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Axisymmetric Cooling of Neutron Stars with Strong Magnetic Fields

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Magnetic fields near 10^17 G can shut down the fastest neutrino-cooling channel in neutron stars.

desk verdict First 2D GR cooling of magnetized neutron stars with a clear DU-suppression mechanism, but the central fast-to-slow contrast rests on an undemonstrated, single-EoS, unpaired assumption. read the letter →

arxiv 2506.09841 v1 pith:XV5TNOBP submitted 2025-06-11 astro-ph.HE

Rodrigo Negreiros , Jeffrey Peterson , Veronica Dexheimer This is my paper · ORCID
classification astro-ph.HE
keywords neutronstarcoolingmagneticfieldsdirectUrcaprocessaxisymmetricgeneralrelativitythermalrelaxationtimeequationofstateneutrinoemission
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

Neutron stars of the same mass can cool very differently depending on how strong their internal magnetic field is. The paper shows that central fields of $3$–$4\times10^{17}$ G — about ten times stronger than typical surface fields inferred from observations — are enough to shut down the direct Urca process, the fastest neutrino cooling channel, even though such fields are too weak to change the equation of state or the Fermi distribution of particles. The effect works because the magnetic field adds to the gravitational mass, so a star with a fixed observed mass and a stronger field has a lower baryonic density and therefore a smaller core region meeting the conditions for direct Urca. The result matters because it turns cooling curves into a possible probe of the interior magnetic field of neutron stars.

What carries the argument

The central mechanism is the coupling between Einstein's and Maxwell's equations for an axisymmetric poloidal magnetic field, solved together with a thermal evolution equation for temperature and heat flux. The named pieces are the chiral mean field (CMF) equation of state, which fixes the proton fraction and therefore whether direct Urca — the fast neutrino-emitting process requiring a proton fraction above a threshold — can run, and the direct Urca threshold itself. The workhorse relation is that the gravitational mass of a magnetized star receives a contribution from the electromagnetic energy, so two stars with the same gravitational mass but different field strengths have different baryonic densities; a stronger field lowers the central density and shrinks the direct Urca region. Thermal relaxation time, defined from the maximum slope of the cooling curve, then grows non-linearly with the field strength, well fitted by a rational function of the current function $f_0$.

What would settle it

A decisive check is to run the same two-dimensional cooling calculation with an equation of state for which a 1.4-solar-mass star never reaches the direct Urca proton fraction: if the cooling curves then barely change with magnetic field strength, the paper's central claim is falsified. Alternatively, observing a 1.4-solar-mass neutron star with an inferred surface field of $7$–$8\times10^{16}$ G that cools as fast as unmagnetized stars would contradict the prediction.

Watch

Extended reading notes

Core claim

Cooling a 1.4-solar-mass neutron star with a poloidal magnetic field in full general relativity, the authors find that stars with central fields around $3$–$4\times10^{17}$ G (surface fields $7$–$8\times10^{16}$ G) remain significantly hotter than their unmagnetized counterparts. The reason is geometric rather than microscopic: the electromagnetic field contributes to curvature and hence to the gravitational mass, so a star with fixed gravitational mass and larger field has lower baryonic content and lower central baryon density. This shrinks the region where the proton fraction exceeds the direct Urca threshold, converting a fast-cooling star into a slow-cooling one and increasing the thermal relaxation time non-linearly with field strength. The transition is seen as a change in cooling regime between current-function values $f_0 = 2.0$ and $f_0 = 2.5$, with the direct-Urca-active volume losing its spherical shape and shrinking as the field grows.

Load-bearing premise

The load-bearing assumption is that a 1.4-solar-mass neutron star built from the chosen equation of state would, without a magnetic field, be just dense enough in its core to run direct Urca; if that threshold were not crossed, or if pairing suppressed the process, the magnetic field could not cause the reported fast-to-slow cooling transition.

