The pinch-type instability of helical magnetic fields

TL;DR

This paper investigates the stability of toroidal magnetic fields in galaxies considering axial magnetic fields and rotation, revealing conditions under which these fields are stabilized or destabilized, with implications for galactic magnetic field behavior.

Contribution

The study provides a detailed analysis of the pinch-type instability of helical magnetic fields, incorporating axial components and rotation effects, which was not comprehensively addressed before.

Findings

Axial magnetic fields can both support and stabilize toroidal field instabilities.

Fast rigid rotation suppresses all modes, especially the m=1 mode.

Galactic magnetic fields are likely marginally unstable with growth rates comparable to galactic rotation periods.

Abstract

To find out whether toroidal field can stably exist in galaxies the current-driven instability of toroidal magnetic fields is considered under the influence of an axial magnetic field component and under the influence of both rigid and differential rotation. The MHD equations are solved in a simplified model with cylindric geometry. We assume the axial field as uniform and the fluid as incompressible. The stability of a toroidal magnetic field is strongly influenced by uniform axial magnetic fields. If both field components are of the same order of magnitude then the instability is slightly supported and modes with m>1 dominate. If the axial field even dominates the most unstable modes have again m>1 but the field is strongly stabilized. All modes are suppressed by a fast rigid rotation where the m=1 mode maximally resists. Just this mode becomes best re-animated for \Omega > \Omega^A (\Omega^A the Alfven frequency) if the rotation has a negative shear. -- Strong indication has been found for a stabilization of the nonaxisymmetric modes for fluids with small magnetic Prandtl number if they are unstable for Pm=1. For rotating fluids the higher modes with m>1 do not play an important role in the linear theory. In the light of our results galactic fields should be marginally unstable against perturbations with m<= 1. The corresponding growth rates are of the order of the rotation period of the inner part of the galaxy.