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Rapidly rotating core-collapse supernova models emit gravitational waves up to 3 kHz—higher than typical non-rotating models—because fast spin shrinks the proto-neutron star's polar radius while angular momentum gradients stabilize lower la

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2026-08-03 18:00 UTC pith:RU3K432Y

load-bearing objection A careful rotation scan with a real empirical trend up to ~3 kHz, but the causal explanation rests on a post-hoc polar-radius fit and an unidentified mode; worth reviewing with revisions. the 4 major comments →

arxiv 2512.07066 v2 pith:RU3K432Y submitted 2025-12-08 astro-ph.HE

Trends in gravitational wave emission in axisymmetric simulations of rotating core-collapse supernovae

Bailey Sykes , Bernhard M\"uller This is my paper
classification astro-ph.HE
keywords core-collapse supernovaegravitational wavesproto-neutron star oscillationsrotationmagnetohydrodynamicsaxisymmetric simulationsBrunt-Väisälä frequencyresonant mode amplification
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish how strong rotation changes the gravitational-wave (GW) signal of core-collapse supernovae. Using 14 axisymmetric magnetohydrodynamic simulations of the same 17-solar-mass progenitor, scanned finely over initial rotation rate, it finds that rotating models emit GWs at frequencies up to about 3 kHz—well above the roughly 1 kHz dominant band typical of non-rotating models. The paper attributes the high frequencies to a rapidly rotating proto-neutron star with a small polar radius and to angular momentum gradients that stabilize the equatorial region, and it shows that both the frequency and amplitude of the dominant emission decrease as rotation speeds up. It also reports that a recently claimed resonant amplification of the GW signal does not appear in these runs, and that linear mode analysis based on spherical averages fails for rotating stars. If correct, these trends shape what detectors should look for and how proto-neutron-star structure could be inferred from a future supernova GW detection.

Core claim

The central claim is that the dominant post-bounce GW emission in rotating core collapse is set by the proto-neutron star's compactness at the poles, not by an equatorial or average radius. Because rapid rotation makes the PNS oblate, the polar radius shrinks while the equator bulges; combined with angular momentum gradients that raise the local oscillation frequency at lower latitudes, this pushes the dominant GW band to 3 kHz and beyond. The paper shows that the analytic estimate f_peak ≈ (1/2π) sqrt(G M / R^2 · 1.1 m_n / ⟨E_ν̄e⟩) reproduces the simulated dominant frequency to within 5–10% when the polar PNS radius is used, for all rotation rates in the main set. It further finds that fast

What carries the argument

The argument leans on Eq. (4), an analytic approximation for the dominant GW frequency built from PNS mass, radius, and mean electron-antineutrino energy—a stand-in for the Brunt-Väisälä frequency—evaluated with the polar radius of the oblate PNS. Around this sits a frequency analysis using the Solberg-Høiland criterion, which combines Brunt-Väisälä and epicyclic frequencies to show that equatorial stabilization by rotation nearly compensates for the lower buoyancy frequency there. A spatial decomposition of the quadrupole signal into radius-dependent contributions identifies the ringdown mode at about 580 Hz and traces acoustic waves propagating from the PNS into the gain region.

Load-bearing premise

The causal story rests on choosing to evaluate the PNS radius at the pole in Eq. (4); the authors select the polar radius after finding it fits the simulated frequency best, so if the dominant mode is actually set by the equatorial structure, an averaged radius, or code-specific compactness, the high-frequency explanation is not established.

What would settle it

Take a rotating core-collapse model from a different code with full general relativity and the same progenitor and rotation rate: if its dominant GW band sits near 1–2 kHz rather than near 3 kHz while the PNS polar compactness is similar, the polar-radius mechanism fails. Equivalently, a two-dimensional rotational eigenmode calculation that identifies the dominant emission as a mode governed by equatorial, rather than polar, structure would falsify the stated cause.

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

If this is right

  • Searches and waveform templates for galactic supernovae should allow a dominant GW band that can exceed 3 kHz in rotating progenitors, not only the roughly 1 kHz band typical of non-rotating models.
  • The trend that faster rotation lowers both GW amplitude and peak frequency means rotation rate may be inferable from the loudness and pitch of the late-time signal.
  • The absence of resonant amplification across a finely spaced rotation scan suggests the phenomenon reported elsewhere is not a universal feature of rotating core collapse, or requires conditions not met here, such as weaker magnetic fields or different code physics.
  • Because magnetized models suppress p-modes that appear in non-magnetic runs, magnetic-field strength leaves an observable imprint on the GW spectrum.
  • Existing linear eigenmode analysis fails even for the slowest rotating model examined, so mode identification for rotating PNSs requires a genuinely two-dimensional perturbative approach.