Editorial extensions

If this is right

  • Magnetized neutron stars with central fields above roughly $3\times10^{17}$ G will cool slowly and stay hotter for longer than field-free stars of the same mass, producing distinct cooling curves after about 100 years of age.
  • The thermal relaxation time increases non-linearly with magnetic field strength, with a fast-to-slow cooling transition around central fields of $3$–$4\times10^{17}$ G.
  • The direct Urca active region shrinks and becomes ellipsoidal as the field grows, so neutrino emission becomes spatially anisotropic inside the star.
  • Observed surface temperatures of neutron stars, combined with an independent mass measurement, can in principle distinguish stars with strong internal fields from those without.
  • Because the field effect operates through baryon density rather than through particle microphysics, it persists at field strengths too low to alter the equation of state.

Reading between the lines

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

  • Inference: the same mechanism should be mass-selective; the cooling contrast induced by magnetic fields should be largest for stars whose field-free proton fraction sits near the direct Urca threshold, and smaller for stars far above or below it.
  • Inference: if nucleon pairing is added, absolute temperatures will change, but the geometry-driven shrinkage of the direct Urca region should survive because it is tied to baryon density, not to the pairing gap.
  • Inference: the ellipsoidal direct Urca region implies anisotropic neutrino emission that may also produce a small aspherical momentum kick, a testable connection to neutron star natal kicks that the paper does not pursue.
  • Inference: a straightforward extension would be to map the same calculation at several masses and compare the resulting cooling curves against a sample of thermally emitting neutron stars with well-measured masses; a clean separation by inferred surface field would test the claim observationally.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper studies the thermal evolution of non-rotating, axisymmetric neutron stars with strong poloidal magnetic fields, using the CMF equation of state for the microphysics and the Astreus code to solve the coupled Einstein-Maxwell equations for stellar structure and a 2D finite-difference scheme for the cooling equations. For a canonical 1.4 solar-mass star, the authors construct configurations with central fields up to about 4.7e17 G, solve the cooling evolution including standard neutrino emission processes, and report that stars with the strongest fields cool more slowly than their unmagnetized counterpart. They attribute this to the magnetic-field-induced reduction in the volume where the direct Urca process operates, and they report a nonlinear increase in the thermal relaxation time with increasing field strength, fitting it with a four-parameter rational function. The central claim is that magnetic fields can alter cooling behavior even when too weak to modify the Fermi distributions directly, through the effect of curvature on the stellar composition and the DU region.

Significance. If the result is robust, it is a novel and interesting proof-of-principle: magnetic fields of the order of 1e17 G could change the thermal evolution of neutron stars by modifying the active direct Urca region through general-relativistic deformation, rather than through a direct effect on the equation of state or on single-particle phase space. The work combines a nontrivial 2D general-relativistic magnetized equilibrium solver with a 2D cooling solver, which is a technical achievement. The paper also provides a concrete falsifiable prediction: for a fixed gravitational mass, stronger magnetic fields produce higher surface temperatures at ages of 1e2-1e6 yr and a longer thermal relaxation time. However, the claim currently rests on a single equation of state, a single mass, an unpaired treatment of nucleons, and a model-specific DU threshold, so its quantitative predictions should be treated cautiously until those dependencies are characterized.

