Long term Variation of the Fractal Dimension of Supergranulation

Abstract

Supergranular solar convection cells are a salient manifestation of the magnetic and dynamical behaviour of the sun. Fractal dimension is a valuable mathematical tool to quantify the complexity of geometrical structures. In the context of solar supergranulation, the network of convective cells observed on the solar photosphere, fractal dimension can reveal the dependence of the cell shape complexity on solar rotation, phase, magnetic activity level, and thereby provide insight into the underlying dynamics. This information can be useful for comparing observations with models. In particular, the study of supergranular fractal dimension can shed light on the turbulence of the magneto-convective process that generates supergranulation. This work investigates the complexity of the supergranular network through fractal dimension by using the Ca II K digitized data archive obtained from the Kodaikanal Solar Observatory. The data consist of over 300 visually selected supergranular cells distributed in the 23rd solar cycle. Only cells that were endowed with a clear and continuous boundary were chosen for the analysis. We study the selection bias that possibly affects this data analysis technique, namely that it favors cells of a smaller size (lt 20 Mm). Within this sample, we analyzed the fractal dimension of supergranules across the solar cycle 23, and found that it is anticorrelated with the activity level. This behavior implies that supergranular cell borders show less complexity and grow smoother with increasing solar activity. This anti-correlation between solar activity and fractal dimension offers a new way of thinking about how magnetic activity might affect the complex structure of supergranular cells. Further, we study the complexity and scale of the supergranular network in this data. Adding to the sample size over the previous data and refining our data analysis, we study supergranular fractal dimension as a function of cell size. We find that across the cycle phases, the cells show a bifractal behavior, with