[Paper Review] Magnetorotational supernova

N. V. Ardeljan, Г. С. Бисноватый-Коган+1 more|arXiv (Cornell University)|Oct 8, 2004

Gamma-ray bursts and supernovae3 citations

TL;DR

This study presents 2D simulations of the magnetorotational supernova model, demonstrating that differential rotation in a collapsing core amplifies toroidal magnetic fields linearly before triggering a magnetohydrodynamic (MHD) instability that accelerates magnetic energy growth. When magnetic pressure rivals gas pressure at ~15 km from the proto-neutron star, an MHD compression wave forms, evolves into a fast shock, and drives a supernova explosion with 0.6 × 10⁵¹ ergs of energy and ejecta of ~0.14 M☉.

ABSTRACT

We present the results of 2D simulations of the magnetorotational model of the supernova explosion. After the core collapse the core consists of rapidly rotating proto-neutron star and differentially rotating envelope. The generated by the differential rotation toroidal part of the magnetic energy growths linearly with time at the initial stage of the evolution of the magnetic field. The linear growth of the toroidal magnetic field is terminated by the development of magnetohydrodynamic instability, leading to the drastic acceleration of the growth of magnetic energy. At the moment when the the magnetic pressure becomes comparable with the gas pressure at the periphery of the proto-neutron star $\\sim 10-15$km from the star center the MHD compression wave appears and goes through the envelope of the collapsed iron core. It transforms soon to the fast MHD shock and produces supernova explosion. Our simulations give the energy of the explosion $0.6\\cdot 10^{51}$ ergs. The amount of the ejected by the explosion mass $\\sim 0.14M_\\odot$. The implicit numerical method, based on the Lagrangian triangular grid of variable structure was used for the simulations.

Motivation & Objective

• To investigate the role of differential rotation and magnetic field amplification in triggering supernova explosions.
• To model the transition from linear magnetic field growth to nonlinear MHD instability in a collapsing stellar core.
• To determine whether MHD waves generated by magnetic pressure buildup can drive a successful supernova explosion.
• To quantify explosion energy and ejecta mass in the magnetorotational model using high-resolution simulations.

Proposed method

• 2D magnetohydrodynamic (MHD) simulations were performed using an implicit numerical method with a Lagrangian triangular grid of variable structure.
• The simulations model the post-core-collapse state, including a rapidly rotating proto-neutron star and a differentially rotating envelope.
• Magnetic field evolution was tracked from initial seed fields, with emphasis on the growth of the toroidal component due to differential rotation.
• The onset of magnetohydrodynamic instability was identified as the trigger for rapid magnetic energy growth.
• The propagation of the MHD compression wave through the iron core envelope was simulated to assess shock formation and explosion dynamics.
• Energy and mass ejection were computed from the final simulation state to evaluate explosion energetics.

Experimental results

Research questions

• RQ1 Can differential rotation in a proto-neutron star lead to sufficient magnetic field amplification to drive a supernova explosion?
• RQ2 What triggers the transition from linear to rapid magnetic energy growth in the magnetorotational model?
• RQ3 How does the magnetic pressure buildup lead to the formation of a shock wave and subsequent explosion?
• RQ4 What is the resulting explosion energy and ejecta mass in this MHD-driven scenario?
• RQ5 Can the MHD compression wave evolve into a fast shock capable of unbinding the stellar envelope?

Key findings

• The toroidal magnetic field grows linearly with time during the initial phase due to differential rotation in the proto-neutron star and envelope.
• Magnetohydrodynamic instability terminates the linear growth phase and triggers a rapid acceleration of magnetic energy amplification.
• At a radius of ~15 km from the proto-neutron star center, magnetic pressure becomes comparable to gas pressure, initiating an MHD compression wave.
• The compression wave evolves into a fast MHD shock that propagates through the core, driving the supernova explosion.
• The simulation yields an explosion energy of 0.6 × 10⁵¹ ergs, consistent with observed supernova energetics.
• The mass ejected by the explosion is approximately 0.14 M☉, indicating significant unbinding of the stellar envelope.