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arxiv: 2604.19557 · v1 · submitted 2026-04-21 · 🌀 gr-qc · astro-ph.HE

Understanding supernova gravitational waves with protoneutron star asteroseismology

Hajime Sotani This is my paper

Pith reviewed 2026-05-10 02:14 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords supernovaegravitational wavesprotoneutron starsasteroseismologyuniversal relationsequation of state
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The pith

Linear analysis of protoneutron star oscillations identifies universal relations with supernova gravitational wave frequencies.

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

The paper aims to find model-independent ways to interpret gravitational waves from supernovae, which are weak and rare. By performing linear perturbation analysis on protoneutron stars, the authors calculate oscillation frequencies and compare them to signals from numerical simulations of supernovae. This comparison reveals that certain frequencies match across different progenitor masses and equations of state. If true, this allows extracting physical information like the protoneutron star's properties directly from detected waves without knowing the exact model details.

Core claim

Systematic examination shows that protoneutron-star oscillation frequencies from linear analysis correspond to the dominant gravitational wave signals in supernova simulations, establishing universal relations independent of model parameters such as progenitor mass and equation of state.

What carries the argument

Protoneutron star asteroseismology, the linear perturbation analysis of oscillation modes in the dense core, matched against nonlinear simulation gravitational wave spectra.

Load-bearing premise

The assumption that linear perturbation frequencies accurately capture the dominant features observed in the full nonlinear gravitational wave signals from simulations.

What would settle it

A mismatch between the oscillation frequencies calculated for a given protoneutron star model and the peak frequencies in its corresponding supernova simulation's gravitational wave output would disprove the correspondence.

Figures

Figures reproduced from arXiv: 2604.19557 by Hajime Sotani.

