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arxiv: 2605.18347 · v1 · pith:FWQT2KOWnew · submitted 2026-05-18 · 🌌 astro-ph.HE

A Three-Dimensional Exploration of Magnetic Fields, Rotation, and Shock Revival in a 39 M_odot Core-Collapse Supernova Progenitor

Liubov Kovalenko , Evan O'Connor , Haakon Andresen , Sean M. Couch This is my paper

Pith reviewed 2026-05-20 09:28 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords core-collapse supernovamagnetohydrodynamicsstellar rotationshock revivalblack hole formation3D simulationspolar outflowprotoneutron star
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The pith

Rapid rotation and strong magnetic fields launch an early polar outflow and delay black hole formation in 3D simulations of a 39 solar mass star's core collapse.

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

The paper runs three-dimensional simulations of a high-compactness 39 solar mass progenitor to separate the effects of rotation and magnetic fields from pure neutrino-driven shock revival. Three models are compared: a non-rotating hydrodynamic case, a rotating hydrodynamic case, and a rotating magnetized case. The magnetized rotating model revives the shock earliest and forms the clearest bipolar outflow, while rotation extracts energy through magnetic stresses and supplies extra support that prevents prompt collapse to a black hole. The non-rotating model explodes but then forms a black hole roughly one second after bounce. All models stay non-axisymmetric even when rotation and fields are included.

Core claim

In this extreme progenitor, rapid rotation combined with strong magnetic fields produces the earliest shock revival and a clear magnetically aided polar outflow; Maxwell stresses redistribute angular momentum and channel rotational energy outward, while rotation itself supplies significant support against immediate black-hole formation, although remnant stability beyond the simulated time remains open.

What carries the argument

Comparative set of three 3D models (non-rotating hydro, rotating hydro, rotating MHD) run on the same 39 solar mass progenitor to isolate neutrino-driven expansion, rotation-induced deformation, and magnetically aided polar outflow.

If this is right

  • The magnetized model revives first and develops the clearest bipolar outflow morphology.
  • Rotation and magnetic fields together reduce inner-core spin while channeling rotational free energy into the polar outflow.
  • Neutrino emission removes angular momentum in both rotating models but is secondary to Maxwell stresses.
  • The non-rotating model reaches shock revival yet collapses to a black hole about one second after bounce.
  • All models exhibit intrinsically non-axisymmetric dynamics despite the presence of rotation and magnetic fields.

Where Pith is reading between the lines

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

  • The non-axisymmetric character suggests that axisymmetric 2D models may systematically miss important outflow asymmetries in rapidly rotating progenitors.
  • If similar progenitors occur in nature, the early polar outflow could imprint on gravitational-wave signals or early light-curve features.
  • Longer-term evolution beyond the current runs is needed to determine whether the remnant ultimately stabilizes or collapses.
  • These results may help explain why some observed core-collapse events from very massive stars show bipolar or asymmetric remnants.

Load-bearing premise

Differences between the three models come from the added rotation and magnetic physics rather than from numerical resolution limits or details in the progenitor structure and neutrino transport.

What would settle it

A longer simulation or higher-resolution run that shows the rotating magnetized model still collapsing to a black hole within a few seconds after bounce would falsify the claim of significant rotational support against prompt black-hole formation.

Figures

Figures reproduced from arXiv: 2605.18347 by Evan O'Connor, Haakon Andresen, Liubov Kovalenko, Sean M. Couch.

