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arxiv: 2605.28944 · v1 · pith:OC2GERWLnew · submitted 2026-05-27 · 🌌 astro-ph.HE · gr-qc

Impact of the equation of state on core collapse supernovae I: the low-T/|W| instability

Marco Cusinato , Martin Obergaulinger , Miguel \'Angel Aloy This is my paper

Pith reviewed 2026-06-29 10:25 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords core-collapse supernovaegravitational wavesequation of statelow-T/|W| instabilityproto-neutron starrapid rotationneutrino-magnetohydrodynamics
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The pith

The dominant gravitational wave frequency from the low-T/|W| instability rises with proto-neutron star stiffness and compactness across five equations of state.

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

Three-dimensional neutrino-magnetohydrodynamics simulations of a rapidly rotating 35 solar-mass progenitor collapse were run with five different finite-temperature nuclear equations of state. The low-T/|W| instability develops in every case, producing spiral modes that emit quasi-periodic gravitational waves and modulate equatorial neutrino luminosities, yet the onset time, dominant azimuthal number, lifetime, and peak frequencies differ between runs. These differences trace to variations in the proto-neutron star's evolving density and rotation profiles induced by each equation of state. The dominant gravitational-wave frequency is higher for stiffer or more compact configurations, implying that the signal frequency itself could serve as an observable diagnostic of dense-matter physics that complements neutrino data.

Core claim

In all five equation-of-state models the low-T/|W| instability occurs and generates large-scale spiral modes whose gravitational-wave emission frequency correlates directly with the effective stiffness and compactness of the proto-neutron star.

What carries the argument

The low-T/|W| instability, a non-axisymmetric dynamical instability in the differentially rotating proto-neutron star that drives m=1 or m=2 spiral modes and associated gravitational-wave emission.

Load-bearing premise

Differences in onset time, dominant mode, lifetime, and gravitational-wave frequency across the five runs are produced by genuine equation-of-state effects on proto-neutron star structure rather than by any of the simulation choices held fixed.

What would settle it

A set of otherwise identical simulations that yields the same dominant gravitational-wave frequency for two equations of state whose proto-neutron stars differ measurably in compactness or stiffness would falsify the reported correlation.

Figures

Figures reproduced from arXiv: 2605.28944 by Marco Cusinato, Martin Obergaulinger, Miguel \'Angel Aloy.

Figure 1
Figure 1. Figure 1: Gravitational mass-radius relations for cold, static, spherically symmetric, and non-rotating neutron [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Normalised rotational parameter, RT /|W| , (left panel), homology deviation parameter, Ξ (middle) as a function of the central density, ρc. Right panel: radial profile of the angle-averaged rotational frequency at core bounce. where vϕ is the azimuthal velocity and Φ the gravitational potential. This quantity exhibits only moderate relative variations (≲ 13%) across the models. The ratio between rotational… view at source ↗
Figure 3
Figure 3. Figure 3: Equatorial slices of the relative deviation from spherical density distribution, [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left and middle panels: polar slices of the relative deviation from the axisymmetric density [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Left panel: evolution of the ratio between rotational and gravitational energy, [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Evolution of the normalised azimuthal Fourier amplitudes of the density for [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Left panel: space-time evolution of the spherical harmonics decomposition of the density for [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Spectrograms of the normalised spherical harmonics decomposition of the density performed with a [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Left panel: normalised Fourier transform of the [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The left and right panels show the evolution of the average corotation radius, and overlap between [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: GW strains emitted by a source at a distance [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Spectrograms of the GW strains measured at the equator (panels [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Left panel: dominant frequency of the GW signal associated with the LTWI against the average [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Evolution of the + polarization of the GW amplitude for an observer on the equatorial plane [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Time evolution of the total GW + polarization for an observer on the equatorial plane (left), and [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Time evolution of the neutrino luminosity for electron neutrinos, [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Time evolution of the isotropic equivalent neutrino luminosity emitted for different values of the [PITH_FULL_IMAGE:figures/full_fig_p024_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Spectrograms of the electron antineutrino luminosity for model [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Characteristic GW spectra for equatorial (left panel) and polar (right) observers, assuming a source [PITH_FULL_IMAGE:figures/full_fig_p025_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Neutrino event rates based on the equatorial, ( [PITH_FULL_IMAGE:figures/full_fig_p027_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Spectrograms of the neutrino event rate of the equatorial neutrino luminosities for model [PITH_FULL_IMAGE:figures/full_fig_p028_21.png] view at source ↗
read the original abstract

