Current helicity and magnetic field anisotropy in solar active regions

TL;DR

This study investigates the anisotropy of magnetic fields in solar active regions, revealing that the commonly assumed local isotropy does not hold, which impacts the interpretation of current helicity measurements.

Contribution

It distinguishes the statistical differences of current helicity terms for isotropic and anisotropic magnetic fields using simulations and assesses the anisotropy degree in solar active regions.

Findings

The degree of anisotropy is approximately 0.8 in active regions.

Assumption of local isotropy is generally not satisfied in solar active regions.

Further analysis is needed to understand the implications of anisotropy on magnetic field studies.

Abstract

The electric current helicity density $\displaystyle \chi=\langle\epsilon_{ijk}b_i\frac{\partial b_k}{\partial x_j}\rangle$ contains six terms, where $b_i$ are components of the magnetic field. Due to the observational limitations, only four of the above six terms can be inferred from solar photospheric vector magnetograms. By comparing the results for simulation we distinguished the statistical difference of above six terms for isotropic and anisotropic cases. We estimated the relative degree of anisotropy for three typical active regions and found that it is of order 0.8 which means the assumption of local isotropy for the observable current helicity density terms is generally not satisfied for solar active regions. Upon studies of the statistical properties of the anisotropy of magnetic field of solar active regions with latitudes and with evolution in the solar cycle, we conclude that the consistency of that assumption of local homogeneity and isotropy requires further analysis in the light of our findings.