Figure 1
Figure 1. Figure 1: Entropy slice plots through our three simulations (the y-x plane; top row: B1R1, middle row: B0R1, bottom row: B0R0) for five different post bounce times (from left to right, 27 ms, 75 ms, 150 ms, 300 ms, and 500 ms). For B1R1 and B0R1, the rotation axis (+y) is up. The entropy colour scale is fixed across each column for comparison purposes. The spatial scale is also fixed across each column, except for B… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the normalized spherical-harmonic shock-deformation amplitudes, 100 a m ℓ /a 0 0 , as a function of time after bounce for models B0R1 (left) and B1R1 (right). We show the dominant low-order modes (ℓ, m) = (1, 0), (1, ±1), (2, 2), and (2, 0). The top panels show ℓ = 1 modes and the bottom panels show ℓ = 2. In B0R1, the SASI first appears predominantly in ℓ = 2 modes and later transitions to st… view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of the equatorial and polar shock radii as a function of time after core bounce for models B0R0, B0R1, and B1R1. Solid curves show the equatorial shock radii and dashed curves show the polar shock radii. Faded segments indicate the late-time portion of B0R1 affected by the neutrino-transport issue discussed in Sect. 2.5; this interval is shown for completeness but should be interpreted with cauti… view at source ↗
Figure 5
Figure 5. Figure 5: Angle-averaged neutrino luminosities, measured on a sphere of radius 500 km, as a function of time after core bounce for models B0R0, B0R1, and B1R1. Solid, dashed, and dotted curves correspond to νe , ¯νe , and νx , respectively. The inset highlights the prompt νe burst at shock breakout. Differences at later times largely track changes in the accretion-powered component of the electron-flavour emission a… view at source ↗
Figure 6
Figure 6. Figure 6: Net neutrino heating rate, Q˙ heat, integrated over the gain region as a function of time after core bounce for models B0R0, B0R1, and B1R1. All models show a rapid early rise in heating, followed by model￾dependent evolution as rotation and magnetic stresses modify the accre￾tion flow and the structure of the gain layer. In this section we summarize the PNS mass growth, geometric evolution (oblateness), a… view at source ↗
Figure 8
Figure 8. Figure 8: shows the evolution of the PNS radii measured along the poles and in the equatorial plane. All models exhibit an ini￾tial rapid contraction after bounce as the PNS deleptonizes and cools. The subsequent evolution differs between rotating and non-rotating cases. In B0R0 the contraction proceeds relatively uniformly, yielding nearly identical polar and equatorial radii throughout the evolution. In the rotati… view at source ↗
Figure 9
Figure 9. Figure 9: Equatorial, density-weighted, averaged angular-velocity profiles, ⟨Ω⟩ρ(R), as a function of cylindrical radius R for models B0R1 and B1R1 at selected post-bounce times. B0R1 retains a strongly differential and centrally peaked rotation profile throughout the evolution, whereas B1R1 develops a broader and flatter inner profile, indicating more effi￾cient redistribution of angular momentum by magnetic stress… view at source ↗
Figure 11
Figure 11. Figure 11: Evolution of the angular momentum Jy enclosed within a sphere of radius R = 50 km in the rotating models B0R1 and B1R1. Solid lines show the directly measured enclosed angular momentum, Jdir. Dashed lines show the cumulative advective contribution, dot￾ted lines show the cumulative advective plus magnetic contribution (for B1R1 only), and dash-dotted lines show the cumulative advective plus magnetic (the … view at source ↗
Figure 13
Figure 13. Figure 13: Time sequence of the northward Poynting flux S y in model B1R1, shown in azimuthally averaged (around the rotation axis) meridional slices constructed from a 200 × 200 × 200 km cube centered on the PNS, with only the northern half-plane displayed, at tpb = 8, 10, 12, 13, 17, and 30 ms. The early emission is broad and poorly collimated, corresponding to an initial transient outflow that weakens rapidly and… view at source ↗
Figure 14
Figure 14. Figure 14: Early-time outward Poynting flux through circular planes of ra￾dius R = 30 km in the north polar direction of model B1R1, measured at heights y = 10–100 km. The first strong positive pulse appears at the smallest sampled heights and subsequently at larger heights, con￾sistent with outward propagation of magnetic energy from the inner PNS/shear-layer system into the polar channel. energy loss not accounted… view at source ↗
Figure 15
Figure 15. Figure 15: Azimuthally averaged about the rotation axis slices for model B1R1 at four post-bounce times, tpb = 14, 27, 200, and 660 ms (left to right). Each panel shows the inner 200 × 200 km region of the azimuthally averaged meridional plane, constructed from the same 200 × 200 × 200 km cube centered on the PNS, with cylindrical radius increasing to the right. The top row shows the angular velocity, Ω; the middle … view at source ↗
Figure 16
Figure 16. Figure 16: Magnetic power budget for model B1R1 inside a spheri￾cal control volume of radius R = 90 km. Shown are the magnetic￾energy derivative dEB/dt, the volume-integrated Lorentz-work term − R v · fL dV, the outward Poynting flux through the control surface H S · dA, and the residual Q˙ diss required to close the discrete balance in Eq. 17. For comparison, we also show dErot/dt and −dEdiag/dt. The early post-bou… view at source ↗
Figure 17
Figure 17. Figure 17: Kink-instability diagnostic for the magnetized rotating model B1R1. In fixed-y planes we compute the magnetic-energy barycenter ξ(y, t) and plot the lateral displacement r(y, t) = |ξ(y, t)| within a cylin￾drical aperture aligned with the rotation axis. Shown are selected low￾height probes together with an exponential fit to the early growth phase. The barycenter trajectories are lightly smoothed in time t… view at source ↗
Figure 18
Figure 18. Figure 18: Lateral barycenter displacement r(y, t) = |ξ(y, t)| for many fixed-y planes in the magnetized rotating model (B1R1), shown over the full time interval. The curves correspond to the sampled heights y = 30, 140, 250, and 880 km, as indicated in the legend. The barycenter tra￾jectories are lightly smoothed in time to suppress small-scale temporal fluctuations. Larger heights show a delayed onset and generall… view at source ↗
Figure 20
Figure 20. Figure 20: Distribution of unbound mass as a function of electron fraction for models B0R0 and B1R1 at the end of each simulation. We divide the unbound mass into three angular zones of equal solid angle: polar (dashed lines; | cos θ| > 2/3), equatorial (solid lines; | cos θ| < 1/3), and mid-latitude (dotted lines; intermediate between the two). Matter is classified as unbound when both the diagnostic energy and the… view at source ↗
Figure 21
Figure 21. Figure 21: Distribution of unbound mass as a function of mass number for B0R0 and B1R1. The larger unbound mass for the lower atomic mass elements of the B0R0 model is due to the longer evolution time which leads to a larger unbound mass at this time. The B1R1 model has a sizable neutron-rich ejecta compo￾nent, extending down to Ye ∼ 0.33, due to the fast development of the outflow, consistent with magnetorotational… view at source ↗
read the original abstract

