Effects of Rotation on 3D Core-Collapse Supernova Models for Low-Mass Progenitors

Adam Burrows; David Vartanyan; Tianshu Wang

REVIEW 2 major objections 5 minor 2 cited by

Effects of Rotation on 3D Core-Collapse Supernova Models for Low-Mass Progenitors

T0 review · 2 major / 5 minor · reviewed 2026-07-10 · grok-4.5

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Pith's one-line read Rotation alone barely changes explosion energy, blast shape, or yields for a low-mass supernova that explodes early.

desk verdict Solid, carefully scoped Fornax continuum: pure rotation is muted for this early-exploding 9 M☉ model except at the fastest spin, where T/|W| spirals and spin-kick alignment appear. read the letter →

arxiv 2607.06664 v1 pith:EBHYKVB7 submitted 2026-07-07 astro-ph.HE astro-ph.SR

Adam Burrows , Tianshu Wang , David Vartanyan This is my paper · ORCID

classification astro-ph.HEastro-ph.SR

keywords core-collapsesupernovaerotation3Dsimulationsexplosionenergyspin-kickalignmentT/|W|instabilitygravitationalwavesnucleosynthesis

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 runs a controlled suite of three-dimensional core-collapse simulations of a single 9-solar-mass star, varying only the initial core spin from zero to rapid rates while deliberately omitting magnetic fields. The authors show that explosion energy, shock asymmetry, neutrino heating, residual neutron-star mass, and nucleosynthetic yields all change only modestly across that range; the dependence is non-monotonic and never large. Only the fastest rotator produces clear spin-kick alignment, low-T/|W| spiral-arm modes, and a distinctly stronger gravitational-wave signal. Because collapse amplifies the core period by a factor of roughly four thousand, the modest observed birth periods of radio pulsars imply that most progenitor cores were already spinning slowly. The result matters because it isolates pure hydrodynamic rotation from the more dramatic magnetorotational effects that dominate the literature, and it suggests that for the common class of early-exploding low-mass progenitors rotation can be treated as a secondary correction.

What carries the argument

A controlled sequence of long-term 3D multi-group radiation-hydrodynamics runs of the same 9-solar-mass progenitor, differing only in the Eriguchi-Müller cylindrical rotation profile (Ω₀ = 0, 0.01, 0.1, 1.0 rad s⁻¹), carried to saturation so that asymptotic observables can be compared directly.

What would settle it

Repeat the same rotation sequence for a higher-compactness progenitor that explodes later; if that model shows large monotonic changes in explosion energy or strong spin-kick alignment already at moderate spins, the generalization fails.

Watch

Extended reading notes

Core claim

For a low-mass, low-compactness progenitor that explodes early, the effects of pure rotation on explosion energy, blast asymmetries, neutrino heating, nucleosynthetic yields, and residual neutron-star mass remain small and non-monotonic across two orders of magnitude in initial spin; only the most rapid rotator develops T/|W| ~ 0.05 corotation instabilities, spiral arms, spin-kick alignment, and elevated gravitational-wave emission.

Load-bearing premise

The claim that rotation is muted for most supernova cores rests on a single early-exploding low-mass progenitor and on the deliberate exclusion of magnetic fields.

Editorial extensions

If this is right

For low-mass early-exploding progenitors, pure rotation can be treated as a small correction to non-rotating models when predicting energy, yields, and residual mass.
Observed radio-pulsar birth periods of hundreds of milliseconds imply typical pre-collapse core periods of minutes rather than seconds.
Clear spin-kick alignment and strong low-T/|W| spiral modes appear only above a high spin threshold, so most ordinary pulsars need not show them.
Gravitational-wave signals from ordinary core-collapse events should lack the cascade of discrete T/|W| bands seen only in the fastest rotator.
Nucleosynthetic differences driven by rotation alone are smaller than those already produced by modest convective seed perturbations.

Reading between the lines

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

Magnetized versions of the same rapid rotator would likely convert the modest rotational reservoir into jet-like morphology and higher energy, recovering the classic magnetorotational channel.
If more massive or binary-stripped progenitors retain higher core spins, the spin-kick correlation observed in some pulsars may be explained without invoking post-explosion mechanisms.
The factor-of-4000 spin-up sets a quantitative target for asteroseismic and white-dwarf spin measurements that can be checked against the same angular-momentum-transport physics.
A denser grid of intermediate spins would locate the sharp threshold between random and aligned kicks, testing whether alignment is a continuous or threshold phenomenon.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This is a clean parameter study that actually answers a practical question: how much does pure rotation change the late-time observables for a low-mass, early-exploding core? The answer, for the Sukhbold 9 M☉ model run with Fornax to saturation, is “not much” until you hit Ω0 = 1 rad s−1.

