Multifractalitiy Of Long-term Behaviour Of Solar Filaments And Sunspots

As an important method of studying the nonlinear property, multifractal methodhas been applied to many solar physics.Many studies have found that the long-termsolar activities characterized by various solar indices present complex nonlinearproperties.By the analysis of multifractal characteristics from solar filaments andsunspots, the multifractal properties and the connection between solar filaments andsunspots have been described and analysed from the viewpoint of fractal theory.By estimating thef α multifractal spectra of solar filament indices and sunspotnumbers, the multifractal properties of long-term activities of solar filaments andsunspots are analysed.By estimatingf α singularity spectrum, the multifractal propertiesof the raw low-latitude (LLSFNs; at the latitudinal bands of0°~50°), high-latitude(HLSFNs; at the latitudinal bands of50°~90°) and full-disk (FDSFNs; at thelatitudinal bands of0°~90°) solar filament numbers (SFNs) and the internationalsunspot numbers (ISNs) in the same period are analysed, respectively.It is found that thelong-term behaviour of the solar filaments and sunspots show the multifractalcharacteristics.The SFNs have more complex behaviour than the ISNs and the HLSFNspresent more complex than the LLSFNs.The ISNs display well symmetry of thedistribution of singularities and the SFNs are dominated by low singularity strengths.Bymeasuring f α singularity spectrums of smoothed (the11-year cycle, i.e. thelong-term solar activities) and detrended (the accidental activities) data, the smoothedISNs and SFNs are found display a much lower degree of multifractality than the rawdata, i.e. a homogeneous structure and regular behaviour, and tend to appear theapproximately monofractal behaviour.Both the detrended ISNs and SFNs display a veryhigher degree of multifractality than the raw data, i.e. inhomogeneous structure andmore complex behaviour.Further, the complexity of the detrended SFNs is higher thanthe ISNs and the complexity of the HLSFNs is higher than the LLSFNs.The detrendeddata are dominated by high singularity strengths, however.The raw solar filamentnumbers are dominated by low singularity strengths maybe just because of modulationof the11-year cycle.And then, it is supposed that the smoothed data mainly present thelarge-scale activities, while the detrended data mainly present the small-scale activitiesfor the ISNs and SFNs. The large-scale activities and the small-scale activities have thedifferent effect on the multifractality of the ISNs and SFNs.