major comments (3)
  1. [Sec. 3] The central mechanism requires that the unmagnetized 1.4 solar-mass CMF star permit the direct Urca process, but the paper does not demonstrate this. The sentence "our microscopic model allows for the DU process in stars with 1.4 M_sun" is asserted without showing the beta-equilibrium proton fraction (or any composition profile) versus density and its relation to the DU threshold. Figure 4 shows DU regions only for magnetized configurations, not for f0 = 0. Without a field-free composition profile demonstrating that the DU threshold is actually crossed, the identification of the fast-cooling branch with direct Urca is unsupported and the central fast-to-slow transition could be an artifact of the particular EoS or the chosen mass.
  2. [Sec. 3, Fig. 2] The omission of nucleon pairing is not a minor simplification here because the paper's stated effect is the suppression of DU: the text even notes that "This is usually alleviated by the inclusion of appropriate pairing among nucleons." In realistic neutron stars, pairing gaps suppress DU neutrino emission over much of the cooling epoch, so including pairing could substantially reduce or even eliminate the contrast between low-field and high-field cooling curves shown in Fig. 2. The authors should either include a pairing model in at least one representative run, or quantitatively argue (e.g., via the relevant temperature range and expected gap magnitudes) that pairing would not erase the reported fast-to-slow transition.
  3. [Sec. 3, Figs. 2-3] The manuscript reports quantitative cooling curves and relaxation times but provides no numerical convergence tests, resolution studies, or uncertainty estimates. The claim of a nonlinear increase in relaxation time, and the fitted parameters of Eq. (7), are only meaningful if the 2D cooling solutions are converged with respect to grid spacing and time step. The paper should show at least one convergence test for a representative strong-field configuration and, if possible, estimates of the numerical error in the extracted relaxation times.
minor comments (6)
  1. [Eq. (6) and Fig. 3] The definition of the relaxation time t_w = max |d ln T_s / d ln t| is not explained: as written the expression is dimensionless, while t_w is presented in years. Please clarify how this quantity is extracted from the cooling curves and what physical condition it represents.
  2. [Sec. 3, Eq. (7)] The four-parameter fit to six data points is presented as "a good fit" with a 95% confidence band in Fig. 3, but no residuals, reduced chi-squared, or parameter uncertainties are given. Since this fit is illustrative rather than load-bearing, a brief statement of the fit quality would suffice.
  3. [Table 1] The caption says the magnetic moment is given "in Gaussians, where 1 Gaussian = 1e-3 A m^2"; the unit and conversion should be defined consistently, and the table would benefit from listing the gravitational mass explicitly for each configuration.
  4. [References] The reference "J Zapata, R Negreiros, T. S., & Jaikumar, P. 2022" has garbled author formatting and should be corrected.
  5. [Sec. 4 vs. text] The introduction refers to conclusions in Sec. 5, but the conclusions section is numbered 4; renumber or adjust the cross-reference.
  6. [Fig. 4] The DU-active regions would be much easier to interpret if the figure also showed the f0 = 0 case and if the color scale for the yellow region were accompanied by a quantitative definition of the DU criterion (e.g., the proton-fraction threshold as a function of density).

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the cooling results are direct simulation outputs, and the fitted relaxation-time curve is illustrative only.

full rationale

The paper's central claim is generated by a self-contained numerical chain: (i) the CMF equation of state provides the microscopic composition; (ii) the Astreus code solves the Einstein-Maxwell equations for 1.4 solar-mass stars with a prescribed current function f0, yielding magnetized stellar structures; (iii) the thermal evolution equation (Eq. 5) is integrated with standard neutrino-emission processes, giving the cooling curves and relaxation times. The reduction of the Direct Urca active region with increasing magnetic field (Fig. 4) is a diagnostic computed from these structures, not an input used to produce them. The analytic fit in Eq. (7) is presented as an illustration ('a good fit to the curve') and is not used to predict the cooling behavior. Self-citations to the Astreus code and to the previous thermal-evolution framework are methodological references, and the citation to Sales et al. (2020) for the association between non-linear relaxation-time growth and fast-to-slow cooling is interpretive support, not a load-bearing uniqueness claim. The omission of nucleon pairing is explicitly flagged as a limitation ('This is usually alleviated by the inclusion of appropriate pairing among nucleons') and affects robustness, but it is an assumption about the microphysics, not a circular step. No equation is defined in terms of the result it is used to derive, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The simulation chains together a specific EoS, a specific current distribution, and standard neutrino physics. The only new tuning parameters are the f0 values scanning field strength and the illustrative fit coefficients.

