A Fractal Analysis of Magnetograms within Active Regions

TL;DR

This study analyzes the fractal dimensions of magnetic fields in active regions' magnetograms, revealing greater complexity in penumbral regions compared to umbral regions, which impacts magnetic field modeling.

Contribution

It introduces a fractal analysis method for magnetic field groups in active regions and compares these with intensity-based fractal dimensions from previous studies.

Findings

Penumbral magnetic fields have higher fractal dimensions than umbral fields.

Inverse relationship between magnetic field fractal dimensions and intensity image dimensions.

Greater complexity observed in penumbral magnetic structures.

Abstract

The magnetograms of sixteen Active Regions, observed during June - November 2015, were obtained from the Joint Science Operations Center and used to determine the fractal dimensions of various magnetic field groups. The fields were divided into strong (positive and negative) and weak (positive and negative) groupings. The area-perimeter method was used to determine the fractal dimensions for the umbral and penumbral regions of the magnetograms. The fractal dimensions were found to be 1.79 \pm 0.49 and 1.96 \pm 0.29 for strong and weak magnetic fields respectively. When compared to the umbral and penumbral fractal dimensions determined by (Rajkumar, Haque and Hrudey, 2017) using white light images, an inverse relationship was found, with the umbra showing lower fractal dimensions than the penumbra for the magnetic field groups compared to the intensity images. This directly implies that there is greater complexity in the penumbral magnetic field groupings than the umbral region. This has implications for models that constrain how the magnetic field groups are contained in the cooler umbral regions.