Morphology of the two-dimensional MRI in Axial Symmetry

TL;DR

This paper investigates the linear stability of stratified, magnetized accretion disks in axial symmetry, revealing that the emergence of unstable MRI modes depends solely on the radial differential rotation profile.

Contribution

It introduces a novel analysis using the magnetic flux function as the fundamental variable, incorporating the co-rotation theorem into the stability assessment.

Findings

Unstable modes depend only on radial differential rotation.

Vertical stratification does not alter the instability condition.

The analysis applies to small-scale perturbations in stratified disks.

Abstract

In this paper, we analyze the linear stability of a stellar accretion disk, having a stratified morphology. The study is performed in the framework of ideal magneto-hydrodynamics and therefore it results in a characterization of the linear unstable magneto-rotational modes. The peculiarity of the present scenario consists of adopting the magnetic flux function as the basic dynamical variable. Such a representation of the dynamics allows to make account of the co-rotation theorem as a fundamental feature of the ideal plasma equilibrium, evaluating its impact on the perturbation evolution too. According to the Alfvenic nature of the Magneto-rotational instability, we consider an incompressible plasma profile and perturbations propagating along the background magnetic field. Furthermore, we develop a local perturbation analysis, around fiducial coordinates of the background configuration and dealing with very small scale of the linear dynamics in comparison to the background inhomogeneity size. The main issue of the present study is that the condition for the emergence of unstable modes is the same in the stratified plasma disk, as in the case of a thin configuration. Such a feature is the result of the cancelation of the vertical derivative of the disk angular frequency from the dispersion relation, which implies that only the radial profile of the differential rotation is responsible for the trigger of growing modes.