free parameters (2)
  • f0 (current function) = 0.0, 0.5, 1.0, 1.5, 2.0, 2.5
    Chosen by hand to set the poloidal magnetic field strength; they control the family of stars studied.
  • Relaxation time fit coefficients a, b, c, d = a=69.2, b=-32.13, c=-0.51, d=0.18
    Fitted to the six computed relaxation time values in Fig. 3; not used to derive the cooling curves.
assumptions (7)
  • standard math Einstein field equations and Maxwell equations in curved spacetime
    Used to compute axisymmetric magnetized equilibrium models (Sec. 2).
  • domain assumption CMF chiral mean field EoS with baryon octet and leptons in beta equilibrium
    Provides P(epsilon); the specific EoS determines whether direct Urca is open at 1.4 solar masses (Sec. 2).
  • domain assumption Temperature effects on EoS are negligible after the proto-neutron star phase
    Justified by T well below Fermi energy; stated in Sec. 2.
  • domain assumption Magnetic field does not affect the microscopic EoS or composition below about 10^18 G
    Cited to Dexheimer et al. 2012 and others; sets the scope of the study (Sec. 2).
  • ad hoc to paper Current distribution j_t=0, j_phi=f0(epsilon+P)
    Standard choice for poloidal fields adopted from Cardall et al. 2001; the functional form of f0 is a modeling input (Sec. 2).
  • domain assumption Isotropic thermal conductivity and neutrino emissivities independent of magnetic field
    The thermal evolution equation (5) does not include anisotropic transport due to B; stated scope.
  • domain assumption Direct Urca threshold depends only on local proton fraction
    Used to map DU active regions in Fig. 4; standard neutron star physics.

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Pith. "Pith review of Axisymmetric Cooling of Neutron Stars with Strong Magnetic Fields." pith.science (2026). https://pith.science/paper/XV5TNOBP

@misc{pith2026250609841,
  author       = {Pith},
  title        = {Pith review of: Axisymmetric Cooling of Neutron Stars with Strong Magnetic Fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XV5TNOBP}},
  note         = {Machine review of arXiv:2506.09841}
}
abstract

We study the cooling evolution of neutron stars with strong poloidal magnetic fields (with strength not far from observed values) using the full general relativity 2-dimensional \textit{Astreus} code, which solves consistently Einstein's and Maxwell's equations. We find that central magnetic fields with strengths $3-4\times10^{17}$ G, corresponding to surface magnetic fields $7-8\times10^{16}$, can significantly modify the cooling behavior of neutron stars, leading to stars with similar masses but different magnetic fields to exhibit different thermal evolution. We show a non-linear increase in the thermal relaxation time with increasing magnetic fields and that this behavior is associated with the reduction of the Direct Urca process in stars with strong magnetic fields. This is a novel result in which we can observe the magnetic field influence on the thermal evolution of stars, even if it is not strong enough to affect the Fermi distribution of particles.

Figures

Figures reproduced from arXiv: 2506.09841 by the authors.

Figure 1
Figure 1. Top: Energy density contours for 1.4 M/MSunneutron stars with different current functions f0. Bottom: Contours for the azimuthal component of the magnetic potential (Aϕ), as well as magnetic field lines, with different current functions f0. The blue contours in all panels indicate the neutron star surfaces. curvature effects rapidly becoming relevant as soon as the field reaches a certain value ∼ 1017G (Gomes et al.… view at source ↗
Figure 2
Figure 2. Redshifted temperature evolution for the equa￾torial region of stars with 1.4 M/MSunand different values of the current function f0. The olive shaded region denotes possible different evolutions for current functions comprised between f0 = 2.0 and 2.5. plicit (ADI) method to integrate the cooling equations. Furthermore, we consider all neutrino emission processes that may occur inside the neutron star, including dir… view at source ↗
Figure 4
Figure 4. Active regions for the Direct Urca process (yellow shaded region) inside of 1.4 solar mass stars with different magnetic fields distribution, according to different values of the current constant f0. Red lines indicate the stellar surface. takes place (Sales et al. 2020) and the thickness of the crust, would naturally be influenced by a neutron star with a magnetized structure. As discussed above, the in￾crease in t… view at source ↗

