Whether magnetic reconnection can release magnetic energy fast enough to influence the magnetorotational (MR) explosion of a core-collapse supernova remains undetermined. Two-dimensional MR-supernova simulations concluded, via a Petschek-type estimate with classical Coulomb conductivity, that reconnection takes about 5 s and is therefore too slow to affect the 0.5-1 s explosion dynamics; but that estimate used a field strength roughly 1000 times below the simulated toroidal field maximum, an unjustified length scale, and a steady laminar reconnection model, while modern reconnection theory shows that current sheets at the relevant dimensionless conductivity (the source's magnetic Reynolds number of about 101510^{15}, and Alfvénic Lundquist numbers far above the plasmoid threshold for any field realized in the simulation) are generically disrupted by the plasmoid instability and reconnect at fast, resistivity-independent rates. Determining which reconnection mechanism operates in the hot, dense, strongly magnetized, MRI-turbulent proto-neutron-star core, and the resulting magnetic-energy release timescale relative to the explosion dynamics, is required to validate the ideal-MHD treatment on which current magnetorotational-supernova simulations rely.

Background

A core-collapse supernova must convert a fraction of the gravitational and rotational energy released when a massive star's iron core collapses into an outgoing shock. One candidate driver is the magnetorotational (MR) mechanism: the newly formed proto-neutron star (PNS, the hot, dense, roughly solar-mass compact object produced at core bounce) rotates differentially, and this differential rotation winds up a weak poloidal magnetic field into a strong toroidal field whose pressure launches a compression wave that steepens into a magnetohydrodynamic shock. Two-dimensional simulations by Moiseenko, Bisnovatyi-Kogan and Ardeljan (2006) showed that the magnetorotational instability (MRI) dramatically accelerates this process. The MRI is a linear instability of differentially rotating magnetized plasma in which magnetic fields threading the shear exchange angular momentum between orbiting fluid rings; the field and the instability grow exponentially, amplifying the field to 101510^{15}-101610^{16} G within a fraction of a second and reducing the explosion time to roughly 0.10.1-11 s.

Because these simulations solved the ideal-MHD equations (formally infinite conductivity), Moiseenko et al. asked whether real, finite conductivity could instead matter: the MRI generates a chaotic, small-scale magnetic structure in which field lines of opposite polarity can reconnect, i.e. change magnetic topology and annihilate, converting magnetic energy into heat. If reconnection were as fast as the MRI growth, it could suppress the field amplification that powers the explosion. They estimated the reconnection time with the Petschek model, a steady, laminar reconnection geometry in which the reconnection speed is a logarithmically suppressed fraction of the Alfvén speed vA=H/4πρv_A=H/\sqrt{4\pi\rho} (the propagation speed of magnetic disturbances in a plasma of field strength HH and density ρ\rho), using a classical Coulomb-collision (Spitzer-type) conductivity σ≈8×1020 s−1\sigma\approx 8\times 10^{20}\,\mathrm{s^{-1}}. For MRI-region parameters (u=0.2×1010u=0.2\times10^{10} cm/s, l=105l=10^5 cm, ρ=7×1012\rho=7\times10^{12} g/cm3^3, H=1.7×1013H=1.7\times10^{13} G) this gives a magnetic Reynolds number Rem=4πσul/c2≈1015\mathrm{Re_m}=4\pi\sigma u l/c^2\approx 10^{15} and a reconnection time τreconn≈5\tau_\mathrm{reconn}\approx 5 s. Since 5 s exceeds the explosion timescale, they concluded that reconnection cannot significantly influence the MR explosion, and, treating Petschek as the fastest possible model, that any other realized reconnection model would only be slower. The companion papers (2007, 2008) repeat this conclusion as τreconn≈5\tau_\mathrm{reconn}\approx 5 s versus an MR explosion time of 0.50.5-11 s.

