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

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.