Extending the range of the inductionless magnetorotational instability

TL;DR

This paper demonstrates that inductionless magnetorotational instabilities, like helical and azimuthal MRI, can destabilize Keplerian flows with minimal magnetic field modifications, extending MRI's applicability in low magnetic Prandtl number regions.

Contribution

It shows how slight modifications to the azimuthal magnetic field profile enable MRI in Keplerian flows, linking the lower and upper Liu limits of Rossby number.

Findings

Inductionless MRI can destabilize Keplerian profiles with minor magnetic field changes.

The connection between the lower and upper Liu limits of Rossby number is established.

The applicability of MRI is extended to low magnetic Prandtl number regions.

Abstract

The magnetorotational instability (MRI) can destabilize hydrodynamically stable rotational flows, thereby allowing angular momentum transport in accretion disks. A notorious problem for MRI is its questionable applicability in regions with low magnetic Prandtl number, as they are typical for protoplanetary disks and the outer parts of accretion disks around black holes. Using the WKB method, we extend the range of applicability of MRI by showing that the inductionless versions of MRI, such as the helical MRI and the azimuthal MRI, can easily destabilize Keplerian profiles ~ 1/r^(3/2) if the radial profile of the azimuthal magnetic field is only slightly modified from the current-free profile ~ 1/r. This way we further show how the formerly known lower Liu limit of the critical Rossby number, Ro=-0.828, connects naturally with the upper Liu limit, Ro=+4.828.