What is new is the controlled continuum (0, 0.01, 0.1, 1.0 rad s−1) carried all the way to asymptotic energy, kicks, yields, and GW, rather than stopping at early explodability. Energy is non-monotonic and stays within ~20 %. Neutrino luminosities and heating barely move except for the fastest model, and even then the early heating anisotropy is weak because the star explodes before the PNS has spun up and become strongly oblate. Spin-kick alignment and clear multi-m spiral arms at T/|W| ~ 0.05 appear only for that fastest run; the GW spectrograms make the modes obvious. The measured initial-to-final period ratio ~4000 is a useful number for the pulsar-birth discussion. Methods, grid, EOS, and neutrino groups are standard Fornax and the trends look internally consistent.

The soft spots are exactly the ones the authors flag: one progenitor, no magnetic fields, and the usual Eriguchi–Müller cylindrical law with fixed A = 1000 km. The abstract and §9 already say the generalization to “most cores” is provisional. That is not a hidden flaw; it is the natural limit of a four-run study. Data and code are not public, which is normal for this group but still a practical friction.

Anyone working on CCSN systematics, pulsar birth spins, or GW from rotating cores will get value from the tables and figures. It is not a mechanism paper and does not reorganize the field, but it is honest computational work that fills a real gap. I would send it to referees without hesitation; the scoped claim holds and the caveats are already written.

Referee Report

2 major / 5 minor

Summary. The paper presents four long-term 3D multi-group radiation-hydrodynamics simulations (Fornax, SFHo EOS, 12 energy groups) of the Sukhbold et al. (2016) 9-M⊙ progenitor, varying only the initial central angular frequency Ω0 = 0, 0.01, 0.1, and 1.0 rad s−1 under the Eriguchi & Müller cylindrical rotation law (A = 1000 km) and deliberately omitting magnetic fields. The runs are carried to asymptotic saturation of explosion energy, residual mass, kicks, nucleosynthesis, and gravitational-wave emission. The central claim is that, for this early-exploding low-mass model, rotation alone produces only weak, non-monotonic changes (≲20 %) in explosion energy, modest increases in blast asymmetry, negligible pole–equator heating anisotropy during the launch phase, and little change in yields; only the fastest rotator develops a T/|W| ≈ 0.05 corotation instability with spiral arms, stronger GW emission, and clear spin–kick alignment, while the initial-to-final core spin-period ratio is measured to be ∼4000.

Significance. If the reported trends hold, the work supplies a clean, systematically varied benchmark isolating pure hydrodynamic rotational effects for an early-exploding progenitor. The long-term (≳2 s) multi-messenger diagnostics—explosion energy, residual mass, recoil kicks, Ye–entropy distributions, production factors, and both matter and neutrino GW spectrograms—are valuable for the community. The clear detection of low-T/|W| spiral modes and the measured spin amplification factor ∼4000 are concrete, falsifiable results that constrain progenitor spin models and GW templates. The careful scoping to one low-compactness progenitor and the explicit omission of magnetic fields are strengths of scientific honesty rather than weaknesses.

major comments (2)

[Table 1, §3] Table 1 and §3: the final spin periods (and therefore the quoted initial-to-final ratio ∼4000) are obtained from L/I_NS with the spherical Breu & Rezzolla (2016) formula and a fixed R_NS = 12 km. For the Ω0 = 1 model (T/|W| ≈ 0.0475 at 2 s) the spherical approximation underestimates the true moment of inertia; a short quantification of the resulting period error (or a non-spherical I estimate) is needed before the ratio is used to infer that “most supernova cores” are born slowly rotating.
[§2, §9] §2 and §9: the Eriguchi & Müller cylindrical law with fixed scale A = 1000 km is adopted without a sensitivity test. Because the paper’s strongest claim is that rotation effects remain muted “across a wide range of initial spins,” at least a brief discussion (or one additional run) of how changing A by a factor of a few alters the early gain-region centrifugal support and the final T/|W| would strengthen the robustness of that claim.

minor comments (5)