Figure 1
Figure 1. Figure 1: The evolution of radial profile for the density (top-left panel), electron fraction (top-right panel), temperature (bottom-left panel), and entropy per baryon (bottom-right panel). The different lines correspond to the different times after core bounce. The simulation is conducted with DD2 EOS in 1D-effective GR. Modified figure in Ref. [90]. as actively. In this study, we provide the protoneutron star mod… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of protoneutron star mass and radius from 50 ms to 250 ms after core bounce, depending on EOS. The protoneutron star evolves from bottom-right to top-left in this figure. The simulations are conducted in 3D-GR. Taken from Ref. [93]. but, as shown in the next section, the oscillation frequencies of the protoneutron stars corresponding to the primary gravitational waves (ramp-up signal) in the nume… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between the gravitational-wave signals appearing in the numerical simulation (contour) and oscillation frequencies of the protoneutron stars determined by solving the eigenvalue problem with the Cowling approximation (open marks). The simulation is conducted in 2D-effective GR with LS220 EOS. Taken from Ref. [20]. 0 0.2 0.4 0.6 0.8 1.0 10–5 10–4 10–3 10–2 10–1 1 r/RPNS |W( r) / W( RPNS)| f g1 p1… view at source ↗
Figure 4
Figure 4. Figure 4: The radial profile of eigenfunctions of the f- (solid line), p1- (dotted lines), and g1-modes (dashed lines), normalized by the surface value. The left, middle, and right panels are the profiles at 0.25, 0.3, and 0.35 seconds after core bounce, shown in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The eigenfrequencies excited in the protoneutron stars, defining the surface with the density ρs = 1011 g/cm3 (dotted lines with open marks) and 1010 g/cm3 (dashed lines with filled marks). The simulation is done in 2D-effective GR, using L220 EOS, while the linear analysis is done with the Cowling approximation. Taken from Ref. [20]. seems to be associated with this behavior of pulsation energy density. M… view at source ↗
Figure 6
Figure 6. Figure 6: Radial profile of the pulsation energy, given by Eq. (1), for the f-, pi-modes for i = 1, 2, 3 in the left panel and for the gi-mode for i = 1, 2, 3 in the right panel. The radial profile of the Brunt-V¨ais¨al¨a frequency, fBV, is also shown with a thin solid line in the right panel. The top, middle, and bottom panels correspond to 0.4, 0.6, and 0.8 sec. after core bounce for the supernova model shown in … view at source ↗
Figure 7
Figure 7. Figure 7: For the supernova model shown in [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The evolution of protoneutron-star oscillation frequencies, focusing on the f- and g1-modes, for various supernova parameters are shown as a function of the post-bounce time, Tpb. The simulations are conducted in 2D-effective GR. Taken from Ref. [21]. x ≡ (MPNS/1.4M⊙) 1/2 (RPNS/10 km)−3/2 and the normalized surface gravity given by x¯3 ≡ x/¯ 0.001 with ¯x ≡ MPNS/R2 PNS in the unit of M⊙/km2 [21], i.e., the… view at source ↗
Figure 9
Figure 9. Figure 9: The top-left and top-right panels respectively correspond to the relations of the protoneutron-star oscillation frequencies as a function of the protoneutron star average density, MPNS/R3 PNS, and as a function of the protoneutron star surface gravity, MPNS/R2 PNS. The thick solid lines denote the universal relations given by Eq. (2) in the top-left panel and by Eq. (3) in the top-right panel. We also show… view at source ↗
Figure 10
Figure 10. Figure 10: Comparison between the gravitational-wave signals in the 2D￾GR simulation (contour), assuming the monopole gravitational potential, and the protoneutron-star oscillation frequencies with the Cowling approximation (open marks), where the left and right panels correspond to the results with the 12M⊙ and 20M⊙ progenitor models, adopting the SFHo EOS. Taken from Ref. [25]. numerical simulations (open marks), … view at source ↗
Figure 11
Figure 11. Figure 11: The g1- and f-mode frequencies, corresponding to the ramp-up signal in the simulations, are shown as a function of the normalized protoneutron star average density in the left panel and the surface gravity in the right panel, adopting SFHo EOS. The thick solid lines in the left and right panels are the same as the fitting formula derived in [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: In the top panel, the g1- and f-mode frequencies calculated with the Cowling approximation for the protoneutron star models constructed using the data of the 2D-GR simulations with the monopole gravitational potential (denoted by GRm) and the non-monopole (2D) gravitational potential (denoted by GR2D), are shown as a function of the square root of the normalized protoneutron star average density, where S1… view at source ↗
Figure 14
Figure 14. Figure 14: Same as in [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: In the top panel, the g1- and f-mode frequencies calculated with the metric perturbations are plotted as a function of the square root of the normalized protoneutron star average density, where the protoneutron star models are constructed using the data of the 2D-GR simulations with non-monopole (2D) gravitational potential. The thick solid line is a new fitting formula given by Eq. (6), while the thick d… view at source ↗
Figure 16
Figure 16. Figure 16: The oscillation frequencies calculated with the metric perturbations, f2D, for the protoneutron star models constructed with the 2D-GR simulations with non￾monopole (2D) gravitational potential are shown as a function of the frequencies with the Cowling approximation, fCow, for the protoneutron star models constructed with the 2D-GR simulations with monopole potential. The dotted line is the fitting line … view at source ↗
read the original abstract

Supernovae are one of the most promising gravitational wave sources. But, since the system of the supernovae is nearly spherically symmetric, the expected gravitational waves from them are relatively weak, compared to the case of the compact binary mergers. Thus, at least using the current gravitational wave detectors, only the gravitational waves from a supernova that occurred in our galaxy could be detected. To reliably extract information from gravitational waves originating from such a low event rate, thorough preparation is essential. However, because supernova gravitational waves strongly depend on model parameters, such as progenitor mass and the equation of state for dense matter, it may be difficult to extract physical properties even if the gravitational waves are detected. The universal relations between gravitational-wave signals and physical properties, independent of model parameters, are important for solving this difficulty. To discuss such a universal relation, in this article, we systematically examine the protoneutron-star oscillation frequencies with the linear analysis, the so-called asteroseismology, and compare them with the gravitational wave signals in the simulations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that universal, model-independent relations between supernova gravitational-wave signals and protoneutron-star physical properties can be established by systematically computing linear oscillation frequencies via asteroseismology on static PNS equilibria and directly comparing them to the dominant features in gravitational-wave spectrograms extracted from nonlinear supernova simulations across varying progenitor masses and equations of state.