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Works this paper leans on

49 extracted references · 17 canonical work pages

  1. [1]

    Anzuini, F., Melatos, A., Dehman, C., Viganò, D., & Pons, J. A. 2021, Monthly Notices of the Royal Astronomical Society, 509, 2609, 10.1093/mnras/stab3126

    work page doi:10.1093/mnras/stab3126 2021

  2. [2]

    1995 a , Astron

    Bocquet, M., Bonazzola, S., Gourgoulhon, E., & Novak, J. 1995 a , Astron. Astrophys., 301, 757. gr-qc/9503044

    arXiv 1995

  3. [3]

    1995 b , Astronomy and Astrophysics, 301, 757

    ---. 1995 b , Astronomy and Astrophysics, 301, 757. https://ui.adsabs.harvard.edu/abs/1995A&A...301..757B/abstract

    work page 1995

  4. [4]

    2013, Reviews of Modern Physics, 85, 245

    Burrows, A. 2013, Reviews of Modern Physics, 85, 245. https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.85.245

    doi:10.1103/revmodphys.85.245 2013

  5. [5]

    M., Bernuzzi, S., & Radice, D

    Camilletti, A., Perego, A., Guercilena, F. M., Bernuzzi, S., & Radice, D. 2024, Phys. Rev. D, 109, 063023, 10.1103/PhysRevD.109.063023

    work page doi:10.1103/physrevd.109.063023 2024

  6. [7]

    2001 b , The Astrophysical Journal, 554, 322

    ---. 2001 b , The Astrophysical Journal, 554, 322. https://iopscience.iop.org/article/10.1086/321370

    doi:10.1086/321370 2001

  7. [8]

    2019, in The Physics and Astrophysics of Neutron Stars (Springer), 1--56

    Cerda-Duran, P., & Elias-Rosa, N. 2019, in The Physics and Astrophysics of Neutron Stars (Springer), 1--56. https://link.springer.com/chapter/10.1007/978-3-319-97616-7_1

    work page doi:10.1007/978-3-319-97616-7_1 2019

  8. [9]

    2015, Mon

    Chatterjee, D., Elghozi, T., Novak, J., & Oertel, M. 2015, Mon. Not. Roy. Astron. Soc., 447, 3785, 10.1093/mnras/stu2706

    doi:10.1093/mnras/stu2706 2015

Show all 49 references
  1. [10]

    B., Shapiro, S

    Cook, G. B., Shapiro, S. L., & Teukolsky, S. A. 1992, The Astrophysical Journal, 398, 203, 10.1086/171849

    1992 doi

  2. [11]

    O., et al

    Dexheimer, V., Franzon, B., Gomes, R. O., et al. 2017, Phys. Lett. B, 773, 487, 10.1016/j.physletb.2017.09.008

    2017 doi

  3. [12]

    2012, Eur

    Dexheimer, V., Negreiros, R., & Schramm, S. 2012, Eur. Phys. J. A, 48, 189, 10.1140/epja/i2012-12189-y

    2012 doi

  4. [13]

    2008, Astrophys

    Dexheimer, V., & Schramm, S. 2008, Astrophys. J., 683, 943, 10.1086/589735

    2008 doi

  5. [14]

    2016 a , Mon

    Franzon, B., Dexheimer, V., & Schramm, S. 2016 a , Mon. Not. Roy. Astron. Soc., 456, 2937, 10.1093/mnras/stv2606

    2016 doi

  6. [15]

    2016 b , Phys

    ---. 2016 b , Phys. Rev. D, 94, 044018, 10.1103/PhysRevD.94.044018

    2016 doi

  7. [16]

    2017, Physical Review D, 96, 123005

    Franzon, B., Negreiros, R., & Schramm, S. 2017, Physical Review D, 96, 123005

    2017

  8. [17]

    2012, Mon

    Frieben, J., & Rezzolla, L. 2012, Mon. Not. Roy. Astron. Soc., 427, 3406, 10.1111/j.1365-2966.2012.22027.x

