COMPARATIVE STUDY OF SOLAR FLARE NORTH-SOUTH HEMISPHERIC AND K-INDEX GEOMAGNETIC ACTIVITY TIME SERIES DATA USING FRACTAL DIMENSION

Danish Hassan; Shaheen Abbas; M.R.K Ansari

Danish Hassan Mathematical Sciences Research Centre Federal Urdu University, Karachi
Shaheen Abbas Mathematical Sciences Research Centre Federal Urdu University, Karachi
M.R.K Ansari Department of Mathematics Sir Syed Engineering University, Karachi, Pakistan

Keywords: Solar Flare, K-index, Fractal Dimension, Geomagnetic, Hurst Exponent

Abstract

The solar flare activity is associated with the sunspots activity. The solar flare index data (monthly flare index cycles "20, 21, 22, 23", available on world data center) is used starting from 1966 to 2008 in this research work. The main purpose of this research is to compare the solar flares activity data of north hemisphere, south hemisphere and total hemisphere with K-index activity data using fractal dimension. Persistency (1 < D < 1.5) is observed for each solar cycle of each hemisphere along with the total hemisphere and compare with the associated K-index activity data. Persistency analysis of solar flares activity and K-index activity data will be useful to understand the effects of solar flares dynamics on the K-index dynamics. There is strong bond found between solar flares north hemisphere and K-index data. Hurst exponent is also obtained with the help of fractal dimension (H = 2- D) to understand the long rang dependence (self-similarity) of solar flares and K-index activity dynamics. The results represent that each solar flare cycle (north, south and total hemisphere) and K-index activity data along with total time series data of both are regular dynamics and continue to long term in future. The complex of time series can be analyzed using Fractal dimension (local property) of the data while smoothness of time series be observe by Hurst Exponent (universal property).