Magneto-Rotational Supernovae

• Magneto-Rotational Supernovae are core-collapse explosions powered by rapid rotation and amplified magnetic fields that drive energetic, aspherical shock waves.
• They involve critical processes such as magnetic winding, magnetorotational instability, and efficient angular momentum transport, resulting in diverse morphologies including jet-like ejections.
• These events produce distinctive nucleosynthesis patterns and gravitational-wave signals, offering key observational probes for hypernovae and long gamma-ray burst progenitors.

Magneto-rotational supernovae are core-collapse supernovae in which the decisive energy source is the rotational energy of a rapidly spinning proto-neutron star or collapsing core, extracted and redistributed by magnetic fields rather than by neutrino heating alone. In this explosion channel, collapse, differential rotation, magnetic winding, and in many models the magnetorotational instability (MRI) combine to amplify the field, transport angular momentum, and launch strongly aspherical outflows that range from broad magnetized explosions to bipolar jets. The mechanism has long been treated as a classical alternative to the neutrino-driven paradigm, and in current multidimensional simulations it is also a candidate explanation for a subset of hypernovae, long gamma-ray-burst progenitors, distinctive nucleosynthesis patterns, and strong gravitational-wave signals (Müller, 2024, Bisnovatyi-Kogan et al., 2019).

1. Energetic basis and defining physical picture

The central idea of the magnetorotational mechanism is that the energy of rotation of the neutron star formed in collapse is transformed into the energy of an expanding shock wave by means of a magnetic field. In the standard estimate reviewed for rapidly rotating remnants, the rotational reservoir is

$$E_\mathrm{rot}=\frac{1}{2}I\omega^2 \approx 2\times 10^{52}\,\mathrm{erg} \left(\frac{M}{1.4M_\odot}\right) \left(\frac{R}{12\,\mathrm{km}}\right)^2 \left(\frac{P}{1\,\mathrm{ms}}\right)^{-2},$$

which is large enough to power hypernova-scale explosions if angular momentum can be extracted efficiently. Earlier magnetorotational calculations summarized the conversion efficiency of rotational energy into explosion energy as about $10\%$, with representative explosion energies of order $10^{51}\,\mathrm{erg}$ (Müller, 2024, Bisnovatyi-Kogan et al., 2019).

This mechanism is distinct from, though not always disjoint from, the neutrino-driven channel. In ordinary neutrino-driven explosions, neutrino heating in the gain region is primary and magnetic fields are subsidiary. In classical magnetorotational explosions, magnetic stresses are the engine: differential rotation winds poloidal field into toroidal field, Maxwell stresses transport angular momentum outward, and magnetic pressure and tension accelerate outflows. Modern simulations also show hybrid regimes in which magnetic fields do not replace neutrino heating but materially assist shock revival, so the dividing line between “magnetically powered” and “magnetically assisted” explosions is model-dependent (Müller, 2024, Sawai et al., 2015).

Field topology is one of the oldest and still most consequential control parameters. In the 2D mechanism papers, a dipole-like initial field produced jet-like ejection along the rotation axis, whereas a quadrupole-like field favored equatorial ejection. More recent 3D work reaches a closely related conclusion at the nucleosynthetic level: aligned dipoles are the configurations most favorable for early, neutron-rich, strongly bipolar ejecta, while tilted dipoles and quadrupoles generally yield weaker or less collimated magnetorotational outflows (Bisnovatyi-Kogan et al., 2019, Reichert et al., 2024).

2. Magnetic amplification, MRI, and angular-momentum transport

Collapse itself amplifies magnetic fields by flux freezing and spin-up. In the homologous estimate summarized in the simulation review, $B_r$ scales as $B_{r,0}(r_0/r)^2$, while $\omega$ scales approximately as $\omega_0(r_0^2/r^2)$, so non-homologous collapse naturally creates strong differential rotation. That differential rotation drives magnetic winding, converting poloidal into toroidal field and establishing the condition $B_\varphi \gg B_p$ emphasized in classical magnetorotational calculations (Müller, 2024, Bisnovatyi-Kogan et al., 2014).

