically, suppresses the proton fraction in the dense core relative to the RMF prediction. That suppression pushes the onset density of the direct Urca process upward, so for $L_0 = 80$ MeV the QMF star has a smaller dUrca-allowed core (volume fractions $2.6\%$ versus $7.8\%$ at $1.4\,M_\odot$, and $24.7\%$ versus $33.7\%$ at $1.8\,M_\odot$) and a correspondingly longer thermal relaxation time in the cooling curve. In the crust, the stronger $\sigma$-meson field of QMF produces heavier nuclear clusters, larger Wigner-Seitz cells, and a lower outer-inner crust transition density, while the free neutron gas density remains nearly unchanged because the larger cells compensate. The paper argues that these differences leave cooling without dUrca almost model-independent, that both models fit the KS 1731-260 crustal cooling data with slightly different core temperatures and impurity parameters, and that the r-mode instability window widens with $L_0$ and narrows with stellar mass.

Load-bearing premise

The load-bearing premise is that the same nucleon pairing gaps (neutron $^3P_2$ and proton $^1S_0$) apply in both QMF and RMF cores, although these gaps depend on effective mass and proton fraction; the paper states that self-consistent critical temperatures are beyond its scope.

Editorial extensions

If this is right

  • If the QMF unified EoS is correct, neutron stars of the same mass are slightly larger and their maximum mass is about $0.13\,M_\odot$ higher than the RMF prediction with the same saturation properties.
  • For $L_0 \gtrsim 80$ MeV, the QMF model predicts that rapid cooling via direct Urca is delayed to later times; an observed late luminosity drop in a massive isolated neutron star would support the quark-level effective-mass behavior.
  • Crustal cooling transients such as KS 1731-260 do not cleanly discriminate between QMF and RMF; both reproduce the data with modest shifts in fitted core temperature and impurity parameter.
  • Larger symmetry-energy slope widens the r-mode instability window, while larger stellar mass narrows it, with the QMF model giving slightly lower critical frequencies and temperatures at high mass.
  • The approximate unified-crust treatment reproduces the full unified EoS for masses above about $0.5\,M_\odot$, so cheaper approximations can be used in parameter scans.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the cooling comparison assumes identical nucleon pairing gaps in QMF and RMF cores, a self-consistent gap calculation could shorten or reverse the predicted longer direct-Urca relaxation time; that is the natural next test.
  • The QMF suppression of the high-density proton fraction would also affect other proton-fraction-sensitive processes the paper does not model, such as ambipolar diffusion in magnetar fields or vortex pinning.
  • The saturation-density viscosity power laws are immediately usable in population-synthesis studies of r-modes, without recomputing the full unified EoS.
  • The near-degeneracy of QMF and RMF cooling curves when direct Urca is absent suggests that distinguishing the two models observationally requires either a star with $L_0$ large enough to open dUrca or very precise crust-cooling measurements.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The paper constructs unified equations of state (EoSs) within the quark mean-field (QMF) framework for three values of the symmetry energy slope L0 (40, 60, 80 MeV), with the crust and core described by the same effective Lagrangian and self-consistent compositions. The QMF unified EoSs are compared with analogous relativistic mean-field (RMF) EoSs through neutron star mass-radius relations, crust compositions (including pasta phases), thermal cooling of isolated neutron stars and of the X-ray transient KS 1731-260, and r-mode instability windows. The main reported results are that the QMF model predicts heavier nuclear clusters and larger Wigner-Seitz cells in the crust, a higher maximum mass, and, when direct Urca cooling is active (L0 ≳ 80 MeV), a longer thermal relaxation time than the RMF model, while both models can reproduce the observed crustal cooling curve of KS 1731-260. The paper also provides power-law fits for the L0 dependence of bulk and shear viscosities at saturation density.

