Detrended fluctuation analysis of magnetic parameters of solar active regions

Many signals in the nature have power-law behaviors, namely they are "scale-free". The method of detrended fluctuation analysis (DFA), as one of the popular methods (e.g., Rescaled range analysis and Spectral analysis) for determining scale-free nature of time series, has a very important advantage that the DFA can be applied to both stationary and non-stationary signals. The analysis of time series using the DFA has been broadly used in physiology, finance, hydrology, meteorology, geology, and so on. We performed the DFA of 16 Spaceweather HMI Active Region Patch (SHARP) parameters for 38 HMI Active Region Patches (HARPs) obtained by Solar Dynamics Observatory (SDO) from May 2010 to June 2014. The main results from this study are as follows. (1) The most of the time series data are non-stationary. (2) The DFA scaling exponents of "mean vertical current density" for 38 HARPs have a negative correlation coefficient (-0.41) with flare index. (3) The DFA scaling exponents of parameters such as "Sum of the absolute value of net currents per polarity", "Absolute value of the net current helicity", and "Mean photospheric excess magnetic energy density" for the most active HARPs having more than 10 major flares, have positive correlation coefficients (0.64, 0.59, and 0.53, respectively) with the ratio of "the number of CMEs associated with major flares" to "the number of major flares". Physical interpretations on our results will be discussed.