Termination of the magnetorotational instability via parasitic instabilities in core-collapse supernovae

TL;DR

This study investigates how parasitic instabilities, especially Kelvin-Helmholtz modes, terminate the magnetorotational instability in core-collapse supernovae, using high-resolution simulations to determine the maximum magnetic stress achievable.

Contribution

The paper provides high-accuracy simulations demonstrating that Kelvin-Helmholtz parasitic modes dominate MRI termination in protoneutron stars, confirming local stability analysis predictions.

Findings

Kelvin-Helmholtz modes dominate tearing modes at high Reynolds numbers.

High numerical resolution is essential for accurate MRI growth and termination modeling.

At least 8 grid zones per MRI channel are needed for ~10% growth rate accuracy.

Abstract

The magnetorotational instability (MRI) can be a powerful mechanism amplifying the magnetic field in core-collapse supernovae. Whether initially weak magnetic fields can be amplified by this instability to dynamically relevant strengths is still a matter of debate. One of the main uncertainties concerns the process that terminates the growth of the instability. Parasitic instabilities of both Kelvin-Helmholtz and tearing-mode type have been suggested to play a crucial role in this process, disrupting MRI channel flows and quenching magnetic field amplification. We perform two-dimensional and three-dimensional sheering-disc simulations of a differentially rotating protoneutron star layer in non-ideal magnetohydrodynamics with unprecedented high numerical accuracy, finding that Kelvin-Helmholtz parasitic modes dominate tearing modes in the regime of large hydrodynamic and magnetic Reynolds numbers, as encountered close to the surface of protoneutron stars. They also determine the maximum magnetic field stress achievable during the exponential growth of the MRI. Our results are consistent with the theory of parasitic instabilities based on a local stability analysis. To simulate the Kelvin-Helmholtz instabilities properly, a very high numerical resolution is necessary. Using ninth-order spatial reconstruction schemes, we find that at least eight grid zones per MRI channel are necessary to simulate the growth phase of the MRI and reach an accuracy of ~10 per cent in the growth rate, while more than ~60 zones per channel are required to achieve convergent results for the value of the magnetic stress at MRI termination.