Significance. If the main claims hold, the paper offers a useful, internally consistent set of unified EoSs that link quark-level input to neutron-star observables, including static structure, cooling, and r-mode stability. The systematic comparison between QMF and RMF at fixed saturation properties isolates the effect of the underlying many-body framework, which is valuable for the dense-matter community. Concrete strengths are the fully self-consistent crust-core construction (except for the quark-level caveat discussed below), the explicit comparison with an approximate unified-EoS method, the Markov-chain Monte Carlo fits to KS 1731-260, and the quantitative bounds on emissivity ratios for non-direct-Urca processes. However, the headline dynamical claim about longer direct-Urca relaxation time rests on volume fractions alone rather than on integrated emissivities, and the adopted approximation of identical pairing gaps in QMF and RMF cores weakens that claim. The paper is therefore a solid contribution that needs additional quantitative support for its central dynamical conclusion.

major comments (1)
  1. [Sec. II E and Sec. III B] The cooling simulations assume identical neutron 3P2 and proton 1S0 critical temperatures in the QMF and RMF cores, even though these pairing gaps depend on effective mass and proton fraction, both of which differ between the models. The paper acknowledges in Sec. IV that a fully self-consistent determination lies beyond the present scope. Because the dUrca relaxation time is sensitive to superfluidity (through suppression of neutrino emissivity and modification of specific heat), the predicted longer QMF relaxation time could be reduced or reversed if the QMF gaps differ from the RMF gaps. At minimum, please provide a sensitivity estimate (e.g., vary the adopted critical temperatures within a reasonable range and show how the cooling curves and relaxation times change) or quantify the expected difference in the core pairing gaps from the differences in effective mass and proton fraction.
minor comments (1)
  1. [Sec. III B, Fig. 5] The text says 'the QMF model predicts a longer thermal relaxation time than the RMF model' but does not define the quantitative measure of relaxation time (e.g., the time when the luminosity drop is steepest). Please specify the definition used in the context of the cooling curves.

Circularity Check

0 steps flagged · score 2.0 of 10

No material circularity: the QMF-to-NS predictions are computed from a saturation-calibrated EoS, the KS 1731-260 agreement is explicitly fit-based, and the single auxiliary self-citation (Ref. [80]) is paired with an independent reference.

full rationale

Walking the derivation chain: the QMF meson couplings are fitted to the saturation properties in Table I (rho0, E/A, K0, J0, L0, M*/MN) and then used to construct core and crust EoSs. The subsequent mass-radius, cooling, viscosity, and r-mode outputs are computed from those EoSs via the TOV equations, NSCool, crustcool, and Eqs. (29)-(41), so they are not equal to the fit inputs by construction. The KS 1731-260 crustal cooling agreement is explicitly a fit, not a prediction: the paper states 'we present the posterior distributions of the the fitting parameters—Tcore, Tt, and Qimp—in Fig. 7' and 'Fig. 8 shows the best-fit cooling curves for KS 1731-260'. Thus the fitted-input-called-prediction pattern does not apply. The longer direct-Urca relaxation-time claim is read off computed NSCool cooling curves and interpreted using 'smaller dUrca cores corresponding to longer relaxation times' with Refs. [79,80]; Ref. [80] is a self-citation, but Ref. [79] independently supports the same relation and the present cooling curves are calculated rather than imposed. The viscosity 'power-law parameterizations' are explicitly fits to the authors' own computed values and are labeled as parameterizations in the abstract, so they are not presented as independent predictions. The shared pairing-gap assumption is an acknowledged limitation ('A fully self-consistent determination of nucleon critical temperatures in the core lies beyond the scope of the present work'), not a circular definition. No equation in the paper reduces to its own input, and no central claim is forced by a self-citation chain. The score of 2 reflects only the minor auxiliary self-citation in the interpretation of the dUrca volume fractions, which is not load-bearing because an external reference and the paper's own simulations also establish the point.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central results depend on model parameters fitted to nuclear saturation data and on several phenomenological inputs (pairing gaps, envelope composition). The paper is transparent about most, but the 'unified' EoS is not fully quark-level in the crust, and the pairing gaps are shared between models despite possible model dependence.