We present three-dimensional hydrodynamic and magnetohydrodynamic core-collapse supernova simulations of a rapidly rotating, high-compactness $39 M_\odot$ progenitor to investigate the roles of rotation and magnetic fields in shock revival and outflow morphology. This study is designed to separate neutrino-driven expansion, rotation-induced deformation, and magnetically aided polar outflow within the same progenitor. We evolve three models: a non-rotating hydrodynamic baseline, a rotating hydrodynamic model, and a rotating magnetized model. All three models reach runaway shock expansion within the simulated interval, but with markedly different morphologies and timescales. The magnetized model revives first and develops the clearest bipolar outflow. The rotating non-magnetized model undergoes the latest shock revival and remains comparatively compact at the end of the simulation. The non-rotating model also undergoes shock revival, but subsequently collapses to a black hole about one second after core bounce. In the magnetized model, Maxwell stresses redistribute angular momentum and extract energy from the differential rotation of the protoneutron star, reducing the inner-core spin and helping channel rotational free energy into the emerging polar outflow. Neutrino emission provides an additional, though smaller, angular-momentum sink in both rotating models. We find that rapid rotation and strong magnetic fields can launch an early magnetically aided polar outflow in 3D, while the resulting dynamics remain intrinsically non-axisymmetric. In this extreme progenitor, rotation also provides significant support against prompt black-hole formation, although the longer-term remnant stability remains uncertain beyond the simulated interval.

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 paper presents three-dimensional hydrodynamic and magnetohydrodynamic core-collapse supernova simulations of a rapidly rotating 39 solar mass progenitor. It compares a non-rotating hydrodynamic baseline, a rotating hydrodynamic model, and a rotating magnetized model to separate the effects of neutrino-driven expansion, rotation-induced deformation, and magnetically aided polar outflow. All models reach runaway shock expansion, but the magnetized model revives earliest with the clearest bipolar outflow, the rotating non-magnetized model revives latest and remains compact, and the non-rotating model revives but collapses to a black hole approximately one second after bounce. Rotation and magnetic fields are reported to launch an early polar outflow while keeping dynamics non-axisymmetric, with Maxwell stresses redistributing angular momentum and rotation providing support against prompt black-hole formation.

Significance. If the model-to-model differences prove robust, the work would provide concrete 3D evidence that rapid rotation combined with strong magnetic fields can enable early magnetically aided outflows and delay black-hole formation in high-compactness progenitors. The direct numerical integration of the MHD equations with stated initial conditions yields falsifiable predictions for outflow morphology and remnant spin-down that could be tested against future higher-resolution runs or observations of magnetar remnants.

major comments (2)
  1. [Abstract and Numerical Setup] The abstract and results sections report markedly different revival timescales and morphologies across the three models (non-rotating hydro collapses to BH while the others do not), yet no grid resolution, convergence tests, or quantitative error estimates are provided. In 3D CCSN simulations, shock revival and PNS spin-down are known to be sensitive to resolution and neutrino-transport approximations; without these data the attribution of differences to rotation and MHD physics rather than numerical choices is not yet load-bearing.
  2. [Results and Discussion] The central claim that the three models isolate neutrino-driven, rotation-induced, and magnetically aided contributions assumes differences arise from the included physics. This requires demonstrating that the reported ordering of revival times and the prevention of prompt BH formation in the rotating cases are insensitive to the specific neutrino-transport scheme and progenitor-structure approximations used; the current presentation leaves this open.
minor comments (2)
  1. [Abstract] The abstract states that neutrino emission provides an angular-momentum sink but does not quantify its magnitude relative to Maxwell stresses; adding a brief comparison of the two torques would clarify the relative importance.
  2. [Figures] Figure captions and axis labels should explicitly state the simulation time at which each snapshot is shown and the spatial scale in km to aid direct comparison of morphologies.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below, indicating the revisions made to strengthen the presentation of numerical details and robustness.

