On the maximum magnetic field amplification by the magnetorotational instability in core-collapse supernovae

Abstract

Whether the magnetorotational instability (MRI) can amplify initially weak magnetic fields to dynamically relevant strengths in core-collapse supernovae is still a matter of active scientific debate. Recent numerical studies have shown that the first phase of MRI growth dominated by channel flows is terminated by parasitic instabilities of the Kelvin-Helmholtz type that disrupt MRI channel flows and quench further magnetic field growth. However, it remains to be properly assessed by what factor the initial magnetic field can be amplified and how it depends on the initial field strength and the amplitude of the perturbations. Different termination criteria leading to different estimates of the amplification factor were proposed within the parasitic model. To determine the amplification factor and test which criterion is a better predictor of the MRI termination, we perform three-dimensional shearing-disc and shearing-box simulations of a region close to the surface of a differentially rotating protoneutron star in non-ideal magnetohydrodynamics with two different numerical codes. We find that independently of the initial magnetic field strength, the MRI channel modes can amplify the magnetic field by, at most, a factor of 100. Under the conditions found in protoneutron stars, a more realistic value for the magnetic field amplification is of the order of 10. This severely limits the role of the MRI channel modes as an agent amplifying the magnetic field in protoneutron stars starting from small seed fields. A further amplification should therefore rely on other physical processes, such as for example an MRI-driven turbulent dynamo.