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

This study presents 3D hydrodynamic and magnetohydrodynamic simulations of a rapidly rotating $39 M_\odot$ core-collapse supernova, demonstrating that while all models achieve shock revival, the inclusion of strong magnetic fields accelerates the process and drives a distinct bipolar outflow by extracting rotational energy, whereas rapid rotation alone delays revival and delays black hole formation compared to the non-rotating case.

Original authors: Liubov Kovalenko, Evan O'Connor, Haakon Andresen, Sean M. Couch

Published 2026-05-19

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CC BY 4.0

Original authors: Liubov Kovalenko, Evan O'Connor, Haakon Andresen, Sean M. Couch

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a massive star, 39 times heavier than our Sun, reaching the end of its life. Its iron core collapses under its own weight, creating a dense, spinning ball of neutrons called a proto-neutron star. Usually, this collapse leads to a supernova explosion, but sometimes the star just crumples into a black hole.

This paper is like a high-speed, 3D movie simulation that asks: What happens if we add two special ingredients to this collapsing star: rapid spin and strong magnetic fields?

To find out, the scientists ran three different "what-if" scenarios using the same star:

The "Still" Star: No spin, no magnetic fields.
The "Spinning" Star: Spins fast, but no magnetic fields.
The "Super-Spinning Magnet" Star: Spins fast and has a powerful magnetic field.

Here is what they found, explained through simple analogies:

1. The "Still" Star: A Short-Lived Spark

In the first scenario (no spin, no magnetism), the star managed to revive its shockwave and start exploding, much like a car engine sputtering back to life. However, because it wasn't spinning, it couldn't hold itself together against gravity for long. About one second after the explosion started, the star collapsed completely into a black hole. It was a "failed" explosion that got cut short.

2. The "Spinning" Star: The Slow, Wobbly Expansion

In the second scenario, the star was spinning like a figure skater. This spin acted like a centrifuge, pushing material outward and giving the star extra support against gravity.

The Result: The explosion happened, but it was slow and messy. The shockwave took a long time to revive. The star remained very compact (small and tight) and didn't develop a clear, directed explosion. It was like trying to push a heavy door open with a wobbly hand; it eventually moved, but not with much force or direction.

3. The "Super-Spinning Magnet" Star: The Magnetic Jet Engine

This was the most dramatic scenario. The star was spinning fast and had a strong magnetic field.

The Result: This star exploded the fastest and most violently. The magnetic field acted like a magnetic funnel. It grabbed the spinning energy of the core and channeled it straight out of the poles (the top and bottom), creating a powerful, bipolar outflow. Think of it like a garden hose with a nozzle: the water (energy) is forced into a tight, high-speed jet.
The Catch (The "Kink"): The paper found that this jet wasn't perfectly straight. Because the simulation was done in full 3D (not just a flat 2D slice), the jet started to wiggle and bend. The scientists call this a "kink instability." Imagine a garden hose that suddenly starts to snake and twist as the water rushes through it. The jet survived and pushed out, but it became a twisted, distorted funnel rather than a perfect, straight laser beam.

The Secret Sauce: How the Magnetic Field Works

The paper explains that the magnetic field does two crucial things:

It acts as a brake: It grabs the spinning core and slows it down, stealing the star's "spin energy."
It acts as a transfer belt: It takes that stolen spin energy and shoots it out the poles to power the explosion.

In the spinning-but-magnetic model, the star's core slowed down significantly because the magnetic field was siphoning off its energy to fuel the blast. In the spinning-but-no-magnetism model, the core kept spinning fast but couldn't use that energy to help the explosion, so the blast remained weak and slow.

What About the Debris?

The scientists also looked at what was left over after the explosion (the "ejecta").

The "Still" Star: The debris was mostly "proton-rich" (a specific type of atomic makeup), typical of standard explosions.
The "Magnet" Star: Because the magnetic jet moved so fast, it created a different environment. It produced some "neutron-rich" material, which is the kind of stuff needed to create heavy elements (like gold or platinum) in the universe. However, because the jet got "kinked" and twisted, it didn't produce the most extreme versions of these heavy elements that some theories predict.

The Bottom Line

This study proves that 3D simulations are essential. If you only look at the problem in 2D (like a flat drawing), you might think the magnetic jet would be a perfect, stable laser beam. But in the real, messy 3D world, the jet twists and kinks.

The paper concludes that while magnetic fields and rapid rotation can definitely help a massive star explode and avoid turning into a black hole immediately, the process is chaotic. The magnetic field helps launch the explosion, but it also twists the jet and slows down the core, creating a complex, dynamic event that is very different from a simple, straight-line explosion.

Technical Summary: A Three-Dimensional Exploration of Magnetic Fields, Rotation, and Shock Revival in a 39 M⊙ Core-Collapse Supernova Progenitor

Problem and Motivation
The revival of the stalled shock in core-collapse supernovae (CCSNe) remains a complex problem involving the interplay of neutrino heating, rotation, magnetic fields, and hydrodynamics. While the neutrino mechanism is robust in many progenitors, particularly high-compactness ones, the magnetorotational (MR) mechanism offers an alternative pathway for shock revival and powering energetic transients (e.g., hypernovae, Type Ic-BL supernovae). This mechanism requires rapid rotation and strong magnetic fields to convert rotational free energy into magnetic energy via winding and instabilities, driving bipolar outflows. However, previous studies have often relied on axisymmetry (2D), which may artificially stabilize jets and suppress non-axisymmetric instabilities like the kink instability. Furthermore, the specific impact of magnetic fields on shock revival timescales, outflow morphology, and the stability of the proto-neutron star (PNS) against black hole formation in high-compactness, rapidly rotating 3D environments requires further investigation.