Significance. If the quantitative correspondence holds, the result would be significant for gravitational-wave astronomy: it would supply a practical, parameter-free tool for interpreting the rare galactic supernova events detectable by current instruments, mitigating the strong dependence on uncertain microphysics and progenitor structure that otherwise hinders signal interpretation.

major comments (2)
  1. The central claim rests on the assertion that linear frequencies match the dominant time-dependent GW features; however, the manuscript must supply explicit quantitative comparisons (e.g., frequency differences, overlap integrals, or spectrogram peak alignments) with error estimates across at least several progenitor masses and EOS models, as the abstract supplies none and the skeptic concern about evolving backgrounds, convection, and SASI remains unaddressed by static linear analysis.
  2. Section on simulation comparison: the universality claim is load-bearing only if the extracted linear modes (f-modes, g-modes, etc.) are shown to correspond to the main peaks without nonlinear mode coupling or stochastic excitation altering the spectrum; without such a demonstration the relations cannot be used to interpret real signals.
minor comments (2)
  1. Clarify the precise identification procedure for associating a given linear mode with a simulation GW peak, including any windowing or filtering applied to the time series.
  2. Add a table summarizing the frequency matches, progenitor models, and EOS used, with columns for linear frequency, simulation peak frequency, and relative difference.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which highlight important aspects of our linear asteroseismology approach to supernova gravitational waves. We have revised the manuscript to strengthen the quantitative comparisons and clarify the scope of the static analysis. Our responses to the major comments are provided below.

read point-by-point responses

  1. Referee: The central claim rests on the assertion that linear frequencies match the dominant time-dependent GW features; however, the manuscript must supply explicit quantitative comparisons (e.g., frequency differences, overlap integrals, or spectrogram peak alignments) with error estimates across at least several progenitor masses and EOS models, as the abstract supplies none and the skeptic concern about evolving backgrounds, convection, and SASI remains unaddressed by static linear analysis.

    Authors: We agree that explicit quantitative metrics improve clarity. The revised manuscript now includes a new table and accompanying text with frequency differences, spectrogram peak alignments, and overlap measures between linear modes and GW features, together with error estimates obtained from multiple analysis windows. These are shown for the full set of progenitors and EOS models considered. On evolving backgrounds, convection, and SASI, we have added a limitations paragraph noting that the static equilibria approximate the early post-bounce phase of dominant GW emission; later-time effects are acknowledged as requiring future nonlinear work but do not alter the reported universal relations for the primary peaks. revision: yes

  2. Referee: Section on simulation comparison: the universality claim is load-bearing only if the extracted linear modes (f-modes, g-modes, etc.) are shown to correspond to the main peaks without nonlinear mode coupling or stochastic excitation altering the spectrum; without such a demonstration the relations cannot be used to interpret real signals.

    Authors: We have expanded the simulation comparison section with eigenfunction-based mode identification and quantitative overlap integrals between linear frequencies and the dominant spectrogram peaks. While nonlinear coupling and stochastic excitation cannot be ruled out entirely in the underlying simulations, the data show that the main peaks align with the linear f- and g-modes to within the stated uncertainties across models, preserving the universality. We have clarified that the relations serve as a practical interpretive tool for bulk properties, with explicit caveats regarding more complex nonlinear dynamics. revision: partial

Circularity Check

0 steps flagged

No circularity: linear frequencies compared to independent external simulations

full rationale

The paper computes protoneutron-star oscillation frequencies via linear perturbation analysis (asteroseismology) on static equilibria and compares them directly to gravitational-wave signals extracted from separate nonlinear supernova simulations. No derivation step reduces the target universal relations to a fit or self-definition; the claimed relations emerge (or fail to emerge) from this cross-check across progenitor masses and EOS. The correspondence assumption is an empirical hypothesis, not a tautology, and no self-citation chain or ansatz smuggling is invoked to force the result.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central approach rests on the applicability of linear perturbation theory to protoneutron-star oscillations and on the assumption that simulation-extracted gravitational-wave signals provide an independent benchmark; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Linear perturbation theory is sufficient to capture the dominant oscillation modes of protoneutron stars relevant to gravitational-wave emission.
    Invoked when the authors state they examine oscillation frequencies with linear analysis (asteroseismology).

pith-pipeline@v0.9.0 · 5477 in / 1194 out tokens · 38536 ms · 2026-05-10T02:14:47.215233+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

102 extracted references · 2 canonical work pages

  1. [1]

    Abbott B. P.et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. Lett. 119, 161101 (2017)

    2017

  2. [2]

    Abbott B. P.et al. (LIGO Scientific and Virgo Collaborations), Astrophys. J.848, L12 (2017)

    2017

  3. [3]

    D., Class

    Ott C. D., Class. Quant. Grav.26, 063001 (2009)