The MRI is central because global core-collapse calculations otherwise cannot rely on field wrapping alone to explain rapid amplification from modest seed fields. The characteristic fastest-growing MRI wavelength in the post-bounce core is extremely small. One direct numerical study estimated

$$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$

i.e. of order $200$ m under typical post-collapse conditions; resolving it with roughly 10 zones requires $10\%$0 m spatial resolution. That requirement motivated remapping strategies in global simulations and local shearing-box calculations aimed specifically at MRI saturation in proto-neutron-star shear layers (Akiyama et al., 2010, Masada et al., 2012).

MRI-driven evolution is not merely a field-amplification story. In the 2D Cosmos++ study, the MRI-unstable region appeared near the equator, magnetic bubbles rose in the cylindrical radial direction, and angular momentum and entropy were transported outward; the higher-resolution remap run showed more vigorous overturns and stronger transport. In the local 3D shearing-box study, the turbulent stress scaled with the shear-vorticity ratio as $10\%$1 with $10\%$2, and for a rapidly rotating proto-neutron star with millisecond spin and $10\%$3 fields the MRI dissipation rate was estimated to exceed $10\%$4 (Akiyama et al., 2010, Masada et al., 2012).

A recurrent point of interpretation is that MRI does not always power the explosion directly through magnetic pressure. In axisymmetric simulations with light-bulb neutrino heating, the MRI enlarged the heating region by outward angular-momentum transport and advected low-$10\%$5 matter into the gain region, thereby reducing cooling and increasing the net neutrino-heating rate. In those models, only the collimated jets were directly magnetic-pressure driven; the global explosion enhancement was primarily an indirect magnetic boost to neutrino heating, with neutrino heating contributing up to $10\%$6 of the explosion energy even in the strongest-field case (Sawai et al., 2015).

Classical 2D magnetorotational calculations framed the rapid nonlinear transition in terms of a supernova-specific “magneto-differential-rotation instability” (MDRI), with explosion times changing from the 1D scaling $10\%$7 to the much weaker multidimensional scaling $10\%$8. This suggests that the generic physical issue is not simply whether fields wind up, but whether multidimensional MHD turbulence and feedback loops make the amplification dynamical on the explosion timescale (Bisnovatyi-Kogan et al., 2014, Bisnovatyi-Kogan et al., 2019).

3. Explosion morphologies in multidimensional simulations

Parameter surveys now show that magneto-rotational supernovae are not a single morphology. A 2D survey of 34 magnetized $10\%$9 core-collapse simulations with self-consistent neutrino transport identified four outcome classes: failed explosions leading to black-hole formation, monopolar jet explosions, bipolar jet explosions, and neutrino-driven explosions. In that survey, non-rotating models required strong seed magnetic fields, with $10^{51}\,\mathrm{erg}$0 for successful explosion, whereas rotation substantially lowered the threshold, allowing explosion at $10^{51}\,\mathrm{erg}$1 in some cases. Explosion onset ranged from $10^{51}\,\mathrm{erg}$2 ms in marginal cases to $10^{51}\,\mathrm{erg}$3 ms in strongly magnetized, rapidly rotating systems (Pan et al., 26 Mar 2026).

The same survey showed that diagnostic explosion energies in the most extreme models approached $10^{51}\,\mathrm{erg}$4 within $10^{51}\,\mathrm{erg}$5 ms and kept growing, making those models plausible hypernova and long-GRB progenitors. At the same time, the mapping from parameter space to morphology was nonlinear: high $10^{51}\,\mathrm{erg}$6 and high $10^{51}\,\mathrm{erg}$7 favored bipolar jets, intermediate regimes could yield monopolar jets, and some high-field but only weak-to-moderate rotation models remained predominantly neutrino-driven (Pan et al., 26 Mar 2026).

