Revised Conditions for MRI due to Isorotation Theorem

TL;DR

This paper revises the conditions for Magneto-rotational Instability (MRI) in astrophysical disks by incorporating the isorotation theorem, showing that magnetic field orientation affects MRI stability criteria.

Contribution

It introduces the isorotation condition into MRI analysis, revealing the influence of magnetic field direction on the instability's emergence.

Findings

MRI conditions depend on magnetic field orientation.

The isorotation condition modifies the classical MRI stability criteria.

Magnetic flux surface dependence is crucial for MRI analysis.

Abstract

We re-analyze the physical conditions for Magneto-rotational Instability (MRI) within a steady axisymmetric stratified disk of plasma, in order to account for the so-called isorotation theory (the spatial profile of differential angular velocity depends on the magnetic flux surface). We develop the study of linear stability around an astrophysical background configuration, following the original derivation in \cite{Ba:1995}, but implementing the isorotation condition as the orthogonality between the background magnetic field and the angular velocity gradient. We demonstrate that a dependence on the background magnetic field direction is restored in the dispersion relation and, hence, the emergence of MRI is also influenced by field orientation.