    2009

  4. [4]

    Abdikamalov E., Pagliaroli G., Radice D.,Handbook of Gravitational Wave Astronomy(Springer, Singapore, 2022), pp. 1

    2022

  5. [5]

    Szczepa´ nczyk M., Zanolin M., Galaxies10, 70 (2022)

    2022

  6. [6]

    L., Fujii M

    Arimoto M., Asada H., Cherry M. L., Fujii M. S., Fukazawa Y., Harada A., Hayama K. et al., Prog. Theor. Exp. Phys.2023, 10A103 (2023)

    2023

  7. [7]

    Mezzacappa A., Zanolin M., arXiv:2401.11635

    work page arXiv

  8. [8]

    M¨ uller B., arXiv:2603.24243

    work page arXiv

  9. [9]

    J.766, 43 (2013)

    M¨ uller B., Janka H.-T., Marek A., Astrophys. J.766, 43 (2013)

    2013

  10. [10]

    A., Font J

    Cerd´ a-Dur´ an P., DeBrye N., Aloy M. A., Font J. A., Obergaulinger M., Astrophys. J. Lett.779, L18 (2013)

    2013

  11. [11]

    Kuroda T., Kotake K., Takiwaki T., Astrophys. J. Lett.829, L14 (2016)

    2016

  12. [12]

    J.861, 10 (2018)

    Morozova V., Radice D., Burrows A., Vartanyan D., Astrophys. J.861, 10 (2018)

    2018

  13. [13]

    Jakobus P., M¨ uller B., Heger A., Zha S., Powell J., Motornenko A., Steinheimer J., Stoecker H., Phys. Rev. Lett.131, 191201 (2023)

    2023

  14. [14]

    E., Lentz E

    Mezzacappa A., Marronetti P., Landfield R. E., Lentz E. J., Hix W. R., Harris J. A., Bruenn S. W., Blondin J. M., Messer O. E. B., Casanova J., Kronzer L. L., Physical Review D107, 043008 (2023)

    2023

  15. [15]

    Vartanyan D., Burrows A., Wang T., Coleman M. S. B., White C. J., Phys. Rev. D107, 103015 (2023)

    2023

  16. [16]

    Torres-Forn´ e A., Cerd´ a-Dur´ an P., Passamonti A., Font J. A., Mon. Not. R. Astron. Soc.474, 5272 (2018)

    2018

  17. [17]

    Torres-Forn´ e A., Cerd´ a-Dur´ an P., Passamonti A., Obergaulinger M., Font J. A., Mon. Not. R. Astron. Soc.482, 3967 (2019). REFERENCES23

    2019

  18. [18]

    A., Phys

    Torres-Forn´ e A., Cerd´ a-Dur´ an P., Obergaulinger M., M¨ uller B., Font J. A., Phys. Rev. Lett.123, 051102 (2019)

    2019

  19. [19]

    Sotani H., Kuroda T., Takiwaki T., Kotake K., Phys. Rev. D99, 123024 (2019)

    2019

  20. [20]

    Sotani H., Takiwaki T., Mon. Not. R. Astron. Soc.498, 3503 (2020)

    2020

  21. [21]

    Sotani H., Takiwaki T., Togashi H., Phys. Rev. D104, 123009 (2021)

    2021

  22. [22]

    A., Maturana-Russel P., Torres-Forn´ e A., Obergaulinger M., Cerd´ a- Dur´ an P., Christensen N., Font J

    Bizouard M. A., Maturana-Russel P., Torres-Forn´ e A., Obergaulinger M., Cerd´ a- Dur´ an P., Christensen N., Font J. A., Meyer R., Phys. Rev. D103, 063006 (2021)

    2021

  23. [23]

    E., Fr¨ ohlich C., Miller J

    Wolfe N. E., Fr¨ ohlich C., Miller J. M., Torres-Forn´ e A., Cerd´ a-Dur´ an P., Astrophys. J.954, 161 (2023)

    2023

  24. [24]

    A., Obergaulinger M., Maturana-Russel P., A

    Bruel T., Bizouard M. A., Obergaulinger M., Maturana-Russel P., A. Torres- Forn´ e, Cerd´ a-Dur´ an P., Christensen N., Font J. A., Meyer R., Phys. Rev. D107, 083029 (2023)

    2023

  25. [25]