[Abstract, §3] Abstract and §3: “a T/|W| corotation instabilities” is grammatically incorrect; change to “a T/|W| corotation instability” or “T/|W| corotation instabilities.”
[Figure 1, §3, §8] Figure 1 caption and several places in the text use inconsistent spacing (“T /|W|”, “T/|W|”); standardize to T/|W|.
[§1] §1: “motive this work” should be “motivate this work.”
[Figure 9, §4] Figure 9 and text: model labels occasionally appear as “9-rot0.0” or “9-rot0.1” without the hyphen; keep the consistent “9-rot-0.0” form used in Table 1.
[§8] §8: the statement that the hydro dump cadence is 1000 Hz (Nyquist-limited to 500 Hz) while GW data are written at 25–50 kHz is useful; a single sentence noting that a higher hydro cadence will be required for a full modal decomposition of the spiral arms would help the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: observables are direct numerical outputs of independent 3D Fornax runs, not rearrangements of fitted inputs or self-citation chains.

full rationale

This is a standard computational survey. Four 3D radiation-hydrodynamics simulations of the Sukhbold et al. (2016) 9-M⊙ progenitor are evolved with prescribed initial cylindrical rotation profiles (Eriguchi & Müller 1985 form, A=1000 km, Ω0 = 0, 0.01, 0.1, 1.0 rad s−1). Explosion energy, shock multipoles, neutrino luminosities/heating rates, recoil kicks, PNS convection, nucleosynthetic yields, and GW strains are extracted by post-processing the time-dependent fields (Table 1, Figs. 1–26). The reported initial-to-final spin-period ratio ∼4000 is simply the ratio of the input central period to the final L/I (I from the external Breu & Rezzolla 2016 formula). Self-citations supply the Fornax code description, prior non-rotating 9a/9b comparison runs, and methodological context; none of them is used as a uniqueness theorem or as the sole warrant for the rotation-dependence claims. No parameter is fitted to a subset of the present data and then re-labeled a prediction, and no algebraic identity equates an output to an input by construction. The paper’s own caveats (single low-mass progenitor, no magnetic fields) are scope limitations, not circularities. Score 0 is therefore required.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The work is a parameter study of initial rotation in an established CCSN code. Load-bearing inputs are the progenitor, the ad-hoc rotation law and rates, the nuclear EOS, neutrino transport discretization, and the deliberate neglect of magnetic fields. No new physical entities are postulated; free parameters are numerical/setup choices that define the experiment rather than fitted constants that force the conclusion.

free parameters (4)

Initial angular frequencies Ω0 = 0, 0.01, 0.1, 1.0 rad s−1
Hand-chosen continuum 0, 0.01, 0.1, 1.0 rad s−1 to span slow to rapid spin; not fitted to data but defines the study axes.
Cylindrical rotation scale A = 1000 km
Fixed at 1000 km in the Eriguchi & Müller law; standard but arbitrary profile choice that sets differential rotation.
Spatial grid and neutrino groups = 1024×128×256; 12 groups
1024×128×256 (r,θ,φ) and 12 energy groups per species; resolution and group structure affect numerics but are not data-fitted.
Cold NS radius in I_NS formula = 12 km
R_NS set to 12 km when converting final angular momentum to period (Table 1); affects reported final periods especially for rapid rotators.

assumptions (5)

domain assumption SFHo nuclear equation of state adequately describes the PNS and shock thermodynamics for this study.
Stated in §2; EOS choice affects compactness, neutrino emission, and T/|W|.
domain assumption Magnetic fields can be omitted when isolating pure rotational hydro/radiation effects.
Explicit scope in abstract and §1–§2; authors note B-fields may matter for rapid rotators.
domain assumption Sukhbold et al. (2016) 9-M⊙ solar-metallicity progenitor structure at collapse is representative of low-mass early-exploding CCSNe.
Single-progenitor choice in §2; compactness ξ_1.75=6.7e-5 used to justify early asymptote.
ad hoc to paper Eriguchi & Müller (1985) cylindrical rotation law is an acceptable proxy for unknown true core spin profiles.
§2 acknowledges true profiles are unavailable and recipes are criticized; parametrization is conventional but not derived from this star.
domain assumption Multi-group neutrino transport and gravity treatment in Fornax are sufficient for asymptotic explosion energy, kicks, and yields.
Method section and prior Fornax literature; community standard but not converged physics.