Methodology
The authors performed three-dimensional hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations of a 39 M⊙ zero-age main sequence (ZAMS) progenitor with high compactness ( $\xi_{2.5} = 0.75$ ) and rapid rotation ( $\Omega_c \approx 0.58$ rad s $^{-1}$ ). The progenitor was evolved using MESA with quasi-chemically homogeneous evolution. Three distinct models were simulated using the FLASH code with the Spark solver, employing adaptive mesh refinement (AMR) and a multidimensional, energy-dependent, two-moment neutrino transport scheme with an M1 closure:

B1R1: A rotating, magnetized model. A poloidal seed field ( $B_0 \approx 5 \times 10^{11}$ G) was initialized, aligned with the rotation axis.
B0R1: A rotating, non-magnetized control model (HD only).
B0R0: A non-rotating, non-magnetized baseline model (HD only).

The simulations evolved from pre-collapse through core bounce and into the early post-bounce phase (up to $\sim$ 1 second), utilizing a Cartesian grid with a finest resolution of $\sim$ 0.61 km near the core. General relativistic effects were approximated using an effective potential (Case A of Marek et al. 2006).

Key Results
All three models achieved runaway shock expansion within the simulated interval, but exhibited markedly different morphologies, timescales, and remnant fates:

Shock Revival and Morphology:
- B1R1 (Magnetized/Rotating): Exhibited the earliest shock revival ( $t_{rev} \approx 150$ ms post-bounce) and developed the clearest bipolar outflow. The outflow was initially jet-like but became broadened and distorted by non-axisymmetric instabilities.
- B0R0 (Non-rotating): Revived later ( $t_{rev} \approx 250$ ms) via strong neutrino-driven turbulence. The shock expanded in large, disordered plumes without a preferred polar orientation. Crucially, this model collapsed to a black hole approximately 1 second after bounce due to the lack of rotational support.
- B0R1 (Rotating/Non-magnetized): Experienced the latest shock revival ( $t_{rev} \approx 370$ ms). Rotation suppressed convection and reduced neutrino luminosities, leading to a more compact evolution compared to B0R0. It did not develop a clear bipolar outflow.
Angular Momentum and Energy Transport:
- In B1R1, Maxwell stresses efficiently redistributed angular momentum outward from the inner PNS, reducing the inner-core spin and extracting rotational free energy. This process tapped the reservoir of differential rotation to power the polar outflow.
- The angular momentum budget revealed that while advection supplied angular momentum to the inner core, magnetic torques provided the dominant sink, offsetting the spin-up. Neutrino emission acted as a secondary, smaller sink.
- The diagnostic energy ( $E_{diag}$ ) in B1R1 grew earliest and most rapidly, consistent with the extraction of rotational energy. The magnetic energy budget indicated that a substantial fraction of the extracted energy passed through an effective dissipation term ( $\dot{Q}_{diss}$ ), likely associated with unresolved reconnection and sub-grid transfer, rather than being retained as resolved magnetic energy.
Instabilities and 3D Dynamics:
- The magnetized outflow in B1R1 was subject to a non-axisymmetric kink instability ( $m=1$ mode). Diagnostics showed an early exponential growth of the magnetic energy barycenter displacement (e-folding time $\sim$ 1.5 ms), consistent with theoretical kink timescales.
- Unlike axisymmetric simulations that might predict a stable, narrow jet, the 3D simulation showed the outflow funnel becoming tilted (several degrees) and broadened over time. The outflow survived and propagated to large radii but lost its narrow collimation, suggesting that 3D effects are critical for accurately modeling jet stability.
Nucleosynthesis:
- Post-processing of ejecta showed distinct compositional differences. B0R0 produced proton-rich ejecta ( $Y_e > 0.5$ ) typical of neutrino-driven explosions, synthesizing up to iron-group elements ( $A \sim 56$ ).
- B1R1 produced a significant neutron-rich component ( $Y_e$ down to $\sim 0.33$ ) due to the rapid outflow development, enabling a weak r-process up to $A \sim 90$ . However, the initial seed field and kink-induced broadening prevented the production of the extremely neutron-rich ejecta ( $Y_e < 0.32$ ) seen in models with more extreme magnetic fields.

Significance and Claims
The paper claims that in an extreme, high-compactness progenitor, rapid rotation combined with strong magnetic fields can open an early, magnetically aided pathway to shock revival that is intrinsically three-dimensional. Key conclusions include:

Magnetic Fields as a Driver: Magnetic stresses do not merely shape the outflow; they actively extract rotational free energy, spin down the inner core, and facilitate shock revival earlier than in non-magnetized rotating cases.
3D Necessity: The evolution of the magnetically driven outflow is inherently non-axisymmetric. The kink instability broadens and tilts the outflow, preventing the formation of a persistent, narrow jet. Axisymmetric simulations may overestimate both the stability and collimation of such outflows.
Remnant Stability: Rotation provides significant support against prompt black hole formation in high-compactness progenitors, though the long-term stability of the remnant remains uncertain beyond the simulated interval.
Energy Pathway: The energy transfer from differential rotation to the outflow involves significant unresolved dissipation, highlighting the importance of sub-grid physics in MHD CCSN simulations.

The authors note limitations, including the use of a strong seed field to compensate for unresolved small-scale dynamo amplification, resolution sensitivity in dissipation diagnostics, and the need for longer simulations to determine the ultimate fate of the rotating models. They emphasize that while the simulations support a picture of magnetorotational shock revival, the specific outcomes depend heavily on the full 3D dynamics of the outflow.