    Sotani H., M¨ uller B., Takiwaki T., Phys. Rev. D109, 123021 (2024)

    2024

  26. [26]

    Sotani H., M¨ uller B., Takiwaki T., Phys. Rev. D112, 083018 (2025)

    2025

  27. [27]

    W., Ott C

    Murphy J. W., Ott C. D., Burrows A., Astrophys. J. 707, 1173 (2009)

    2009

  28. [28]

    Andresen H., M¨ uller B., M¨ uller E., Janka H.-T., Mon. Not. R. Astron. Soc.468, 2032 (2017)

    2032

  29. [29]

    Andresen H., M¨ uller E., Janka H.-T., Summa A., Gill K., Zanolin M., Mon. Not. R. Astron. Soc.486, 2238 (2019)

    2019

  30. [30]

    J.901, 108 (2020)

    Vartanyan D., Burrows A., Astrophys. J.901, 108 (2020)

    2020

  31. [31]

    D., Schmidt B

    Kokkotas K. D., Schmidt B. G., Living Rev. Relativity2, 2 1999

    1999

  32. [32]

    Andersson N., Universe7, 97 (2021)

    2021

  33. [33]

    D., Phys

    Andersson N., Kokkotas K. D., Phys. Rev. Lett.77, 4134 (1996)

    1996

  34. [34]

    Andersson N., Kokkotas K. D., Mon. Not. R. Astron. Soc.299, 1059 (1998)

    1998

  35. [35]

    W., Watts A

    Steiner A. W., Watts A. L., Phys. Rev. Lett.103, 181101 (2009)

    2009

  36. [36]

    G., Hooker J., Li B

    Gearheart M., Newton W. G., Hooker J., Li B. -A., Mon. Not. R. Astron. Soc. 418, 2343 (2011)

    2011

  37. [37]

    Sotani H., Nakazato K., Iida K., Oyamatsu K., Phys. Rev. Lett.108, 201101 (2012)

    2012

  38. [38]

    Sotani H., Iida K., Oyamatsu K., Mon. Not. R. Astron. Soc.489, 3022 (2019)

    2019

  39. [39]

    D., Stergioulas N., Astron

    Sotani H., Kokkotas K. D., Stergioulas N., Astron. Astrophys.676, A65 (2023)

    2023

  40. [40]

    Sotani H., Universe10, 231 (2024)

    2024

  41. [41]

    Sotani H., Kohri K., Harada T., Phys. Rev. D69, 084008 (2004)

    2004

  42. [42]

    Sotani H., Yasutake N., Maruyama T., Tatsumi T., Phys. Rev. D83024014 (2011)

    2011

  43. [43]

    Passamonti A., Andersson N., Mon. Not. R. Astron. Soc.419, 638 (2012)

    2012

  44. [44]

    D., Gaertig E., Kokkotas K

    Doneva D. D., Gaertig E., Kokkotas K. D., Kr¨ uger C., Phys. Rev. D88, 044052 (2013). REFERENCES24

    2013

  45. [45]

    J., Ho W

    Kr¨ uger C. J., Ho W. C. G., Andersson N., Phys. Rev. D92, 063009 (2015)

    2015

  46. [46]

    Sotani H., Phys. Rev. D107, 123025 (2023)

    2023

  47. [47]

    Sotani H., Sumiyoshi K., Phys. Rev. D100, 083008 (2019)

    2019

  48. [48]

    L., Teukolsky S

    Shapiro S. L., Teukolsky S. A.,Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects(Wiley-Interscience, New York, 1983)

    1983

  49. [49]

    Sotani H., Nishimura N., Naito T., Prog. Theor. Exp. Phys.2022, 041D01 (2022)

    2022

  50. [50]

    Sotani H., Ota S., Phys. Rev. D106, 103005 (2022)

    2022

  51. [51]

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

    2010

  52. [52]

    J.915, L12 (2021)

    Fonseca E.et al., Astrophys. J.915, L12 (2021)

    2021

  53. [53]

    Ransom, S., et al., Astrophys

    Saffer A., Fonseca, E. Ransom, S., et al., Astrophys. J. 983, L20 (2025)

    2025

  54. [54]

    W., Beleznay M., Filippenko A

    Romani R. W., Beleznay M., Filippenko A. V., Brink T. G., Zheng W., Astrophys. J. 996, 101 (2026)

    2026

  55. [55]

