Study of sunspot cycles using fractal dimensions: wave-spectrum scaling

Abstract

The fractal dimension analysis provides more appropriate evolution of several solar phenomena related to the sun and its environment. The novelty of this research is to use self-similar fractal dimension (FDS) and self-affine fractal dimension (FDA) to calculate fractal parameters including universal parameter such as the exponent scale β, spectral exponent (α), and fractal autocorrelation coefficient (C∇). First, the mean monthly data of each sunspot cycle from 1755 to 2008 (23 cycles) is analyzed separately. Then, the total data of 24 cycles is analyzed. The study focuses on finding an adequate value of the wave-spectral exponent α for which the cycles are more strongly correlated with each other. Self-similar fractal dimension is found to be more persistent and positively correlated as compared to self-affine fractal dimension. The fractal parameters are found to exist on a significant scale. The exponent scale β is calculated by both of the fractal dimensions FDS and FDA. Both the fractal dimensions are also related to the wave-spectral exponent α which is calculated by the Hurst exponent (HE). The self-similar and self-affine spectral exponents αS and αA are used to determine whether the value of α is greater than 2 or not. The spectrum for sunspot cycles is considered to be Gaussian if the value of α is greater than 2. This demonstrates that the cycles are strongly correlated to other cycles. The self-similar fractal autocorrelation coefficient (C∇) is found to be more persistent and correlated as compared to the self-affine fractal dimension. It can be concluded that the fractal approach can study more rigorously the local and global aspects of the dynamical processes and activities associated with the sun and its climate.