Three-dimensional simulations complicate the older textbook picture of an explosion launched primarily by a stable jet. In the 3D CoCoNuT-FMT calculations of a rapidly rotating $10^{51}\,\mathrm{erg}$8 progenitor, both $10^{51}\,\mathrm{erg}$9 G and $B_r$0 G seed-field models underwent shock revival after about $B_r$1 ms, and the explosion energy reached about $B_r$2 to $B_r$3 by $B_r$4 ms. Magnetically collimated jets formed in both models, but the jets were not the primary engine; the bulk explosion occurred before jet formation, and the jets contributed at most about $B_r$5 of the explosion energy. The more weakly magnetized model showed more clearly collimated bipolar jets, whereas the stronger-field model evolved less collimated, more off-axis jets because of non-axisymmetric kink-like instabilities (Zha et al., 2024).

A related 3D study of the same progenitor family likewise found early shock revival and $B_r$6 asymptotic energies, but concluded that the models did not immediately fit the canonical hypernova/long-GRB picture: the jets were non-relativistic and unstable, rapid spin-down left birth periods of about $B_r$7 ms, and the iron-group ejecta were not strongly bipolar by the end of the runs (Powell et al., 2022). This suggests that “magneto-rotational” need not imply a prompt collapsar-like jet engine even when the explosion is strongly magnetized.

For mechanism diagnostics, one SRMHD plus two-moment neutrino-transport study proposed that neutrino-driven cases are approximately explained by $B_r$8, whereas magnetically driven cases correspond more closely to $B_r$9, where $B_{r,0}(r_0/r)^2$0 is the Alfvén-wave crossing time through the gain region. That formulation is especially useful in high-compactness, rapidly rotating progenitors near the border between successful explosion and black-hole formation (Obergaulinger et al., 2019).

4. Nucleosynthesis and chemical evolution

Magneto-rotational supernovae are of particular interest because they can eject matter under thermodynamic conditions that are inaccessible, or only weakly accessible, in ordinary neutrino-driven core-collapse supernovae. An early 3D MHD jet calculation with approximate neutrino transport found ejecta with $B_{r,0}(r_0/r)^2$1 peaking near $B_{r,0}(r_0/r)^2$2, shifted to $B_{r,0}(r_0/r)^2$3 when neutrino absorption was included, yet still able to reproduce the second and third solar $B_{r,0}(r_0/r)^2$4-process peaks. In that model the gravitationally unbound ejecta mass was $B_{r,0}(r_0/r)^2$5 and the explosion energy $B_{r,0}(r_0/r)^2$6, both lower bounds because they were still increasing at the end of the run (Winteler et al., 2012).

Subsequent work established that the nucleosynthesis is not monolithic. Special-relativistic MHD jet models separated prompt-magnetic-jet explosions, which produced a main $B_{r,0}(r_0/r)^2$7-process up to actinides, from delayed-magnetic-jet explosions, which generally synthesized only a weak $B_{r,0}(r_0/r)^2$8-process up to $B_{r,0}(r_0/r)^2$9. MRI-resolving axisymmetric models extended this into a continuum: neutrino-heating-dominated explosions produced weak $\omega$0-process material up to the second peak, strong magnetic jets reproduced a solar-like $\omega$1-process pattern, and many intermediate cases yielded an “intermediate $\omega$2-process” compatible with several abundance patterns in $\omega$3-process-enhanced metal-poor stars (Nishimura et al., 2015, Nishimura et al., 2016).

Accurate neutrino transport sharpened this picture. In 2D radiation-MHD models, the strong-field case produced heavy elements up to the third $\omega$4-process peak at $\omega$5, while weak-field models required late-time neutron-rich ejecta from proto-neutron-star deformation to reach only the second peak. That study estimated a lower limit of $\omega$6 for $\omega$7Ni in the strong-field model, explicitly noting that longer simulations including accretion-disk evolution were needed for final hypernova nucleosynthesis predictions (Reichert et al., 2020).