Rapidly rotating core-collapse supernovae are promising sources of multimessenger emission, as non-axisymmetric dynamics in the newly formed proto-neutron star can leave characteristic imprints on both gravitational waves and neutrinos. We present three-dimensional neutrino-magnetohydrodynamics simulations of the collapse of a rapidly rotating $35\,\mathrm{M}_\odot$ progenitor, performed with five different finite-temperature nuclear equations of state, to investigate how dense-matter physics affects the development of the low-$T/|W|$ instability and its associated multimessenger signatures. We find that the low-$T/|W|$ instability develops in all equation of state models considered, indicating that its occurrence is robust for this rapidly rotating progenitor. However, its onset time, dominant azimuthal structure, lifetime, and characteristic multimessenger frequencies vary among models, reflecting differences in the evolving proto-neutron star structure and rotation profile. The instability produces large-scale spiral modes that generate quasi-periodic gravitational wave emission and modulate the neutrino luminosities, especially along directions close to the equatorial plane. The dominant gravitational wave frequency associated with the instability correlates with the effective stiffness and compactness of the proto-neutron star: models with more compact/stiffer configurations emit at higher frequencies. This suggests that, in rapidly rotating core-collapse supernovae, the frequency of the low-$T/|W|$ instability-driven gravitational wave signal may provide a diagnostic of the dense-matter equation of state, complementary to the information carried by the neutrino signal.

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

1 major / 1 minor

Summary. The manuscript reports three-dimensional neutrino-magnetohydrodynamics simulations of the collapse of a rapidly rotating 35 M_⊙ progenitor using five different finite-temperature nuclear equations of state. It claims that the low-T/|W| instability develops in all five models, with variations in onset time, dominant azimuthal mode, lifetime, and multimessenger frequencies that reflect EOS-dependent differences in proto-neutron star structure and rotation; the dominant gravitational-wave frequency is reported to correlate with PNS compactness and stiffness, suggesting a potential EOS diagnostic complementary to the neutrino signal.

Significance. If the reported frequency variations prove robust, the work would identify a potentially useful multimessenger signature linking gravitational-wave observations to the dense-matter equation of state in rapidly rotating core-collapse supernovae. The demonstration that the instability occurs across all five EOS models is a clear strength.

major comments (1)
  1. [Abstract] Abstract, paragraph 2: the claim that onset time, dominant mode, lifetime, and GW frequency vary across the five EOS runs and that frequency correlates with compactness/stiffness (thereby providing an EOS diagnostic) is load-bearing for the central multimessenger inference, yet the abstract supplies no quantitative frequencies, compactness values, correlation metrics, error bars, or resolution studies. Without these, it is impossible to assess whether the ordering survives changes in grid resolution or neutrino-transport approximations.
minor comments (1)
  1. [Abstract] Abstract: the notation T/|W| is used without a brief parenthetical definition or reference to its standard meaning in the rotating stellar context.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their careful reading and constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract, paragraph 2: the claim that onset time, dominant mode, lifetime, and GW frequency vary across the five EOS runs and that frequency correlates with compactness/stiffness (thereby providing an EOS diagnostic) is load-bearing for the central multimessenger inference, yet the abstract supplies no quantitative frequencies, compactness values, correlation metrics, error bars, or resolution studies. Without these, it is impossible to assess whether the ordering survives changes in grid resolution or neutrino-transport approximations.

    Authors: We agree that the abstract would benefit from quantitative support for the reported variations and correlation. In the revised manuscript we will incorporate specific dominant GW frequencies, PNS compactness values, and the correlation metric drawn from the results section. The study was performed at a single fiducial resolution with our standard neutrino-transport treatment; no dedicated resolution or transport-approximation scans were carried out. We have added an explicit statement of this limitation to the discussion. revision: partial

standing simulated objections not resolved
  • Robustness of the reported frequency ordering and correlation under changes in grid resolution or neutrino-transport approximations.

Circularity Check

0 steps flagged

No circularity: empirical simulation outcomes independent of inputs

full rationale

The paper reports results from a suite of 3D neutrino-MHD simulations run with five different finite-temperature EOS models on the same 35 M⊙ progenitor. Observed variations in onset time, dominant mode, lifetime, and GW frequency are presented as direct numerical outcomes reflecting EOS-induced differences in PNS structure and rotation. No equations are fitted to subsets of the data and then re-predicted, no self-definitional relations equate outputs to inputs, and no uniqueness theorems or ansatzes are imported via self-citation to force the reported correlation. The suggested diagnostic use of GW frequency follows from the empirical ordering across runs rather than reducing to the simulation inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on numerical simulation outcomes; no free parameters, invented entities, or non-standard axioms are identifiable from the abstract alone.

axioms (1)
  • domain assumption Ideal magnetohydrodynamics and the chosen neutrino transport scheme accurately capture the relevant dynamics of the proto-neutron star.
    Implicit in any neutrino-MHD simulation described at this level of detail.

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