free parameters (5)
  • L0 (symmetry energy slope) = 40, 60, 80 MeV (50, 70 MeV in Table III)
    Varied by hand to probe the L0 dependence; all other saturation properties held fixed (Table I).
  • Meson couplings (g_sigma_q, g_omega_q, g_rho_q, g2, g3, Lambda_v) = Not reported numerically; fitted to saturation properties in Table I
    Six parameters of the Lagrangian Eq. (5) are determined by reproducing rho0, E/A, K0, J0, L0, M*/MN.
  • QMF potential parameters a and V0 = Not reported; fixed by MN=939 MeV and rN=0.87 fm
    Parameters of the confinement potential U(r) in Eq. (1) are fitted to free-space nucleon properties.
  • Tcore, Tt, Qimp for KS 1731-260 fits = Values in Table III, e.g., Tcore=4.32 x 10^7 K, log10 Qimp=0.49 for QMF L0=40, M=1.4 solar mass
    Three parameters fitted via MCMC with crustcool to reproduce the observed crustal cooling curve.
  • Power-law coefficients for viscosities = log10 xi = 12.9285 L0^0.0767; log10 eta = 17.5192 L0^-0.0028
    Coefficients fitted to the authors' own computed xi and eta at saturation density (Fig. 9).
assumptions (5)
  • domain assumption Nuclear saturation properties in Table I (rho0=0.16 fm^-3, E/A=-16 MeV, K0=240 MeV, J0=31 MeV, M*/MN=0.77) are taken as empirical inputs.
    Used to fit the six meson-nucleon or meson-quark couplings; if these saturation values are inaccurate, all derived EoSs and NS properties shift.
  • domain assumption QMF model specifics from prior work: harmonic oscillator confinement potential U(r), quark mass mq=300 MeV, meson masses m_sigma=510, m_omega=783, m_rho=770 MeV.
    These are inherited parameters of the QMF model, not re-derived in this paper.
  • domain assumption Thomas-Fermi approximation and plane-wave fermion wave functions for the Wigner-Seitz cell calculations.
    Approximation for inhomogeneous crust matter; standard but not exact, and it affects the crust composition results.
  • domain assumption Identical nucleon pairing gaps for QMF and RMF: neutron 3P2 rescaled to maximum 0.5 x 10^9 K, neutron 1S0 from Ref. [57], proton 1S0 from Ref. [58].
    The paper notes these may differ between models and are not computed self-consistently (Sec. III B).
  • domain assumption Envelope composition (pure He to 10^9 g cm^-2, pure Fe to 10^12 g cm^-2) and the Te(Tb) relation of Ref. [59].
    Standard input for thermal evolution; affects surface temperature and hence the cooling curves.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Unified QMF equation of state for neutron star matter: Static and dynamic properties." pith.science (2026). https://pith.science/paper/VTWZMTON

@misc{pith2026250500539,
  author       = {Pith},
  title        = {Pith review of: Unified QMF equation of state for neutron star matter: Static and dynamic properties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VTWZMTON}},
  note         = {Machine review of arXiv:2505.00539}
}
abstract

We construct a set of unified equations of state based on the quark mean field (QMF) model, calibrated to different values of nuclear symmetry energy slope at the saturation density ($L_0$), with the aim of exploring both the static properties and dynamical behavior of neutron stars (NSs), and building a coherent picture of their internal structure. We assess the performance of these QMF models in describing the mass-radius relation, the cooling evolution of isolated NSs and X-ray transients, and the instabilities (e.g., the r-mode). In comparison to relativistic mean field (RMF) models formulated at the hadronic level, the QMF model predicts heavier nuclear clusters and larger Wigner-Seitz cell sizes in the NS crust, while the density of the free neutron gas remains largely similar between the two approaches. For the cooling of isolated NSs, the thermal evolution is found to be insensitive to both the many-body model and the symmetry energy slope in the absence of the direct Urca (dUrca) process. However, when rapid cooling via the dUrca process is allowed, in the case of large $L_0$ values (e.g., $L_0 \gtrsim 80$ MeV) in our study, the QMF model predicts a longer thermal relaxation time. Both the QMF and RMF models can reproduce cooling curves consistent with observations of X-ray transients (e.g., KS 1731--260) during their crustal cooling phase, although stellar parameters show slight variations depending on the model and symmetry energy slope. Within our unified framework, a larger $L_0$ value generally results in a wider instability window, while increasing the stellar mass tends to suppress the instability window. We also provide simple power-law parameterizations that quantify the dependence of bulk and shear viscosities on the symmetry energy slope for nuclear matter at saturation density.

