Fractal dimensions of umbral and penumbral regions of sunspots

TL;DR

This study measures the fractal dimensions of sunspot regions to analyze their morphological complexity and explores the correlation between umbral and penumbral structures over time.

Contribution

It provides new measurements of fractal dimensions for sunspot regions and examines their temporal correlation, extending previous work with a larger dataset and time series analysis.

Findings

Fractal dimensions of umbral regions: 2.09 ± 0.42.

Fractal dimensions of penumbral regions: 1.72 ± 0.4.

Positive correlation (r=0.58 to 0.623) between umbral and penumbral fractal dimensions.

Abstract

The images of sunspots in sixteen active regions taken at the UCCI Observatory in Grand Cayman during June - November 2015, were used to determine their fractal dimensions using the perimeter-area method for the umbral and the penumbral region. Scale free fractal dimensions of 2.09 $\pm$ 0.42 and 1.72 $\pm$ 0.4 were found respectively. This value was higher than the value determined by Chumak and Chumak (1996) who used a similar method but for the penumbral region only for their sample set. There is a positive correlation r = 0.58 between umbral and the penumbral fractal dimensions for the specific sunspots. Furthermore, a time series analysis was done similarly on eight images of AR 12403, from 21st August 2015 - 28th August 2015 taken from the Debrecen Photoheliographic Data (DPD). The correlation, r = 0.623 between the umbral and penumbral fractal dimensions in the time series indicating that the complexity in morphology indicated by the fractal dimension between the umbra and penumbra followed each other in time as well.