Explosive magnetorotational instability in Keplerian disks

TL;DR

This paper investigates the nonlinear explosive magnetorotational instability (EMRI) in Keplerian disks, deriving dynamic equations for mode interactions, identifying conditions for explosive growth or bounded oscillations, and providing asymptotic solutions.

Contribution

It introduces a new theoretical framework for understanding EMRI through dynamic equations of resonant mode interactions and derives explicit asymptotic solutions.

Findings

EMRI can cause finite-time amplitude explosion

Two types of perturbation behaviors are identified: explosive and bounded oscillations

Asymptotic solutions match numerical results near explosion time

Abstract

Differentially rotating disks under the effect of axial magnetic field are prone to a nonlinear explosive magnetorotational instability (EMRI). The dynamic equations that govern the temporal evolution of the amplitudes of three weakly-detuned resonantly interacting modes are derived. As distinct from exponential growth in the strict resonance triads EMRI occurs due to the resonant interactions of a MRI mode with stable Alfv\'en-Coriolis and magnetosonic modes. Numerical solutions of the dynamic equations for amplitudes of a triad indicate that two types of perturbations behavior can be excited for resonance conditions: (i) EMRI which leads to infinite values of the three amplitudes within a finite time, and (ii) bounded irregular oscillations of all three amplitudes. Asymptotic explicit solutions of the dynamic equations are obtained for EMRI regimes and are shown to match the numerical solutions near the explosion time.