Figures

Figures reproduced from arXiv: 2505.00539 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Total nucleon number [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Unified EoSs calculated using the QMF and RMF models [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Effective nucleon mass in uniform nuclear matter cal [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Mass–radius relations and (b) density profiles calculated using the QMF and RMF models for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Ratio of neutrino emissivities, summed over the mUrca and [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Cooling curves of the isolated NS based on the QMF and [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Posterior distributions of [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Light curves for KS 1731-260 based on the QMF and RMF [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Bulk (upper panel) and shear (lower panel) viscosi [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Critical frequency [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

89 extracted references · 31 canonical work pages

  1. [1]

    Neutron Matter from Low to High Density

    S. Gandolfi, A. Gezerlis, and J. Carlson, Annual Review of Nuclear and Particle Science65, 303 (2015), arXiv:1501.05675 [nucl-th]. 14

    work page Pith review arXiv 2015

  2. [2]

    Oertel, M

    M. Oertel, M. Hempel, T. Kl ¨ahn, and S. Typel, Reviews of Modern Physics 89, 015007 (2017), arXiv:1610.03361 [astro- ph.HE]

    arXiv 2017

  3. [3]

    A. L. Watts, N. Andersson, D. Chakrabarty, M. Feroci, K. Hebeler, G. Israel, F. K. Lamb, M. C. Miller, S. Morsink, F. ¨Ozel, A. Patruno, J. Poutanen, D. Psaltis, A. Schwenk, A. W. Steiner, L. Stella, L. Tolos, and M. van der Klis, Reviews of Modern Physics 88, 021001 (2016), arXiv:1602.01081 [astro- ph.HE]

    arXiv 2016

  4. [4]

    4(a), the higher pressure predicted by the QMF model at high densities leads to a larger maximum mass com- pared to the RMF model, with a difference of approximately ∆M≈ 0.13M⊙

    In Fig. 4(a), the higher pressure predicted by the QMF model at high densities leads to a larger maximum mass com- pared to the RMF model, with a difference of approximately ∆M≈ 0.13M⊙. The symmetry energy slope parameter L0 governs the behavior of the EoS in the intermediate-density regime and consequently affects t he radii of typical NSs with M = 1.4M⊙...

  5. [5]

    Since the neutrino emissivity of the dUrca process is ap- proximately 105 times higher than that of the mUrca process, this leads to rapid cooling, resulting in significant deviations from observational data. The thermal relaxation time of an NS is marked by a sharp drop in surface temperature or luminos- ity.We find that the QMF model predicts a longer t...

    2012

  6. [6]

    Yan, Research in Astronomy and Astrophysics 19, 072 (2019)

    Y . Yan, Research in Astronomy and Astrophysics 19, 072 (2019)

    2019

  7. [7]

    D. G. Yakovlev and C. J. Pethick, Annual Review of Astronomy & Astrophysics 42, 169 (2004), arXiv:astro-ph/0402143 [astro- ph]

    arXiv 2004

  8. [8]

    Haensel, Space Science Reviews 74, 427 (1995)

    P. Haensel, Space Science Reviews 74, 427 (1995)

    1995

Show all 89 references
  1. [9]

    Danielewicz, R

    P. Danielewicz, R. Lacey, and W. G. Lynch, Science 298, 1592 (2002), arXiv:nucl-th/0208016 [nucl-th]

    2002 arXiv

  2. [10]

    Adhikari, H

    D. Adhikari, H. Albataineh, D. Androic, K. A. Aniol, D. S. Armstrong, T. Averett, C. Ayerbe Gayoso, S. K. Barcus, V . Bellini, R. S. Beminiwattha, J. F. Benesch, H. Bhatt, D. Bhatta Pathak, D. Bhetuwal, B. Blaikie, J. Boyd, Q. Cam- pagna, A. Camsonne, G. D. Cates, Y . Chen, C....

    2022 arXiv

  3. [11]

    Adhikari, H

    D. Adhikari, H. Albataineh, D. Androic, K. Aniol, D. S. Arm- strong, T. Averett, C. Ayerbe Gayoso, S. Barcus, V . Bellini, R. S. Beminiwattha, J. F. Benesch, H. Bhatt, D. Bhatta Pathak, D. Bhetuwal, B. Blaikie, Q. Campagna, A. Camsonne, G. D. Cates, Y . Chen, C. Clarke, J. C. ...