Current 3D results are more conservative for the heaviest nuclei. In the 3D CoCoNuT-FMT innermost-ejecta study, the magnetorotational models had neutron-rich tails down to $\omega$8 and produced a robust weak $\omega$9-process up to $\omega_0(r_0^2/r^2)$0, with negligible differences in heavy-element synthesis between seed fields of $\omega_0(r_0^2/r^2)$1 and $\omega_0(r_0^2/r^2)$2 G because the explosion dynamics were similar. The radioactive $\omega_0(r_0^2/r^2)$3Ni yields were $\omega_0(r_0^2/r^2)$4 and $\omega_0(r_0^2/r^2)$5 in the two magnetized models, on the low end of inferred hypernova nickel masses. The authors argued that these events are promising but likely rare contributors to early enrichment, not dominant producers of the full Galactic $\omega_0(r_0^2/r^2)$6-process inventory (Zha et al., 2024).

A more expansive 3D post-processing study of sophisticated neutrino-MHD models identified three distinct heavy-element production channels: prompt post-bounce ejection, late-time neutron-rich ejection associated with a reconfiguration of proto-neutron-star shape, and small amounts of high-entropy ejecta in the jet core. In those models, $\omega_0(r_0^2/r^2)$7Ni masses varied between $\omega_0(r_0^2/r^2)$8 and $\omega_0(r_0^2/r^2)$9, the strongest cases reached diagnostic energies up to $B_\varphi \gg B_p$0, and simplified light curves reached peak luminosities of a few $B_\varphi \gg B_p$1, with the $B_\varphi \gg B_p$2Ni decay chain capable of raising the peak luminosity by up to $B_\varphi \gg B_p$3 relative to a $B_\varphi \gg B_p$4Ni-only treatment (Reichert et al., 2022).

Magnetic topology now appears as important for nucleosynthesis as magnetic strength. In a 3D topology study of the same rapidly rotating Wolf-Rayet progenitor, the no-field model produced mainly iron-group nuclei, quadrupolar and $B_\varphi \gg B_p$5-tilted dipolar models produced significant second-peak material, and only the aligned dipole reached appreciable third-peak production, with a total mass in $B_\varphi \gg B_p$6 nuclei of about $B_\varphi \gg B_p$7. The study concluded that the explosion dynamics and magnetic-field configuration dominate the ejecta composition more strongly than the explored nuclear-physics uncertainties (Reichert et al., 2024).

5. Compact remnants, gravitational waves, and transient connections

Because the explosion channel is strongly aspherical and often rapidly rotating, magneto-rotational supernovae are expected to be distinctive multimessenger sources. In the 2D $B_\varphi \gg B_p$8 survey, gravitational-wave peak frequencies mainly depended on rotation rate rather than field strength or explosion morphology, typically rising from $B_\varphi \gg B_p$9–$$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$0 Hz shortly after bounce to $$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$1–$$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$2 Hz at late times. By contrast, amplitudes depended strongly on morphology and magnetization: jet models reached strains of roughly $$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$3–$$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$4 at 10 kpc, while failed-collapse and neutrino-driven models were closer to $$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$5 (Pan et al., 26 Mar 2026).

A fully 3D GRMHD study with dynamical spacetime found a complementary trend: stronger seed magnetic fields of $$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$6 suppressed gravitational-wave strain amplitudes relative to $$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$7 models because the stronger-field explosions evolved toward more axisymmetric, highly collimated flows with reduced non-axisymmetric quadrupole variation. Faster rotation strengthened the signal, and progenitor structure altered waveform morphology and bounce amplitude. The dominant characteristic-strain emission appeared near $$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$8 Hz, with additional power in the $$\lambda_{\rm MRI} \sim 0.18\ \mathrm{km} \left(\frac{B}{10^{12}\ \mathrm{G}}\right) \left(\frac{1000\ \mathrm{rad/s}}{\Omega}\right) \left(\frac{10^{13}\ \mathrm{g/cm^3}}{\rho}\right)^{1/2},$$9–$200$0 Hz range; all models lay above third-generation detector thresholds at 10 kpc, and most remained detectable at 10 Mpc (Schnauck et al., 23 Sep 2025).