    2012

  9. [18]

    O., Pais, H., Dexheimer, V., Provid\^encia, C., & Schramm, S

    Gomes, R. O., Pais, H., Dexheimer, V., Provid\^encia, C., & Schramm, S. 2019, Astron. Astrophys., 627, A61, 10.1051/0004-6361/201935310

    2019 doi

  10. [19]

    Hayasaki, K., & Okazaki, A. T. 2004, Monthly Notices of the Royal Astronomical Society, 350, 971, 10.1111/j.1365-2966.2004.07702.x

    2004

  11. [20]

    S., & Jaikumar, P

    J Zapata, R Negreiros, T. S., & Jaikumar, P. 2022, Astronomy & Astrophysics, 663, A19

    2022

  12. [21]

    2012, Annual Review of Nuclear and Particle Science, 62, 407

    Janka, H.-T. 2012, Annual Review of Nuclear and Particle Science, 62, 407. https://www.annualreviews.org/doi/10.1146/annurev-nucl-102711-094901

    2012 doi

  13. [22]

    2019, Publications of the Astronomical Society of Japan, 71, 58, 10.1093/pasj/psz034

    Karino, S., Nakamura, K., & Taani, A. 2019, Publications of the Astronomical Society of Japan, 71, 58, 10.1093/pasj/psz034

    2019 doi

  14. [23]

    M., & Beloborodov, A

    Kaspi, V. M., & Beloborodov, A. 2017, Ann. Rev. Astron. Astrophys., 55, 261, 10.1146/annurev-astro-081915-023329

    2017 doi

  15. [24]

    Kiziltan, B., Kottas, A., De Yoreo, M., & Thorsett, S. E. 2013, Astrophys. J., 778, 66, 10.1088/0004-637X/778/1/66

    2013 doi

  16. [25]

    1989, Monthly Notices of the Royal Astronomical Society, 237, 355, 10.1093/mnras/237.2.355

    Komatsu, H., Eriguchi, Y., & Hachisu, I. 1989, Monthly Notices of the Royal Astronomical Society, 237, 355, 10.1093/mnras/237.2.355

    1989 doi

  17. [26]

    2024, Living Rev

    Kumar, R., et al. 2024, Living Rev. Rel., 27, 3, 10.1007/s41114-024-00049-6

    2024 doi

  18. [27]

    Lai , D., & Shapiro , S. L. 1991, , 383, 745, 10.1086/170831

    1991 doi

  19. [28]

    K., Haensel, P., Haskell, B., Zdunik, J

    Lander, S. K., Haensel, P., Haskell, B., Zdunik, J. L., & Fortin, M. 2021, Mon. Not. Roy. Astron. Soc., 503, 875, 10.1093/mnras/stab460

    2021 doi

  20. [29]

    Landry, P., & Read, J. S. 2021, Astrophys. J. Lett., 921, L25, 10.3847/2041-8213/ac2f3e

    2021 doi

  21. [30]

    S., et al

    Makishima, K., Enoto, T., Hiraga, J. S., et al. 2014, Phys. Rev. Lett., 112, 171102, 10.1103/PhysRevLett.112.171102

    2014 doi

  22. [31]

    2021, Mon

    Makishima, K., Enoto, T., Yoneda, H., & Odaka, H. 2021, Mon. Not. Roy. Astron. Soc., 502, 2266, 10.1093/mnras/stab149

    2021 doi

  23. [32]

    2019, Publ

    Makishima, K., Murakami, H., Enoto, T., & Nakazawa, K. 2019, Publ. Astron. Soc. Jap., 71, Publications of the Astronomical Society of Japan, Volume 71, Issue 1, 1 January 2019, 15, https://doi.org/10.1093/pasj/psy129, 10.1093/pasj/psy129

    2019 doi

  24. [33]

    2018, Universe, 4, 43

    Negreiros, R., Bernal, C., Dexheimer, V., & Troconis, O. 2018, Universe, 4, 43

    2018

  25. [34]