    2021 arXiv

  4. [12]

    Vinciguerra, T

    S. Vinciguerra, T. Salmi, A. L. Watts, D. Choudhury, T. E. Ri- ley, P. S. Ray, S. Bogdanov, Y . Kini, S. Guillot, D. Chakrabarty, W. C. G. Ho, D. Huppenkothen, S. M. Morsink, Z. Wa- diasingh, and M. T. Wolff, Astrophys. J. 961, 62 (2024), arXiv:2308.09469 [astro-ph.HE]

    2024 arXiv

  5. [13]

    Fuchs, Progress in Particle and Nuclear Physics56, 1 (2006), arXiv:nucl-th/0507017 [nucl-th]

    C. Fuchs, Progress in Particle and Nuclear Physics56, 1 (2006), arXiv:nucl-th/0507017 [nucl-th]

    2006 arXiv

  6. [14]

    B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, V . B. Adya, C. Affeldt, M. Afrough, B. Agarwal, M. Agathos, K. Agatsuma, N. Aggarwal, O. D. Aguiar, L. Aiello, A. Ain, P. Ajith, B. Allen, G. Allen, A. Allocca, P. A...

    2017 arXiv

  7. [15]

    Nik ˇsi´c, D

    T. Nik ˇsi´c, D. Vretenar, and P. Ring, Progress in Particle and Nuclear Physics 66, 519 (2011), arXiv:1102.4193 [nucl-th]

    2011 arXiv

  8. [16]

    Salmi, D

    T. Salmi, D. Choudhury, Y . Kini, T. E. Riley, S. Vinciguerra, A. L. Watts, M. T. Wolff, Z. Arzoumanian, S. Bogdanov, D. Chakrabarty, K. Gendreau, S. Guillot, W. C. G. Ho, D. Hup- penkothen, R. M. Ludlam, S. M. Morsink, and P. S. Ray, As- trophys. J. 974, 294 (2024), arXiv:240...

    2024 arXiv

  9. [17]

    J. D. Walecka, Annals of Physics 83, 491 (1974)

    1974

  10. [18]

    H. Toki, U. Meyer, A. Faessler, and R. Brockmann, Phys. Rev. C 58, 3749 (1998). 15

    1998

  11. [19]

    Passarella, J

    L. Passarella, J. Margueron, and G. Pagliara, arXiv e-prints , arXiv:2503.23028 (2025), arXiv:2503.23028 [nucl-th]

    2025 arXiv

  12. [20]

    Shen and H

    H. Shen and H. Toki, Phys. Rev. C 61, 045205 (2000), arXiv:nucl-th/9911046 [nucl-th]

    2000 arXiv

  13. [21]

    Zhu, E.-P

    Z.-Y . Zhu, E.-P. Zhou, and A. Li, Astrophys. J.862, 98 (2018), arXiv:1802.05510 [nucl-th]

    2018 arXiv

  14. [22]

    Zhu and A

    Z.-Y . Zhu and A. Li, Phys. Rev. C 97, 035805 (2018), arXiv:1802.07441 [nucl-th]

    2018 arXiv

  15. [23]

    Z.-Y . Zhu, A. Li, J.-N. Hu, and H. Shen, Phys. Rev. C 99, 025804 (2019), arXiv:1805.04678 [nucl-th]

    2019 arXiv

  16. [24]

    Mondal and A

    A. Mondal and A. Mishra, Phys. Rev. C 110, 055201 (2024), arXiv:2407.19896 [nucl-th]

    2024 arXiv

  17. [25]

    Z. Miao, A. Li, Z. Zhu, and S. Han, Astrophys. J. 904, 103 (2020), arXiv:2006.00839 [nucl-th]

    2020 arXiv

  18. [26]

    J. Hu, Y . Zhang, and H. Shen, Journal of Physics G Nuclear Physics 49, 025104 (2022), arXiv:2104.13567 [nucl-th]

    2022 arXiv

  19. [27]

    Li and A

    J.-J. Li and A. Sedrakian, Astrophys. J. 957, 41 (2023), arXiv:2308.14457 [nucl-th]

    2023 arXiv

  20. [28]

    K. M. M. Paglinawan, A. W. Thomas, P. A. M. Guichon, and J. R. Stone, arXiv e-prints , arXiv:2504.03498 (2025), arXiv:2504.03498 [nucl-th]

    2025 arXiv

  21. [29]

    Cao, arXiv e-prints , arXiv:2504.18874 (2025), arXiv:2504.18874 [hep-ph]

    G. Cao, arXiv e-prints , arXiv:2504.18874 (2025), arXiv:2504.18874 [hep-ph]

    2025 arXiv

  22. [30]