Remnant properties are equally varied. Magneto-rotational explosions can leave rapidly spinning, strongly magnetized neutron stars, but not necessarily the ultra-fast remnants required for canonical millisecond-magnetar long-GRB engines. In the 3D $200$1 simulations, magnetic torques reduced proto-neutron-star angular momentum by about a factor of 10, yielding final angular momenta of $200$2–$200$3, spin periods of about $200$4 ms, and kicks of $200$5 and $200$6 in the two magnetic models. The same study found no spin-kick alignment (Powell et al., 2022).

Black-hole formation remains a frequent outcome in high-compactness models. The 2D morphology survey explicitly included failed explosions leading to black-hole formation as one of its four major classes, and the SRMHD GRB-progenitor study emphasized that successful explosion and later black-hole formation are not mutually exclusive: continued accretion through downflows can drive the proto-neutron star beyond the maximum mass within a few seconds (Pan et al., 26 Mar 2026, Obergaulinger et al., 2019). This is one reason magneto-rotational supernovae remain relevant both to proto-magnetar and collapsar central-engine discussions.

6. Progenitors, pre-collapse evolution, and unresolved issues

The largest uncertainty is upstream of collapse. The simulation review stresses that typical modern stellar-evolution models predict slow pre-collapse core rotation, with periods of tens to hundreds of seconds and fields around $200$7, generally too slow for magnetorotational power to be generic. Rare channels can preserve much faster rotation, with pre-collapse periods of order $200$8, and stellar mergers may generate fossil fields of $200$9–$10\%$00. Uncertainties in one-dimensional stellar evolution for angular-momentum transport and magnetic amplification remain a major bottleneck (Müller, 2024).

Three-dimensional pre-collapse magnetoconvection calculations indicate that this uncertainty is not merely technical. In a rapidly rotating $10\%$01 progenitor, oxygen- and neon-shell fields saturated at about $10\%$02 and $10\%$03, Maxwell stresses became comparable to radial Reynolds stresses, and magnetic angular-momentum transport spun down the inner region inside about $10\%$04 by more than an order of magnitude, pushing the shells toward rigid rotation. The authors argued that this rapid redistribution of angular momentum casts doubt on the possibility of retaining enough core angular momentum for a millisecond-magnetar-driven explosion (Varma et al., 2023).

There are also substantial modeling limitations. MRI-resolving calculations require meter-scale resolution in regions whose global evolution must still be followed for hundreds of milliseconds to seconds. Axisymmetry suppresses non-axisymmetric instabilities such as kink modes and eliminates important gravitational-wave channels; several papers therefore caution that 2D jet coherence overstates how cleanly magnetic fields can collimate the explosion (Müller, 2024, Powell et al., 2022). Even in sophisticated 3D models, simulations often end before shock breakout, before all fallback is known, or before the outer envelope binding energy has been fully overcome. One 3D nucleosynthesis study explicitly noted an outer-envelope binding energy of $10\%$05, implying that long-term fallback could materially alter the final ejecta mass and abundance yields (Zha et al., 2024).

Several points that were once treated as defining features are therefore better regarded as contingent. Magneto-rotational supernovae do not always produce prompt, stable bipolar jets; they do not always synthesize a full main $10\%$06-process; they do not necessarily leave a millisecond magnetar; and they are not generically the same as hypernovae or long-GRB engines. What the current literature supports more robustly is narrower and more precise: for a subset of rapidly rotating, sufficiently magnetized progenitors, magnetic stresses can dominate or strongly reshape shock revival, produce early energetic and strongly aspherical explosions, and imprint distinctive signatures in heavy-element yields and gravitational-wave emission (Müller, 2024, Reichert et al., 2024).