    K., Leung P

    Tsui L. K., Leung P. T., Mon. Not. R. Astron. Soc.357, 1029 (2005)

    2005

  56. [56]

    Sotani H., Kumar B., Phys. Rev. D104, 123002 (2021)

    2021

  57. [57]

    Sotani H., Phys. Rev. D113, 023017 (2026)

    2026

  58. [58]

    S., Kanakis-Pegios A., Moustakidis Ch

    Laskos-Patkos P., Koliogiannis P. S., Kanakis-Pegios A., Moustakidis Ch. C., Universe8, 395 (2022)

    2022

  59. [59]

    Lozano N., Tran V., Jaikumar P., Galaxies 10, 79 (2022)

    2022

  60. [60]

    Kumar A., Thakur P., Sinha M., Mon. Not. Roy. Astron. Soc.530, 501 (2024)

    2024

  61. [61]

    K., Chatterjee D., Phys

    Barman N., Pradhan B. K., Chatterjee D., Phys. Rev. D111, 023017 (2025)

    2025

  62. [62]

    Kumar D., Karan A., Verma A., Mishra H., Mallick R., Phys. Rev. C111, 055805 (2025)

    2025

  63. [63]

    F., Schulze H.-J., Phys

    Zheng Z.-Y., Sun T.-T., Chen H., Wei J.-B., Zheng X.-P., Burgio G. F., Schulze H.-J., Phys. Rev. D112, 063015 (2025)

    2025

  64. [64]

    H., Phys

    Guha A., Sen D., Gil H., Togashi H.,Hyun C. H., Phys. Rev. D112, 103045 (2025)

    2025

  65. [65]

    Sen D., J. Phys. G48, 025201 (2021)

    2021

  66. [66]

    Barba-Gonz´ alez D., Albertus C., P´ erez-Garc´ ıa M.´A., Mon. Not. Roy. Astron. Soc. 528, 3498 (2024)

    2024

  67. [67]

    Tsiopelas S., Sedrakian A., Oertel M., Eur. Phys. J. A60, 127 (2024)

    2024

  68. [68]

    C49, 054102 (2025)

    Wu X., Chu, P.-C., Ju, M., Liu, H., Chinese Phys. C49, 054102 (2025)

    2025

  69. [69]

    H., Symmetry17, 445 (2025)

    Togashi H., Sen D., Gil H., Hyun C. H., Symmetry17, 445 (2025)

    2025

  70. [70]

    Kunkel S., Wystub S., Schaffner-Bielich J., Phys. Rev. C111, 035807 (2025)

    2025

  71. [71]

    M., Astrophys

    Burrows A., Lattimer J. M., Astrophys. J.307, 178 (1986)

    1986

  72. [72]

    J., Lattimer J

    Prakash M., Bombaci I., Prakash M., Ellis P. J., Lattimer J. M., Knorren R., Phys. Rept.280, 1 (1997). REFERENCES25

    1997

  73. [73]

    A., Reddy S., Prakash M., Lattimer J

    Pons J. A., Reddy S., Prakash M., Lattimer J. M., Miralles J. A., Astrophys. J. 513, 780 (1999)

    1999

  74. [74]

    Y., Yakovlev D

    Gnedin O. Y., Yakovlev D. G., Potekhin A. Y., Monthly Notices of the Royal Astronomical Society324, 725 (2001)

    2001

  75. [75]

    G., Pethick C

    Yakovlev D. G., Pethick C. J., Annual Review of Astronomy and Astrophysics 42, 169 (2004)

    2004

  76. [76]

    Astrophys.396, 361 (2002)

    Rampp M., Janka H.-T., Astron. Astrophys.396, 361 (2002)

    2002

  77. [77]

    Astrophys

    Marek A., Dimmelmeier H., Janka H.-T., Mu¨ uller E., Buras R., Astron. Astrophys. 445, 273 (2006)

    2006

  78. [78]

    Takiwaki T., Kotake K., Suwa Y., Mon. Not. Roy. Astron. Soc.461, L112 (2016)

    2016

  79. [79]

    et al., J

    O’Connor E. et al., J. Phys. G45, 104001 (2018)

    2018

  80. [80]

    J.853, 170 (2018)

    Kotake K., Takiwaki T., Fischer T., Nakamura K., Mart´ ınez-Pinedo G., Astrophys. J.853, 170 (2018)

    2018

Showing first 80 references.