    I. A. Rather, A. A. Usmani, and S. K. Patra, Nuclear Physics A 1010, 122189 (2021), arXiv:2009.12613 [nucl-th]

    2021 arXiv

  23. [31]

    W. M. Seif, A. S. Hashem, and H. A. Abualhamd, Journal of Physics G Nuclear Physics 51, 065203 (2024)

    2024

  24. [32]

    Fortin, C

    M. Fortin, C. Provid ˆencia, A. R. Raduta, F. Gulminelli, J. L. Zdunik, P. Haensel, and M. Bejger, Phys. Rev. C 94, 035804 (2016), arXiv:1604.01944 [astro-ph.SR]

    2016 arXiv

  25. [33]

    Schatz, Z

    H. Schatz, Z. Meisel, E. F. Brown, S. S. Gupta, G. W. Hitt, W. R. Hix, R. Jain, R. Lau, P. M¨oller, W. J. Ong, P. S. Shternin, Y . Xu, and M. Wiescher, Astrophys. J. 925, 205 (2022), arXiv:2112.11544 [astro-ph.HE]

    2022 arXiv

  26. [34]

    A. Y . Potekhin, J. A. Pons, and D. Page, Space Science Reviews 191, 239 (2015), arXiv:1507.06186 [astro-ph.HE]

    2015 arXiv

  27. [35]

    A. R. Raduta, J. J. Li, A. Sedrakian, and F. Weber, Mon. Not. R. Astron. Soc. 487, 2639 (2019), arXiv:1903.01295 [nucl-th]

    2019 arXiv

  28. [36]

    X. Zhou, A. Li, and B.-A. Li, Astrophys. J. 910, 62 (2021), arXiv:2011.11934 [astro-ph.HE]

    2021 arXiv

  29. [37]

    A. Y . Potekhin, M. E. Gusakov, and A. I. Chugunov, Mon. Not. R. Astron. Soc. 522, 4830 (2023), arXiv:2303.08716 [astro- ph.HE]

    2023 arXiv

  30. [38]

    B. J. Owen, L. Lindblom, C. Cutler, B. F. Schutz, A. Vecchio, and N. Andersson, Phys. Rev. D 58, 084020 (1998)

    1998

  31. [39]

    A. F. Fantina, N. Chamel, J. M. Pearson, and S. Goriely, As- tron. Astrophys. 559, A128 (2013)

    2013

  32. [40]

    C. C. Moustakidis, Phys. Rev. C 91, 035804 (2015)

    2015

  33. [41]

    Suleiman, M

    L. Suleiman, M. Fortin, J. L. Zdunik, and P. Haensel, Phys. Rev. C 104, 015801 (2021), arXiv:2106.12845 [astro-ph.HE]

    2021 arXiv

  34. [42]

    A. Li, Z. Miao, S. Han, and B. Zhang, Astrophys. J. 913, 27 (2021), arXiv:2103.15119 [astro-ph.HE]

    2021 arXiv

  35. [43]

    B. K. Sharma, M. Centelles, X. Vi˜nas, M. Baldo, and G. F. Bur- gio, Astron. Astrophys. 584, A103 (2015), arXiv:1506.00375 [nucl-th]

    2015 arXiv

  36. [44]

    Chamel, N

    N. Chamel, N. N. Shchechilin, and A. I. Chugunov, Phys. Rev. C 111, 015805 (2025), arXiv:2501.08075 [nucl-th]

    2025 arXiv

  37. [45]

    Tu and A

    Z. Tu and A. Li, Astrophys. J. 984, 200 (2025), arXiv:2412.09219 [nucl-th]

    2025 arXiv

  38. [46]

    Z. Miao, A. Li, and Z.-G. Dai, Mon. Not. R. Astron. Soc. 515, 5071 (2022), arXiv:2107.07979 [astro-ph.HE]

    2022 arXiv

  39. [47]

    Z. Zhu, A. Li, J. Hu, and H. Shen, Phys. Rev. C 108, 025809 (2023), arXiv:2305.16058 [nucl-th]

    2023 arXiv

  40. [48]

    J. R. Oppenheimer and G. M. V olkoff, Phys. Rev 055, 374 (1939)

    1939

  41. [49]

    A. Li, Z. Y . Zhu, E. P. Zhou, J. M. Dong, J. N. Hu, and C. J. Xia, Journal of High Energy Astrophysics 28, 19 (2020), arXiv:2007.05116 [nucl-th]

