MRI-driven $\alpha\Omega$ dynamo at high Pm numbers

Abstract

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. The magnetorotational instability (MRI) is a key mechanism for angular momentum transport and large-scale magnetic field amplification. Recent work has begun to address the regime of high magnetic Prandtl number $\mathrm{Pm}$, the ratio of viscosity to resistivity, in which angular momentum and magnetic energy increase with $\mathrm{Pm}$. This regime reveals unique dynamics of small-scale turbulence in disk mid-planes and buoyancy instabilities in the atmosphere. This study aims to build on these findings, focusing on the MRI-driven $\alpha\Omega$ dynamo in stratified simulations to understand magnetic field generation in the high-$\mathrm{Pm}$ regime. We analyze data taken from stratified shearing box simulations both in the regime of magnetic Prandtl number of order unity, and also in the high $\mathrm{Pm}$ regime employing new techniques to compute the dynamo coefficients. We find that the mean-magnetic field evolution can be described by an $\alpha\Omega$ 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. Overall, the magnetic field amplification found in global simulations should be increased by at least a factor of $\sim 5$, which could lead to more powerful jets and stronger winds from astrophysical disks in the high-Pm regime.