Interface Region Imaging Spectrograph (IRIS) Observations of the Fractal Dimension in the Solar Atmosphere

TL;DR

This study measures the fractal dimensions of various solar phenomena observed with IRIS, revealing how different features exhibit varying degrees of complexity and linking these to self-organized criticality models.

Contribution

It provides new measurements of fractal dimensions across multiple solar features and interprets these in terms of transport processes and SOC models.

Findings

Fractal dimensions range from 1.21 to 1.89 across phenomena.

Transition region phenomena are consistent with SOC size distributions.

Large flares exhibit higher fractal dimensions indicating space-filling processes.

Abstract

While previous work explored the fractality and self-organized criticality (SOC) of flares and nanoflares in wavelengths emitted in the solar corona (such as in hard X-rays, soft X-rays, and EUV wavelenghts), we focus here on impulsive phenomena in the photosphere and transition region, as observed with the {\sl Interface Region Imaging Spectrograph (IRIS)} in the temperature range of $T_e \approx 10^4-10^6$ K. We find the following fractal dimensions (in increasing order): $D_A=1.21 \pm 0.07$ for photospheric granulation, $D_A=1.29 \pm 0.15$ for plages in the transition region, $D_A=1.54 \pm 0.16$ for sunspots in the transition region, $D_A=1.59 \pm 0.08$ for magnetograms in active regions, $D_A=1.56 \pm 0.08$ for EUV nanoflares, $D_A=1.76 \pm 0.14$ for large solar flares, and up to $D_A=1.89 \pm 0.05$ for the largest X-class flares. We interpret low values of the fractal dimension ($1.0 \lapprox D_A \lapprox 1.5$) in terms of sparse curvi-linear flow patterns, while high values of the fractal dimension ($1.5 \lapprox D_A \lapprox 2.0$) indicate near space-filling transport processes, such as chromospheric evaporation. Phenomena in the solar transition region appear to be consistent with SOC models, based on their size distributions of fractal areas $A$ and (radiative) energies $E$, which show power law slopes of $\alpha_A^{obs}=2.51 \pm 0.21$ (with $\alpha_A^{theo}=2.33$ predicted), and $\alpha_E^{obs}=2.03 \pm 0.18$ (with $\alpha_E^{theo}=1.80$ predicted).