Magnetic helicity flux in the presence of shear

TL;DR

This paper investigates magnetic helicity fluxes in shearing systems, revealing that while small-scale helicity flux divergences can be gauge-independent, the Vishniac-Cho flux divergence remains finite, highlighting complexities in gauge choices.

Contribution

It demonstrates that in shearing systems, the divergence of small-scale helicity flux can vanish in a suitable gauge, challenging previous assumptions about the Vishniac-Cho flux.

Findings

Divergence of small-scale helicity flux vanishes in a usable gauge.

Vishniac-Cho flux divergence remains finite in simulations.

Horizontal fluxes of small-scale magnetic helicity exist with finite divergences.

Abstract

Magnetic helicity has risen to be a major player in dynamo theory, with the helicity of the small-scale field being linked to the dynamo saturation process for the large-scale field. It is a nearly conserved quantity, which allows its evolution equation to be written in terms of production and flux terms. The flux term can be decomposed in a variety of fashions. One particular contribution that has been expected to play a significant role in dynamos in the presence of mean shear was isolated by Vishniac & Cho (2001, ApJ 550, 752). Magnetic helicity fluxes are explicitly gauge dependent however, and the correlations that have come to be called the Vishniac-Cho flux were determined in the Coulomb gauge, which turns out to be fraught with complications in shearing systems. While the fluxes of small-scale helicity are explicitly gauge dependent, their divergences can be gauge independent. We use this property to investigate magnetic helicity fluxes of small-scale field through direct numerical simulations in a shearing-box system and find that in a numerically usable gauge the divergence of the small-scale helicity flux vanishes, while the divergence of the Vishniac-Cho flux remains finite. We attribute this seeming contradiction to the existence of horizontal fluxes of small-scale magnetic helicity with finite divergences even in our shearing-periodic domain.