AUTHOR=Aschwanden Markus J. , Vilangot Nhalil Nived 

TITLE=Interface region imaging spectrograph (IRIS) observations of the fractal dimension in the solar atmosphere

JOURNAL=Frontiers in Astronomy and Space Sciences

VOLUME=9

YEAR=2022

URL=https://www.frontiersin.org/journals/astronomy-and-space-sciences/articles/10.3389/fspas.2022.999319

DOI=10.3389/fspas.2022.999319

ISSN=2296-987X

ABSTRACT=<p>We focus here on impulsive phenomena and Quiet-Sun features in the solar transition region, observed with the Interface Region Imaging Spectrograph (IRIS) at 1,400 Å (at formation temperatures of <italic>T</italic><sub><italic>e</italic></sub> ≈ 10<sup>4</sup>–10<sup>6</sup> K). Summarizing additional literature values we find the following fractal dimensions (in increasing order): <italic>D</italic><sub><italic>A</italic></sub> = 1.23 ± 0.09 for photospheric granulation, <italic>D</italic><sub><italic>A</italic></sub> =1.40 ± 0.09 for chromospheric (network) patterns, <italic>D</italic><sub><italic>A</italic></sub> = 1.54 ± 0.04 for plages in the transition region, <italic>D</italic><sub><italic>A</italic></sub> = 1.56 ± 0.08 for extreme ultra-violet (EUV) nanoflares, <italic>D</italic><sub><italic>A</italic></sub> = 1.59 ± 0.20 for active regions in photospheric magnetograms, and <italic>D</italic><sub><italic>A</italic></sub> = 1.76 ± 0.14 for large solar flares. We interpret low values of the fractal dimension (1.0 ≲ <italic>D</italic><sub><italic>A</italic></sub> ≲ 1.5) in terms of sparse curvi-linear flow patterns, while high values of the fractal dimension (1.5 ≲ <italic>D</italic><sub><italic>A</italic></sub> ≲ 2.0) indicate quasi-space-filling transport processes, such as chromospheric evaporation in flares. Phenomena in the solar transition region appear to be consistent with self-organized criticality (SOC) models, based on their fractality and their size distributions of fractal areas <italic>A</italic> and (radiative) energies <italic>E</italic>, which show power law slopes of <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">obs</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>2.51</mml:mn><mml:mo>±</mml:mo><mml:mn>0.21</mml:mn></mml:math></inline-formula> (with <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">theo</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>2.33</mml:mn></mml:math></inline-formula> predicted), and <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">obs</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>2.03</mml:mn><mml:mo>±</mml:mo><mml:mn>0.18</mml:mn></mml:math></inline-formula> (with <inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">theo</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>1.80</mml:mn></mml:math></inline-formula> predicted). This agreement suggests that brightenings detected with IRIS at 1,400 Å reveal the same nonlinear SOC statistics as their coronal counterparts in EUV.</p>