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Cite this review

Pith. "Pith review of Effects of Rotation on 3D Core-Collapse Supernova Models for Low-Mass Progenitors." pith.science (2026). https://pith.science/paper/EBHYKVB7

@misc{pith2026260706664,
  author       = {Pith},
  title        = {Pith review of: Effects of Rotation on 3D Core-Collapse Supernova Models for Low-Mass Progenitors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EBHYKVB7}},
  note         = {Machine review of arXiv:2607.06664}
}

abstract

We explore the dependence upon rotation rate alone of various supernova observables simulated to their saturation for the explosion of a 9-$M_{\odot}$ progenitor. We find that the explosion energy is non-monotonic with, and weakly dependent upon, spin across a broad range of initial spins. The asymmetries of the blast depend weakly on spin, with faster spins leading to only slightly greater asymmetries. There is little significant pole-equator neutrino heating asymmetry during explosion, even for rapid rotation, and only for the fastest rotator does the neutrino heating rate diminish noticeably. Hence, the effects of rotation alone on all salient aspects of supernova dynamics are not large. We find that the recoil kick and spin are clearly aligned only for the most rapidly rotating model. Interestingly, for the fastest rotator, we witness a $T/|W|$ corotation instabilities near a value of 0.05 and spiral arm modes emerge. We find that the nucleosynthetic yields depend little upon the rotation rate and determine that the ratio of initial to final core spin period is near $\sim$4000, implying, given the modest inferred radio pulsar periods at birth, that the initial spin periods of most supernova cores are likely quite long. However, we focus on only one progenitor and do not include magnetic fields. Nevertheless, at least for low-mass progenitors which explode early, we find muted consequences of rotation in most major particulars across a wide range of initial spins.

Figures

Figures reproduced from arXiv: 2607.06664 by the authors.

**Figure 1.** Maximum shock radius (left) and normalized spherical harmonic decomposition of the shock radius (right). The decomposition is done using al = qPm=l m=−l | R f(θ, ϕ)Ylm(θ, ϕ)dΩ| 2/(4π(2l + 1)). We note that the mean shock radius and the time of explosion are weak functions of initial spin rate. It is only at and faster than Ω0 ≈ 0.1 rad s−1 that we see the shock radius peel off from the other models, and this only sl… view at source ↗

**Figure 2.** Proto-neutron star baryon mass and gravitational mass (left) and PNS radius (right, defined as the mean radius at which the mass density is 1011 g cm −3 ). Note that the evolution of the gravitational mass tracks the integrated neutrino energy losses. By the end of the simulations ∼0.04 M⊙c 2 has radiated. Note also that the final baryon mass of the residues changes little after ∼0.5 seconds post-bounce, decreasing … view at source ↗

**Figure 3.** Cutaway slices depicting electron fraction (Ye; blue low and red higher) on the surfaces, with an inner embedded isodensity surface (at 109.5 g cm−3 , colored by Ye), for the non-rotating and most rapidly rotating (9-rot-1.0) models at 100 (left) and ∼200 milliseconds (right) after bounce. On the left plots, the darker regions depict those in which there has been significant electron capture behind the shock that bo… view at source ↗

Figures from the paper (23 more)

**Figure 4.** Figure 4: Nested isodensity spheres (at 109.5 and 1011 g cm−3 ), colored by Ye, bounding the inner protoneutron star convective region indicated by particle trajectories, for the non-rotating (left) and Ω0 = 1.0 radian per second (right) models. Noted that rotation for the initi…

**Figure 5.** Figure 5: Entropy slices in the x-z plane of all models at 0.4 seconds post-bounce. The Ω0 = 0.0 and 0.01 rad s−1 models show more spherical explosions, while modest pole-equator structures develop in the faster rotating 9-rot-1.0 model. This behavior is consistent with the shoc…

**Figure 6.** Figure 6: Density (top) and electron fraction (bottom) profiles at 500, 1000, and 1500 ms post-bounce along polar (left) and equatorial (right) directions. Compactification with time is manifest for all models. It is only the fastest rotating model (red) that clearly deviates fr…

**Figure 7.** Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

**Figure 8.** Figure 8: Specific angular momentum flux in the y-x (left) and z-x (right) planes at 0.5 (top) and 2 (bottom) seconds postbounce for the 9-rot-1.0 model. Within ∼300 ms of bounce, the core that is shrinking quasi-statically due to neutrino losses during its Kelvin-Helmholtz coo…

**Figure 9.** Figure 9: Angle-integrated neutrino energy luminosity (left, in Bethes per second) and average energy (right, in MeV) for the various neutrino species in the laboratory frame at 10000 km. One Bethe ≡ 1051 ergs. The dotted lines are for the νµ, ντ , ¯νµ, and ¯ντ neutrinos collect…

**Figure 10.** Figure 10: Net heating rate in the gain region in Bethes per second as a function of time (in seconds) for all new models of this paper. Centrifugal support for model 9-rot-1.0 lowers its mean neutrino energies and luminosities in the gain region behind the shock during the firs…

**Figure 11.** Figure 11: Explosion energy (in Bethes, B) versus time after bounce (in seconds) for all four models of this study. The blue curve depicts the baseline behavior of the initially non-rotating model. The behavior is not monotonic, with the 9-rot-0.1 and 9-rot-1.0 models separating…

