Photospheric Imprints of Coronal Electric Currents, I. Magnetic Structure Near Polarity Inversion Lines

TL;DR

This paper investigates the magnetic structure near polarity inversion lines in active regions that produced major solar flares, revealing how coronal currents imprint on the photosphere and relate to flare activity.

Contribution

It introduces a method to partition photospheric magnetic fields into components associated with different coronal current structures, providing new insights into magnetic configurations linked to solar eruptions.

Findings

Parallel currents along PILs are more stable and attract each other.

Coronal currents imprint on the photosphere, influencing magnetic gradients.

Strong cross-PIL magnetic gradients are linked to flare and CME occurrence.

Abstract

Coronal electric currents store the magnetic energy that is released in solar flares and coronal mass ejections (CMEs). Here, we use photospheric vector magnetic field observations to study currents in active regions 10930 and 11158, which both produced eruptive, X-class flares. We employ Gauss's separation method in Cartesian geometry to partition the photospheric field into three distinct components: (i) the toroidal field, $\vec B_T$, from vertical currents, $J_z$, passing through the photosphere; (ii) $\vec B^<$, from horizontal currents, $\vec J_h^<$, flowing below it; and (iii) $\vec B^>$, from horizontal currents, $\vec J_h^>$, flowing above it. We refer to $\vec B^>$ as the photospheric imprint of coronal currents. We give two representations of $\vec B^<$ and $\vec B^>$: (i) as second-order derivatives of poloidal potentials $P^<$ and $P^>$, respectively; and (ii) in terms of gradients of interior and exterior scalar potentials, respectively. The central polarity inversion line (PIL) in each region possesses magnetic structure similar to that reported in AR 12673 by Schuck et al. (2022): (i) $\vec B_T$, which arises from $J_z$, produces sheared fields along the PIL; (ii) $\vec B^>$ exhibits large-scale, spatially coherent structure, consistent with $\vec J_h^>$ flowing above and along the PIL; and (iii) the near-PIL currents $\vec J_h^<$ and $\vec J_h^>$ are roughly parallel. Because parallel currents attract, such parallel-current configurations are likely more stable than misaligned-current configurations. Current $\vec J_h^>$ flowing along a PIL increases the magnitued of the gradient of $B_z$ across the PIL, providing a physical explanation for previously reported empirical associations of strong, cross-PIL gradients in $B_z$ with flare and CME occurrence.