    2020 arXiv

  42. [50]

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

    1939

  43. [51]

    Schaab, F

    C. Schaab, F. Weber, M. K. Weigel, and N. K. Glendenning, Nuclear Physics A 605, 531 (1996), arXiv:astro-ph/9603142 [astro-ph]

    1996 arXiv

  44. [52]

    J. L. Zdunik, M. Fortin, and P. Haensel, arXiv e-prints , arXiv:1611.01357 (2016), arXiv:1611.01357 [astro-ph.HE]

    2016 arXiv

  45. [53]

    D. Page, U. Geppert, and F. Weber, Nuclear Physics A 777, 497 (2006), arXiv:astro-ph/0508056 [astro-ph]

    2006 arXiv

  46. [54]

    B. L. Friman and O. V . Maxwell, Astrophys. J.232, 541 (1979)

    1979

  47. [55]

    J. M. Lattimer, C. J. Pethick, M. Prakash, and P. Haensel, Phys. Rev. Lett. 66, 2701 (1991)

    1991

  48. [56]

    Chiu and E

    H.-Y . Chiu and E. E. Salpeter, Phys. Rev. Lett.12, 413 (1964)

    1964

  49. [57]

    The neutron 3P2 critical temper- ature is based on the work of Ref

    and [58], respectively. The neutron 3P2 critical temper- ature is based on the work of Ref. [59], i.e. model maintains the same momentum dependence as model “a” but the specific values are rescaled to half of their original values (with maxi- mum critical temperature 0.5× 109 ...

  50. [58]

    E. G. Flowers, P. G. Sutherland, and J. R. Bond, Phys. Rev. D 12, 315 (1975)

    1975

  51. [59]

    Flowers, M

    E. Flowers, M. Ruderman, and P. Sutherland, Astrophys. J. 205, 541 (1976)

    1976

  52. [60]

    Wambach, T

    J. Wambach, T. Ainsworth, and D. Pines, Nucl. Phys. A 555, 128 (1993)

    1993

  53. [61]

    Amundsen and E

    L. Amundsen and E. Østgaard, Nucl. Phys. A 437, 487 (1985)

    1985

  54. [62]

    D. Page, J. M. Lattimer, M. Prakash, and A. W. Steiner, Astro- phys. J. Supp 155, 623 (2004)

    2004

  55. [63]

    Miralda-Escude, P

    J. Miralda-Escude, P. Haensel, and B. Paczynski, Astrophys. J. 362, 572 (1990)

    1990

  56. [64]

    Colpi, U

    M. Colpi, U. Geppert, D. Page, and A. Possenti, Astrophys. J. Lett. 548, L175 (2001), arXiv:astro-ph/0010572 [astro-ph]

    2001 arXiv

  57. [65]

    E. F. Brown, L. Bildsten, and R. E. Rutledge, Astrophys. J. Lett. 504, L95 (1998), arXiv:astro-ph/9807179 [astro-ph]

    1998 arXiv

  58. [66]

    R. E. Rutledge, L. Bildsten, E. F. Brown, G. G. Pavlov, V . E. Zavlin, and G. Ushomirsky, Astrophys. J. 580, 413 (2002), arXiv:astro-ph/0108125 [astro-ph]

    2002 arXiv

  59. [67]

    E. F. Brown and A. Cumming, Astrophys. J. 698, 1020 (2009), arXiv:0901.3115 [astro-ph.SR]

    2009 arXiv

  60. [68]

    Allard and N

    V . Allard and N. Chamel, European Physical Journal A60, 116 (2024)

    2024

  61. [69]

    Deibel, A

    A. Deibel, A. Cumming, E. F. Brown, and S. Reddy, Astro- phys. J. 839, 95 (2017), arXiv:1609.07155 [astro-ph.HE]

    2017 arXiv

  62. [70]

    R. L. Merritt, E. M. Cackett, E. F. Brown, D. Page, A. Cum- ming, N. Degenaar, A. Deibel, J. Homan, J. M. Miller, and R. Wijnands, Astrophys. J 833, 186 (2016)

    2016

  63. [71]

    Haensel, K

    P. Haensel, K. P. Levenfish, and D. G. Yakovlev, Astron. As- trophys. 357, 1157 (2000), arXiv:astro-ph/0004183 [astro-ph]

