Magnetorotational instability-driven αΩ dynamo at high Prandtl numbers

¹ Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany
² Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
³ Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

^⋆ Corresponding author: alexis.reboul-salze@aei.mpg.de

Received: 9 January 2025
Accepted: 27 May 2025

Abstract

Context. To power gamma-ray bursts and other high-energy events, large-scale magnetic fields are required to extract rotational energy from compact objects such as black holes and neutron stars. Magnetorotational instability (MRI) is a key mechanism for angular momentum transport and large-scale magnetic field amplification. Recent works have begun to address the regime of high magnetic Prandtl number, Pm, which represents the ratio of viscosity to resistivity. The angular momentum transport and saturated magnetic energy increase with Pm. This regime reveals the unique dynamics of small-scale turbulence in disk mid-planes and buoyancy instabilities in the atmosphere.

Aims. This study aims to build on these findings, focusing on the MRI-driven αΩ dynamo in stratified simulations to understand magnetic field generation in the high-Pm regime.

Methods. We analyzed data taken from stratified shearing box simulations both in the regime of magnetic Prandtl number of order unity, as well as in the high Pm regime. We employed new techniques to compute the dynamo coefficients.

Results. We find that the mean-magnetic field evolution can be described by an αΩ dynamo, even in the high-Pm regime. The mean magnetic field as well as the dynamo coefficients increase with Pm. This leads to a shorter dynamo period and a faster growth rate. We also find that the off-diagonal coefficients have an impact on the propagation of the magnetic field in the dynamo region.

Conclusions. Overall, the magnetic field amplification found in global simulations is expected to increase by at least a factor of 5. This could lead to more powerful jets and stronger winds from astrophysical disks in the high-Pm regime.