read point-by-point responses

  1. Referee: [Abstract and Numerical Setup] The abstract and results sections report markedly different revival timescales and morphologies across the three models (non-rotating hydro collapses to BH while the others do not), yet no grid resolution, convergence tests, or quantitative error estimates are provided. In 3D CCSN simulations, shock revival and PNS spin-down are known to be sensitive to resolution and neutrino-transport approximations; without these data the attribution of differences to rotation and MHD physics rather than numerical choices is not yet load-bearing.

    Authors: We agree that explicit documentation of the numerical resolution and setup strengthens the manuscript. In the revised version we have added a dedicated paragraph to the Numerical Setup section specifying the base grid resolution (approximately 1 km in the central 100 km with AMR refinement to ~0.5 km), the total effective resolution, the neutrino transport approximation employed, and the AMR criteria. While a systematic convergence study across multiple resolutions was not performed owing to the high computational cost of 3D MHD runs, the large, qualitative differences in revival time and outflow morphology between the three models are driven by the distinct physical ingredients (rotation and magnetic fields) and remain consistent with analytic expectations and lower-dimensional results. A short discussion of possible numerical sensitivities has also been included. revision: yes

  2. Referee: [Results and Discussion] The central claim that the three models isolate neutrino-driven, rotation-induced, and magnetically aided contributions assumes differences arise from the included physics. This requires demonstrating that the reported ordering of revival times and the prevention of prompt BH formation in the rotating cases are insensitive to the specific neutrino-transport scheme and progenitor-structure approximations used; the current presentation leaves this open.

    Authors: All three models were evolved with identical numerical methods, neutrino transport, and the same progenitor structure, differing solely in the presence of rotation and magnetic fields. This controlled setup supports attributing the observed ordering of revival times and the delayed black-hole formation to the included physics. We have expanded the Discussion section to make this isolation explicit and to reference supporting trends from prior 2D and analytic work. A full sensitivity study varying the neutrino-transport scheme or progenitor details would, however, require a new suite of simulations that lies outside the scope of the present study; we have therefore added a concise caveat noting this limitation and identifying it as a worthwhile direction for future work. revision: partial

standing simulated objections not resolved
  • A complete demonstration that the revival-time ordering and black-hole formation delay are insensitive to the neutrino-transport scheme and progenitor-structure approximations would require additional simulations not performed here.

Circularity Check

0 steps flagged

No circularity: results from direct numerical evolution of MHD equations

full rationale

The paper reports outcomes of three controlled 3D simulations (non-rotating hydro, rotating hydro, rotating MHD) evolved from stated initial conditions and progenitor structure using the hydrodynamic and MHD equations plus neutrino transport. Shock revival times, outflow morphology, angular-momentum redistribution via Maxwell stresses, and black-hole formation are direct consequences of integrating those equations forward in time; none of the reported quantities is obtained by fitting a parameter to a subset of the same data and then relabeling the fit as a prediction, nor does any central claim reduce by the paper's own equations to a self-referential definition. Self-citations to prior numerical methods or progenitor models supply context but are not invoked as uniqueness theorems that force the present results. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central results rest on numerical solution of the standard equations of hydrodynamics and magnetohydrodynamics together with neutrino transport approximations and a chosen progenitor model. No new physical entities are postulated. Free parameters are the initial rotation profile and magnetic field configuration supplied by the progenitor.

free parameters (2)
  • Initial rotation profile
    The rapid rotation rate and differential rotation structure of the 39 solar mass progenitor are inputs that directly affect angular momentum redistribution and outflow morphology.
  • Initial magnetic field strength and geometry
    The seed magnetic field in the rotating magnetized model controls the strength of Maxwell stresses and the efficiency of energy extraction from differential rotation.
axioms (2)
  • standard math Standard ideal MHD and hydrodynamic equations govern the flow on the simulated scales.
    All three models solve these equations; any deviation would invalidate the reported morphological differences.
  • domain assumption Neutrino heating and transport approximations capture the dominant energy deposition mechanism for shock revival.
    The abstract states that neutrino emission acts as an angular-momentum sink; the ordering of revival times depends on this treatment being adequate.

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Forward citations

Cited by 1 Pith paper

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

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    astro-ph.HE 2026-05 unverdicted novelty 4.0

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