Paradoxes of magnetorotational instability and their geometrical resolution

TL;DR

This paper resolves two paradoxes of magnetorotational instability (MRI) using advanced mathematical methods, deriving new limits for MRI behavior at extreme magnetic Prandtl numbers and extending known stability thresholds.

Contribution

It provides a geometrical resolution to MRI paradoxes and derives a new critical Rossby number limit at finite Lundquist number, advancing understanding of MRI stability.

Findings

Derived a new strict limit of the critical Rossby number at ${ m Ro_c}=-0.802$

Extended the inductionless Liu limit of ${ m Ro_c}=-0.828$ to finite Lundquist number

Resolved paradoxes of MRI in extreme magnetic Prandtl number regimes

Abstract

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable accretion discs. By using the WKB approximation and methods of singular function theory, we resolve two different paradoxes of MRI that appear in the limits of infinite and vanishing magnetic Prandtl number. For the latter case we derive a new strict limit of the critical Rossby number. This new limit of ${\rm Ro_c}=-0.802$, which appears for a finite Lundquist number of ${\rm Lu}=0.618$, extends the formerly known inductionless Liu limit of ${\rm Ro_c}=-0.828$ valid at ${\rm Lu}=0$.