Where Pith is reading between the lines

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

  • A testable extension would be to run the same rotation scan with magnetic-field strengths bracketing the value used here; if resonant amplification reappears at weaker field, the authors' null result would point to magnetic braking of PNS differential rotation as the controlling factor.
  • If the polar-radius interpretation holds generally, then inverting a detected GW frequency with Eq. (4) would constrain the polar—not the equatorial—compactness of a newborn neutron star, a probe of the equation of state under rapid rotation.
  • The spatial decomposition hints that PNS interior oscillations couple to the gain region at the same frequency; checking this coupling across different codes could clarify whether acoustic power helps revive stalled shocks, connecting GW emission to the explosion mechanism.
  • The high-frequency trend strengthens the case for dedicated high-frequency GW detectors, since a Milky Way rotating collapse would put its dominant emission exactly in the band where current broadband detectors lose sensitivity.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper presents 17 axisymmetric (2D) simulations of a 17 M_sun progenitor with the CoCoNuT-FMT code, scanning initial rotation boosts from 0.29 to 3.48 rad/s (plus two non-MHD controls and a high-cadence model), with the aim of mapping GW frequency and amplitude trends and testing the resonant mode amplification reported by Cusinato et al. [31]. The authors report that the dominant post-bounce GW band reaches frequencies up to ~3 kHz, exceeds typical values in non-rotating models, and is well reproduced by Eq. (4) when the PNS radius is evaluated near the pole; frequencies and amplitudes tend to decrease with faster rotation; MHD models lack p-modes seen in non-MHD counterparts; and no resonant amplification is found. The paper also presents a radial decomposition of the quadrupole signal and a linear eigenmode analysis that works for the non-rotating model but fails for the rotating SR1 model.

Significance. If the central claims hold, the paper provides a useful counterpoint to the common picture that rotation mainly lowers GW frequencies: for this massive, compact progenitor family, rapidly rotating PNSs can emit a dominant band above 2 kHz, with amplitude suppression from angular-momentum stabilization and shock expansion. The finely spaced rotation scan around the resonant rate and the 3D check of the SR1 model are strengths, as is the clear demonstration that the existing 1D eigenmode framework breaks down at even the slowest rotation considered. The radial decomposition of the quadrupole emission and the direct comparison with the non-MHD controls are also valuable. However, the paper's causal interpretation—small polar radius plus centrifugal stabilization—rests on a post-hoc choice of radius definition and on an unidentified mode, so the significance of the 3 kHz result as a robust physical prediction is currently qualified. The null result on resonance is reported with appropriate caution and is code/system dependent.

major comments (4)
  1. [IVA1, Eq. (4), Fig. 5] The central causal claim that the high frequencies arise from small polar radii is supported only by a post-hoc choice of radius definition. The text states that 'using the PNS radius near the polar axis produces the best fit', but no comparison is shown among polar, equatorial, mean, minimum, or volume-averaged radii, or against an independent mode identification. Since the PNS is oblate by a factor of ~1.7 in radius (§IVA1), M/R^2 varies by a large factor depending on the choice, so agreement with Eq. (4) at the 5–10% level does not by itself establish the polar-radius mechanism. Please quantify the goodness-of-fit for alternative definitions and/or provide independent evidence from the oscillation eigenfunction.
  2. [IVC, Fig. 16, footnote 4] The linear eigenmode analysis for SR1 finds no computed mode matching the dominant GW band; the p-modes decrease when the shock expands while the GW signal increases, and the authors state in footnote 4 that they are 'unable to identify the modal character of the dominant emission band.' That is a direct gap between the data and the abstract's claim that the 3 kHz emission is due to polar Brunt-Väisälä compression plus angular-momentum stabilization. Eq. (4) is itself only a global approximation to the Brunt-Väisälä frequency (footnote 1), so a fit to it cannot substitute for mode identification. The conclusion appropriately calls for 2D perturbative techniques; the causal statement in the abstract should be softened or the mode identification supplied.
  3. [IVA1, Fig. 7] The 3D verification run covers only t_pb < 0.3 s and uses the same modified Newtonian potential and the same code, so it does not confirm frequencies near 3 kHz, nor does it rule out code/EoS-specific effects. The text says the 3D run 'confirms' that the large frequencies are not an artifact of 2D, but at 0.3 s the dominant band is still around or below ~1.5–2 kHz in the 2D model. Please present a longer 3D evolution or clearly delimit the verification statement to early times.
  4. [IVA1/IVA3, Sec. V] The paper reasonably notes a ~20% upward shift from the modified Newtonian potential and known structural differences between CoCoNuT and Aenus-ALCAR, but when combined with the polar-radius choice, the absolute statement 'frequencies of up to 3 kHz' carries an unquantified systematic error. Please provide a quantitative estimate of the combined uncertainty (e.g., a range of f_peak under alternative radius definitions and a GR-correction estimate) so that the 3 kHz claim is robust.
minor comments (5)
  1. [IVA2, Eq. (7)] Equation (7) as printed is dimensionally inconsistent: f_Omega^2 = (Omega/2pi)^2 r d(r^2 Omega)/dr has dimensions L^3/T^3 rather than T^-2. It should presumably be the standard epicyclic frequency expression, e.g. f_Omega^2 = (1/(4pi^2 r^3)) d(r^4 Omega^2)/dr. Please correct.
  2. [Table I, Sec. IVA] The claim that 'peak frequencies also decrease as the angular velocity increases' is based on a rough guide in Table I, but the listed f_1s values are nonmonotonic (e.g. BF3.7 = 2.3 kHz, BF4 = 2.5 kHz, BF5.6 = 2.4 kHz). The text hedges with 'tend to', but a systematic ridge-extraction estimate with uncertainties would make the trend more convincing.
  3. [Figure 5 / Fig. 4 captions] The black line representing f_peak from Eq. (4) is identified in Fig. 4, but in Fig. 5 (top panel) the two curves are nearly indistinguishable. Please use distinct line styles and a legend that explicitly states the polar-radius choice used in Eq. (4).
  4. [IVA1, Sec. IVA3] The comparison with the 3D model is described as confirming 'that the PNS structure, and particularly the transport of angular momentum within the PNS, is reliably captured in axisymmetry.' Given the short 3D runtime and the same gravitational-potential approximation, this statement is stronger than the evidence; please qualify it.
  5. [II, Sec. III] The paper explicitly acknowledges that uniformly boosting the angular velocity without restoring hydrostatic equilibrium is a shortcoming. Since the artificial quadrupole offset is subtracted in post-processing, it would be helpful to state whether this subtraction affects the quoted amplitudes or the extraction of the high-frequency band in any systematic way.