    2012, Physical Review D—Particles, Fields, Gravitation, and Cosmology, 85, 104019

    Negreiros, R., Schramm, S., & Weber, F. 2012, Physical Review D—Particles, Fields, Gravitation, and Cosmology, 85, 104019

    2012

  26. [35]

    2017, Astronomy & Astrophysics, 603, A44

    ---. 2017, Astronomy & Astrophysics, 603, A44

    2017

  27. [36]

    D., Roberts, L

    Ott, C. D., Roberts, L. F., da Silva Schneider, A., et al. 2018, The Astrophysical Journal Letters, 855, L3, 10.3847/2041-8213/aaa967

    2018 doi

  28. [37]

    Ozel, F., Psaltis, D., Narayan, R., & Villarreal, A. S. 2012, Astrophys. J., 757, 55, 10.1088/0004-637X/757/1/55

    2012 doi

  29. [38]

    2006, Nuclear Physics A, 777, 497, 10.1016/j.nuclphysa.2005.09.019

    Page, D., Geppert, U., & Weber, F. 2006, Nuclear Physics A, 777, 497, 10.1016/j.nuclphysa.2005.09.019

    2006 doi

  30. [39]

    M., Prakash, M., & Steiner, A

    Page, D., Lattimer, J. M., Prakash, M., & Steiner, A. W. 2004, The Astrophysical Journal Supplement Series, 155, 623, 10.1086/424844

    2004 doi

  31. [40]

    2023, Phys

    Peterson, J., Costa, P., Kumar, R., et al. 2023, Phys. Rev. D, 108, 063011, 10.1103/PhysRevD.108.063011

    2023 doi

  32. [41]

    2021, The Astrophysical Journal, 921, 1

    Peterson, J., Dexheimer, V., Negreiros, R., & Castanheira, B. 2021, The Astrophysical Journal, 921, 1

    2021

  33. [42]

    G., Bucciantini, N., & Del Zanna, L

    Pili, A. G., Bucciantini, N., & Del Zanna, L. 2014, Mon. Not. Roy. Astron. Soc., 439, 3541, 10.1093/mnras/stu215

    2014 doi

  34. [43]

    A., Rather, A

    Rather, I. A., Rather, A. A., Dexheimer, V., et al. 2023, Astrophys. J., 943, 52, 10.3847/1538-4357/aca85c

    2023 doi

  35. [44]

    2020, Astronomy & Astrophysics, 642, A42

    Sales, T., Louren c o, O., Dutra, M., & Negreiros, R. 2020, Astronomy & Astrophysics, 642, A42

    2020

  36. [45]

    2015, Physical Review C, 91, 035805

    Sinha, M., & Sedrakian, A. 2015, Physical Review C, 91, 035805

    2015

  37. [46]

    Tolman, R. C. 1939, Phys. Rev., 55, 364, 10.1103/PhysRev.55.364

    1939 doi

  38. [47]

    L., & Ury\= u , K

    Tsokaros, A., Ruiz, M., Shapiro, S. L., & Ury\= u , K. 2022, Phys. Rev. Lett., 128, 061101, 10.1103/PhysRevLett.128.061101

    2022 doi

  39. [48]

    Valentim, R., Rangel, E., & Horvath, J. E. 2011, Mon. Not. Roy. Astron. Soc., 414, 1427, 10.1111/j.1365-2966.2011.18477.x

    2011

  40. [49]

    G., & Singh, C

    Yadav, S., Mishra, M., Sarkar, T. G., & Singh, C. R. 2024, The European Physical Journal C, 84, 225

    2024

  41. [50]

    2004, Annual Review of Astronomy and Astrophysics, 42, 169, 10.1146/annurev.astro.42.053102.134013

    Yakovlev, D., & Pethick, C. 2004, Annual Review of Astronomy and Astrophysics, 42, 169, 10.1146/annurev.astro.42.053102.134013

    2004

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