The estimate is, however, internally contested. The field strength H=1.7×1013H=1.7\times 10^{13} G used for the Alfvén speed is about 1000 times below the toroidal field maximum Hφ≈1.8×1016H_\varphi\approx 1.8\times 10^{16} G that the same simulation reaches at a radius of about 10 km; the length scale l=105l=10^5 cm is asserted without justification from the simulation or from physical argument; and three-dimensional effects could change the explosion timescale itself. Moreover, reconnection theory has moved decisively since 2006. The Alfvénic Lundquist number S=vAL/ηS=v_A L/\eta, with magnetic diffusivity η=c2/(4πσ)\eta=c^2/(4\pi\sigma), measures the ratio of advective to resistive magnetic transport on the scale LL; it is distinct from the source's magnetic Reynolds number Rem=4πσul/c2=ul/η\mathrm{Re_m}=4\pi\sigma u l/c^2=ul/\eta, which is built from the bulk flow speed uu rather than from vAv_A, although for the fields realized in these simulations both exceed the plasmoid threshold S≳104S\gtrsim 10^4 by many orders of magnitude. The classical Sweet-Parker sheet, a long, thin laminar diffusion layer of relative thickness S−1/2S^{-1/2}, is violently unstable to the plasmoid instability for S≳104S\gtrsim 10^4: the sheet fragments into chains of magnetic islands (plasmoids) whose coalescence-driven reconnection proceeds at a fast rate of order 0.01vA0.01v_A, essentially independent of resistivity (Loureiro, Schekochihin and Cowley 2007; Bhattacharjee et al. 2009; Huang and Bhattacharjee 2010; Uzdensky, Loureiro and Schekochihin 2010). Independently, reconnection in a weakly stochastic magnetic field is fast and resistivity-independent (Lazarian and Vishniac 1999). At the enormous dimensionless conductivity of a PNS core (Rem∼1015\mathrm{Re_m}\sim 10^{15}, with the corresponding Alfvénic Lundquist number likewise far above 10410^4), such fast reconnection is generically expected, and simulations of MRI turbulence in the accretion-disk context indeed show self-consistent plasmoid-mediated reconnection and intense current-sheet dissipation (Sano and Inutsuka 2001; Ross and Latter 2018; Rosenberg and Ebrahimi 2021; Kadowaki et al. 2018). Whether, and how fast, this transfers to the dense, hot, strongly stratified interior of a PNS, where electrons are relativistic and partially degenerate, fields reach 101510^{15}-101610^{16} G, and neutrino cooling operates, has not been determined: state-of-the-art three-dimensional general-relativistic MHD simulations of MR supernovae remain ideal-MHD, with reconnection represented only through numerical diffusivity (Mösta et al. 2014, 2015; Shankar et al. 2026).

Problem Statement

For the plasma conditions realized in the MRI-active core of a magnetorotational supernova, namely a hot, dense, differentially rotating proto-neutron-star interior with densities ρ∼1012\rho\sim 10^{12}-1014 g cm−310^{14}\,\mathrm{g\,cm^{-3}}, temperatures of order 101110^{11} K, MRI-amplified magnetic fields reaching 101510^{15}-101610^{16} G, Coulomb (Spitzer-type) magnetic Reynolds numbers of order 101510^{15}, relativistic partially degenerate electrons, and strong stratification, determine which magnetic reconnection mechanism operates (for example collisional plasmoid-mediated, turbulent, or collisionless reconnection) and the timescale on which it converts the MRI-amplified magnetic energy into heat. In particular, establish whether this timescale is comparable to or shorter than the magnetorotational explosion timescale (of order 0.10.1-11 s across the simulated models, quoted as 0.50.5-11 s in the companion papers, and compared in the 2006 source against the MRI development time of roughly 0.50.5 s), such that reconnection suppresses, delays, or enhances the MRI-driven field amplification and the explosion itself; and thereby establish whether the classical Petschek-type estimate τreconn≈5\tau_\mathrm{reconn}\approx 5 s, obtained with a field strength about 10310^3 times below the simulated toroidal maximum, an unjustified length scale l=105l=10^5 cm, and a steady laminar reconnection model, can be trusted or must be replaced by a quantitative reconnection theory for this regime. A complete answer identifies the operative reconnection regime as a function of the physical parameters (density, temperature, field strength, and driving scale), gives the resulting reconnection rate or energy-release timescale, and states the dynamical consequence for the magnetorotational explosion mechanism and for the validity of ideal-MHD simulations of it.

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