Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

TL;DR

This study uses high-resolution local simulations to analyze magnetic field amplification and back-reaction in Kelvin-Helmholtz instabilities relevant to neutron-star mergers, revealing rapid amplification and short-lived strong fields.

Contribution

It provides detailed scaling laws and insights into magnetic field saturation and back-reaction in KH instabilities through high-resolution 2D and 3D simulations.

Findings

Magnetic fields reach up to 10^16 G locally in 2D simulations.

Field amplification saturates due to resistive instabilities, limiting growth.

In 3D, hydrodynamic instabilities may limit magnetic amplification.

Abstract

Context. Global MHD simulations show Kelvin-Helmholtz (KH) instabilities at the contact surface of two merging neutron stars. That region has been identified as the site of efficient amplification of magnetic fields. However, these global simulations, due to numerical limitations, were unable to determine the saturation level of the field strength, and thus the possible back-reaction of the magnetic field onto the flow. Aims. We investigate the amplification of initially weak fields in KH unstable shear flows, and the back-reaction of the field onto the flow. Methods. We use a high-resolution ideal MHD code to perform 2D and 3D local simulations of shear flows. Results. In 2D, the magnetic field is amplified in less than 0.01ms until it reaches locally equipartition with the kinetic energy. Subsequently, it saturates due to resistive instabilities that disrupt the KH vortex and decelerate the shear flow on a secular time scale. We determine scaling laws of the field amplification with the initial field strength and the grid resolution. In 3D, this hydromagnetic mechanism may be dominated by purely hydrodynamic instabilities limiting the amplification. We find maximum magnetic fields of 10^16 G locally, and r.m.s. maxima within the box of 10^15 G. However, such strong fields exist only for a short period. In the saturated state, the magnetic field is mainly oriented parallel to the shear flow for strong initial fields, while weaker initial fields tend to lead to a more balanced distribution of the field energy. In all models the flow shows small-scale features. The magnetic field is at most in equipartition with the decaying shear flow. (abridged)