Cross helicity and turbulent magnetic diffusivity in the solar convection zone

TL;DR

This paper investigates the relationship between cross helicity and turbulent magnetic diffusivity in the solar convection zone, providing theoretical and numerical insights that can help interpret solar magnetic field observations.

Contribution

It introduces a quasilinear theory and numerical simulations to relate cross helicity to magnetic diffusivity and mean magnetic fields in the solar convection zone.

Findings

Cross helicity is anti-correlated with the mean vertical magnetic field.

The ratio of cross helicity to magnetic field relates to magnetic eddy diffusivity.

Predicted cross helicity at the solar surface exceeds 1 Gauss km/s.

Abstract

In a density-stratified turbulent medium the cross helicity <u'.B'> is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations we find the cross helicity and the mean vertical magnetic field anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface exceeds the value of 1 Gauss km/s. Its sign is anti-correlated with that of the radial mean magnetic field. Alternatively, we can use our result to determine the value of the turbulent magnetic diffusivity from observations of the cross helicity.