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

Tomasz Rembiasz, Martin Obergaulinger, Pablo Cerdá-Durán, Ewald Müller, Miguel-Ángel Aloy

Published 2015-08-19Version 1

The magnetorotational instability (MRI) can be a powerful mechanism amplifying the magnetic field in core collapse supernovae. However, whether initially weak magnetic fields can be amplified by this instability to dynamically relevant strengths is still a matter of active scientific debate. One of the main uncertainties concerns the process that terminates the growth of the instability. Parasitic instabilities of both Kelvin-Helmholtz (KH) 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 performed two-dimensional and three-dimensional sheering-disc simulations of a differentially rotating proto-neutron star layer in non-ideal MHD with unprecedented high numerical resolution. Our simulations show that KH parasitic modes dominate tearing modes in the regime of large hydrodynamic and magnetic Reynolds numbers, as encountered in proto-neutron 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 KH instabilities properly a very high numerical resolution is necessary. Using 9th order spatial reconstruction schemes, we find that at least $8$ grid zones per MRI channel are necessary to simulate the growth phase of the MRI and reach an accuracy of $\sim 10\%$ in the growth rate, while more than $\sim 60$ zones per channel are required to achieve convergent results (errors $\lesssim 10\%$) for the value of the magnetic stress at MRI termination. The assumption of axisymmetry hinders the development of the KH instability and results in artificially large magnetic stresses at MRI termination. These numerical requirements impose strong restrictions on future global simulations of the scenario.