Circularity Check

1 steps flagged

Central causal claim ('high frequencies from small polar radii') rests on a post-hoc polar-radius choice for Eq. (4) that is selected to match the simulated GW frequency.

specific steps
  1. fitted input called prediction [Section IV A 1 ('Understanding the dominant mode'), around Eq. (4) and Fig. 5]
    "However, this varies depending on how the PNS radius is defined due to rotation-induced oblateness – in this analysis we find that using the PNS radius near the polar axis produces the best fit of f_peak to the simulated GW data. The reasonable goodness-of-fit of the f_peak approximation allows us to attribute the high frequencies of the dominant GW emission in our models with physical properties of the PNS, specifically the PNS compactness term (M/R^2) computed at the poles"

    The paper's causal explanation is that small polar radii produce the ~3 kHz GW band. The evidence is that Eq. (4), evaluated with the polar radius, reproduces the simulated GW frequency. But the radius definition entering Eq. (4) is not fixed a priori; the authors explicitly select the polar radius because it gives the best fit to the GW data. Thus the agreement between f_peak and the observed band is partly manufactured by the choice of R, and using that agreement as evidence for the polar-radius cause is circular. The formulas' time evolution and constants are not fitted, so the circularity is partial, but the central attribution is not an independent prediction. The linear mode analysis in Sec. IVC cannot identify the mode, leaving the physical interpretation unvalidated.

full rationale

The GW frequencies and amplitudes are genuinely simulated: they are computed from the hydrodynamic flow via the quadrupole formula (Eq. 2), independent of Eq. (4). The use of Eq. (4) from Müller et al. [6], a co-authored paper, is not itself objectionable — it is an analytic relation with independent physical content and is compared against the simulated signal. The circularity is localized to the adaptation of that relation to a rotating, oblate PNS: the authors choose the polar radius definition post hoc because it 'produces the best fit', and then use the resulting match to claim that polar compactness sets the high GW frequency. That makes the central causal claim partially a fitted input rather than a prediction. Additional supporting evidence exists (fast polar downflows, polar/equatorial f_BV profiles, the f_SH analysis), but the modal character of the 3 kHz band is explicitly not identified, and the 3D verification covers only t_pb < 0.3 s, before the band reaches its highest frequencies. These are limitations and correctness risks, but the specific circular step is the polar-radius selection for Eq. (4).