    2000 arXiv

  64. [72]

    Haensel, K

    P. Haensel, K. P. Levenfish, and D. G. Yakovlev, Astron. As- trophys. 372, 130 (2001), arXiv:astro-ph/0103290 [astro-ph]

    2001 arXiv

  65. [73]

    Vida ˜na, Phys

    I. Vida ˜na, Phys. Rev. C 85, 045808 (2012), arXiv:1202.4731 [nucl-th]

    2012 arXiv

  66. [74]

    Andersson, Classical and Quantum Gravity20, R105 (2003), arXiv:astro-ph/0211057 [astro-ph]

    N. Andersson, Classical and Quantum Gravity20, R105 (2003), arXiv:astro-ph/0211057 [astro-ph]

    2003 arXiv

  67. [75]

    P. S. Shternin and D. G. Yakovlev, Phys. Rev. D 78, 063006 (2008), arXiv:0808.2018 [astro-ph]

    2008 arXiv

  68. [76]

    Cutler and L

    C. Cutler and L. Lindblom, Astrophys. J. 314, 234 (1987)

    1987

  69. [77]

    Lindblom, B

    L. Lindblom, B. J. Owen, and S. M. Morsink, Phys. Rev. Lett. 80, 4843 (1998), arXiv:gr-qc/9803053 [gr-qc]

    1998 arXiv

  70. [78]

    W. C. G. Ho, N. Andersson, and B. Haskell, Phys. Rev. Lett. 107, 101101 (2011), arXiv:1107.5064 [astro-ph.HE]

    2011 arXiv

  71. [79]

    Andersson, T

    N. Andersson, T. Sidery, and G. L. Comer, Mon. Not. R. As- tron. Soc. 368, 162 (2006), arXiv:astro-ph/0510057 [astro-ph]

    2006 arXiv

  72. [80]

    Beloin, S

    S. Beloin, S. Han, A. W. Steiner, and D. Page, Phys. Rev. C 97, 015804 (2018)

    2018

  73. [81]

    D. Page, M. Prakash, J. M. Lattimer, and A. W. Steiner, Phys. Rev. Lett.106, 081101 (2011), arXiv:1011.6142 [astro-ph.HE]

    2011 arXiv

  74. [82]

    Sales, O

    T. Sales, O. Lourenc ¸o, M. Dutra, and R. Negreiros, Astron. Astrophys 642, A42 (2020). 16

    2020

  75. [83]

    Tu and A

    Z. Tu and A. Li, Astrophys. J. 987, 6 (2025), arXiv:2503.14059 [nucl-th]

    2025 arXiv

  76. [84]

    Allard and N

    V . Allard and N. Chamel, Phys. Rev. Lett.132, 181001 (2024), arXiv:2403.07740 [astro-ph.HE]

    2024 arXiv

  77. [85]

    J. W. T. Hessels, S. M. Ransom, I. H. Stairs, P. C. C. Freire, V . M. Kaspi, and F. Camilo, Science 311, 1901 (2006), arXiv:astro-ph/0601337 [astro-ph]

    2006 arXiv

  78. [86]

    Li, in European Physical Journal Web of Conferences , Eu- ropean Physical Journal Web of Conferences, V ol

    A. Li, in European Physical Journal Web of Conferences , Eu- ropean Physical Journal Web of Conferences, V ol. 260 (EDP,

  79. [87]

    J. M. Lattimer and M. Prakash, Physics reports442, 109 (2007), arXiv:astro-ph/0612440 [astro-ph]

    2007 arXiv

  80. [88]

    Ascenzi, V

    S. Ascenzi, V . Graber, and N. Rea, Astroparticle Physics 158, 102935 (2024), arXiv:2401.14930 [astro-ph.HE]

    2024 arXiv

  81. [89]

    A. Li, A. L. Watts, G. Zhang, S. Guillot, Y . Xu, A. Santan- gelo, S. Zane, H. Feng, S.-N. Zhang, M. Ge, L. Qi, T. Salmi, B. Dorsman, Z. Miao, Z. Tu, Y . Cavecchi, X. Zhou, X. Zheng, W. Wang, Q. Cheng, X. Liu, Y . Wei, W. Wang, Y . Xu, S. Weng, W. Zhu, Z. Li, L. Shao, Y . Tuo,...

    2025

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.