Properties of multifractality in time series of the Sun’s magnetic parameters

Abstract

The magnetic field in solar active regions (ARs) evolves dynamically and can play an important role in triggering solar flares as one of the Sun’s major eruptive phenomena. It is, therefore, crucial to better understand the time-varying magnetic field in ARs in relation to flare occurrence. Here we applied the multifractal detrended fluctuation analysis (MF-DFA) method to time series of various magnetic parameters derived from the observed magnetic field in the photospheric surface of a total of 236 ARs consisting of 118 flare-quiet and 118 flaring cases. As a result, the nature of multifractality in various levels was identified in all the investigated time series of solar magnetic parameters. Comparing properties of multifractality in the time series of the flare-quiet versus flaring ARs, we first found that the magnetic parameter time series of the flaring ARs tend to have a higher generalized Hurst exponent than those of the flare-quiet ARs. Through the Student’s t-test, it was also found that the distribution of generalized Hurst exponents is statistically different between the magnetic parameter time series of the flare-quiet and flaring ARs. In addition, for most of the magnetic parameters under investigation, the multifractal spectra derived from the relevant time series exhibit a higher degree of left truncation in the case of the flare-quiet ARs compared to the flaring ARs. These results support the fact reported in previous studies that the magnetic field in flaring ARs is more dynamic in terms of its rapid and large variations prior to and around times of flare occurrence. We expect that further detailed analysis of multifractality in time series of the Sun’s various physical quantities not only in the photosphere but also in the upper atmosphere may help us to better understand the fundamental physics of solar eruptive phenomena.