Local and global aspects of the linear MRI in accretion disks

TL;DR

This paper explores the linear magnetorotational instability (MRI) in accretion disks, connecting local and global modes, and demonstrates that local analysis accurately predicts global growth rates, with numerical validation.

Contribution

It reveals the relationship between local and global MRI modes, showing local analysis's effectiveness and clarifying the nature of channel flows in global disks.

Findings

Global modes reproduce local dispersion relations without approximation

Local channel flows are a subset of global modes

Numerical simulations confirm theoretical results

Abstract

We revisit the linear MRI in a cylindrical model of an accretion disk and uncover a number of attractive results overlooked in previous treatments. In particular, we elucidate the connection between local axisymmetric modes and global modes, and show that a local channel flow corresponds to the evanescent part of a global mode. In addition, we find that the global problem reproduces the local dispersion relation without approximation, a result that helps explain the success the local analysis enjoys in predicting global growth rates. MRI channel flows are nonlinear solutions to the governing equations in the local shearing box. However, only a small subset of MRI modes share the same property in global disk models, providing further evidence that the prominence of channels in local boxes is artificial. Finally, we verify our results via direct numerical simulations with the Godunov code RAMSES.