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The paper postulates no new particles, forces, or conserved quantities. The dominant GW emission band is an observed oscillatory feature, not an invented entity. The main input choices are rotation boosts, the magnetic field configuration, and the PNS radius definition, with the latter being post-hoc and therefore a genuine free parameter in the explanatory relation.

free parameters (5)
  • PNS radius definition used in Eq. (4) = rho=10^11 g cm^-3 isosurface, polar axis
    Chosen post hoc because it 'produces the best fit' of f_peak to simulated GW frequencies (Sec. IVA1, Fig. 5).
  • Initial magnetic field strength = B_tor = B_pol = 10^10 G
    Manually chosen input, motivated by prior MHD CCSN studies; central to the claimed magnetic suppression of p-modes.
  • Rotation boost factors = 1x, 1.5x, 2x, ..., 12x (Omega_c from 0.29 to 3.48 rad/s)
    Hand-chosen grid of initial rotation rates, intentionally dense near the Cusinato et al. resonance rate; defines the trend claimed in the paper.
  • Radial cutoff for maximum f_BV and f_Omega = 100 km
    Analysis choice for comparing dynamical frequencies to GW bands; changes which peak is selected in Figure 4.
  • PNS boundary density for mass and radius = rho = 10^11 g cm^-3
    Defines the PNS mass/radius entering Eq. (4); the paper notes the definition matters because of rotation-induced oblateness.
axioms (5)
  • domain assumption The axisymmetric quadrupole formula Eq. (2), using only the plus polarization, adequately represents the physically relevant GW emission.
    Sec. IVA; standard in CCSN literature, but 2D simulations omit the cross-polarization and may overestimate amplitude, as the paper itself notes citing [14,22,23].
  • ad hoc to paper Uniformly multiplying the entire progenitor's angular velocity by a constant factor, without restoring hydrostatic equilibrium, does not invalidate the rotation trends.
    Sec. II flags this as a shortcoming; an artificial low-frequency quadrupole is subtracted in post-processing, and fast-rotator PNS structure is assumed to remain physical.
  • domain assumption The Newtonian Brunt-Väisälä and epicyclic frequency definitions, Eqs. (5)-(7), capture the mode-relevant dynamical frequencies in a rapidly rotating, deformed PNS.
    Sec. IVA2; the paper uses these spherical-average/local definitions despite the PNS being strongly oblate at late times.
  • domain assumption The mean antineutrino energy and PNS compactness from the FMT transport and SFHo EoS determine the peak GW frequency via Eq. (4), even in rotating non-spherical stars.
    Sec. IVA1; Eq. (4) has no rotational terms and is applied by choosing the polar radius; the paper acknowledges this choice is post hoc.
  • domain assumption The linear eigenmode framework of Torres-Forné et al. with the Cowling approximation is a valid ground truth for the non-rotating BF0_noB model.
    Sec. IVC; the great code assumes spherical symmetry and static perturbations, which is appropriate for BF0_noB but explicitly fails for SR1.

pith-pipeline@v1.3.0-alltime-deepseek · 24200 in / 15009 out tokens · 140734 ms · 2026-08-03T18:00:26.504297+00:00 · methodology

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read the original abstract

The quantitative impact of strong rotation on the amplitudes and frequencies of the post-bounce gravitational wave (GW) signal from core-collapse supernovae (CCSNe) is still not fully understood. To study trends in frequencies and amplitudes, and possibly spectacular phenomena like resonant amplification, we perform a series of axisymmetric long-duration magnetohydrodynamic CCSN simulations of a 17 $M_\odot$ progenitor using a finely spaced grid in initial rotation rate from 0.29 rad/s to 3.48 rad/s. We find that these rotating models produce GWs at frequencies of up to 3 kHz, higher than in typical non-rotating models in the literature. The high frequencies arise due to small polar radii of rapidly rotating proto-neutron stars and stabilization by angular momentum gradients at lower latitude. GW frequencies and amplitudes tend to decrease with faster rotation. Different from two complementary simulations without magnetic fields, the magnetohydrodynamic models are characterized by an absence of p-modes above the dominant high-frequency emission band. We find no indication of resonant mode amplification for any rotation rate, although a temporo-spatial and space-frequency analysis reveals some interesting couplings of quadrupolar motions across the proto-neutron star and the gain region. Generalized, multi-dimensional perturbative techniques need to be developed to study the mode structure and mode interaction in the collapse of rapidly rotating massive stars.

Figures

Figures reproduced from arXiv: 2512.07066 by Bailey Sykes, Bernhard M\"uller.

Figure 1
Figure 1. Figure 1: FIG. 1: Initial angular velocities of models in the main set, as [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Shock radius as function of post-bounce time for simulations in the main set. The mean radius is shown as a solid line, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: GW amplitudes, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Normalized wavelet spectra of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Slice of radial velocity of the SR1 model at [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Normalized wavelet spectra of GWs from a [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Exemplar radial profiles of the dynamical frequencies [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Time series of GW amplitudes, [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Same as Figure 4 but for the two additional non-magnetic simulations. The epicyclic frequency, [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Normalized quadrupole amplitude [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Slices of the time-derivative of the integrand in the [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Close-up of a brief period in box A (although with [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Frequency evolution of several low node count eigenmodes over-plotted on the spectrogram for [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Same as Figure 15 but for model SR1. The spectrogram is reproduced from the corresponding panel of Figure 4. [PITH_FULL_IMAGE:figures/full_fig_p019_16.png] view at source ↗

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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