**Figure 12.** Figure 12: Specific net heating rate in the x-z plane at 0.1, 0.3, 0.5, and 2.0 seconds post-bounce of the 9-rot-0.0 model. Despite transient variations with angle of the energy deposition rate in the turbulent heating rate exterior to the inner PNS, there is no pole-equator dic…

**Figure 13.** Figure 13: Specific net heating rate in the x-z plane at 0.1, 0.3, 0.5, and 2.0 seconds post-bounce of the 9-rot-1.0 model. Unlike for model 9-rot-0.0 depicted in [PITH_FULL_IMAGE:figures/full_fig_p024_13.png]

**Figure 14.** Figure 14: Total (left) and neutrino (right) recoil kicks in km s−1 versus time after bounce (in seconds). We see a nonmonotonic dependence upon initial spin rate, with the intermediate spin rates manifesting the lowest overall kicks. However, we are not confident this is not a…

**Figure 15.** Figure 15: The angle-integrated convective luminosity profile in the protoneutron star versus time after bounce in seconds. The red regions depict where lepton-driven convection in the core is found. It begins in a shell, whose inner boundary slowly moves inward until it reaches…

**Figure 16.** Figure 16: Radial Mach number in the x-z plane at ∼0.5 and ∼1.5 seconds post-bounce of the 9-rot-0.0 (top) and 9-rot-1.0 (bottom) models. From the radial dominance (even at late times) and roughly alternating sign of the mean convective velocity, the convective zone in the initi…

**Figure 17.** Figure 17: Final ejecta Ye distributions for all four 9.0-M⊙ models simulated for this paper, along with those for the 9a and 9b models from Burrows et al. (2024a), Wang & Burrows (2024b), and Wang & Burrows (2024a). The latter differ only in the fact that the 9a model accreted …

**Figure 18.** Figure 18: Ejecta Ye and entropy distribution for all models. The two 9 M⊙ models published before, 9a and 9b (with/without initial perturbation), are plotted for comparison. With increasing initial spin rate, the ejecta become more and more neutronrich, which is consistent wit…

**Figure 19.** Figure 19: Nucleosynthetic yields (left) and production factors (right) of all six of our 9.0-M⊙models. The two 9 M⊙ models published before, 9a and 9b (with/without initial perturbation), are plotted for comparison. As discussed in [PITH_FULL_IMAGE:figures/full_fig_p029_19.png]

**Figure 20.** Figure 20: Matter GW strain (cm) versus time after bounce (in seconds) for the sequence of rotating models. See the text for details and a discussion. 0.010 0.005 0.000 0.005 0.010 0.015 0.020 0.025 0.030 40 20 0 20 40 Solid: Equator Dashed: Pole h + h × Solid: Equator Dashed: P…

**Figure 21.** Figure 21: Matter GW strain (cm) versus time after bounce (in seconds) for the sequence of rotating models in the first 30 ms after core bounce for both polarizations and along the pole (dashed) and equator (solid). The bounce signature for the 9-M⊙ model is only weakly sensitiv…

**Figure 22.** Figure 22: Matter (left) and neutrino memory (right) total GW energy emitted versus time after bounce. We see a quasimonotonic increase in the asymptotic gravitational wave energy with increasing rotation for both the matter and neutrino GW contributions, with the exception tha…

**Figure 23.** Figure 23: Matter-driven gravitational wave strain spectrogram plotted against time after bounce (in seconds). We see prominent prompt convection and/or rotational bounce signatures for all models in the very early phase, followed by weak early g/f-mode signals, slightly suppres…

**Figure 24.** Figure 24: Matter-driven gravitational wave energy spectrograph. All models except the rapid-rotating model show a power gap near 1000 Hz. The 9-M⊙ model rotating with an initial angular frequency of 0.1 rad s−1 shows a stronger ‘fan’ of GW radiation powered by accretion in the …

**Figure 25.** Figure 25: Neutrino-driven GW strain versus time after bounce (in seconds) (left: h+; right: h×) comparing the pole (dashed) versus equator (solid) emission along the positive x-axis. Only for the rapidly-rotating 9-rot-1.0 model do we see a significant pole/equator strain asymm…

**Figure 26.** Figure 26: Top left: Matter-driven GW spectra as viewed along the pole (dashed, low opacity) and equator (solid) on the positive x-axis plotted against frequency [Hz], extending to 10 kHz. Top right: Likewise, but for the neutrino memory (extending to 500 Hz, limited by our neut…

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