Astronomical time series analysis is one of the hottest and most important problems, and becomes the suitable way to deal with the underlying dynamical behavior of the considered nonlinear systems. The quasi-periodic analysis of solar magnetic activity has been carried out by various authors during the past fifty years. In this work, the novel Hilbert-Huang transform approach is applied to investigate the yearly numbers of polar faculae in the time interval from 1705 to 1999. The detected periodicities can be allocated to three components: the first one is the short-term variations with periods smaller than 11 years, the second one is the mid- term variations with classical periods from 11 years to 50 years, and the last one is the long-term variations with periods larger than 50 years. The analysis results improve our knowledge on the quasi-periodic variations of solar magnetic activity and could be provided valuable constraints for solar dynamo theory. Furthermore, our analysis results could be useful for understanding the long-term variations of solar magnetic activity, providing crucial information to describe and forecast solar magnetic activity indicators.
Statistical signal processing is one of the most important tasks in a large amount of areas of scientific studies, such as astrophysics, geophysics, and space physics. Phase recurrence analysis and long-range persistence are the two dynamical structures of the underlying processes for the given natural phenomenon. Linear and nonlinear time series analysis approaches (cross-correlation analysis, cross-recurrence plot, wavelet coherent transform, and Hurst analysis) are combined to investigate the relative phase interconnection and long-range correlation between solar activity and geomagnetic activity for the time interval from 1932 January to 2017 January. The following prominent results are found: (1) geomagnetic activity lags behind sunspot numbers with a phase shift of 21 months, and they have a high level of asynchronous behavior; (2) their relative phase interconnections are in phase for the periodic scales during 8-16 years, but have a mixing behavior for the periodic belts below 8 years; (3) both sunspot numbers and geomagnetic activity can not be regarded as a stochastic phenomenon because their dynamical behaviors display a long-term correlation and a fractal nature. We believe that the presented conclusions could provide further information on understanding the dynamical coupling of solar dynamo process with geomagnetic activity variation, and the crucial role of solar and geomagnetic activity in the long-term climate change.
Statistical data processing has been one of the most important activities in many fields of scientific studies, and has become the only way through which one can deal with the underlying processes of the given phenomenon. The two classical techniques to solar time series analysis are related to the space domain and the spectral. In the present paper, the relative phase relationship of sunspot unit area on both hemispheres is investigated by the long-range correlation and the wavelet transform analysis. It is found that, (1) the north-south asynchrony of sunspot unit area can not be regarded as a stochastic phenomenon because its behavior exhibits a long-term tendency; (2) The leading hemisphere of sunspot unit area is the southern hemisphere before the year of 1962, and then the northern hemisphere till the year of 2008; (3) the sunspot unit area should be used to represent the long-term solar magnetic activity. Our analysis results could be instructive to put further research on the physical mechanisms of north-south asynchrony of magnetic activity on the Sun. Moreover, the long-range correlation analysis and the wavelet transform technique of solar time series provide crucial information to understand, describe, and predict long-term solar variability.
Solar magnetic structures exhibit a wealth of different spatial and temporal scales. Presently, solar magnetic element is believed to be the ultra-fine magnetic structure in the lower solar atmospheric layer, and the diffraction limit of the largest-aperture solar telescope (New Vacuum Solar Telescope; NVST) of China is close to the spatial scale of magnetic element. This implies that modern solar observations have entered the era of high resolution better than 0.2 arc-second. Since the year of 2011, the NVST have successfully established and obtained huge observational data. Moreover, the ultra-fine magnetic structure rooted in the dark inter-graunlar lanes can be easily resolved. Studies on the observational characteristics and physical mechanism of magnetic bright points is one of the most important aspects in the field of solar physics, so it is very important to determine the statistical and physical parameters of magnetic bright points with the feature extraction techniques and numerical analysis approaches. For identifying such ultra-fine magnetic structure, an automatically and effectively detection algorithm, employed the Laplacian transform and the morphological dilation technique, is proposed and examined. Then, the statistical parameters such as the typical diameter, the area distribution, the eccentricity, and the intensity contrast are obtained. And finally, the scientific meaning for investigating the physical parameters of magnetic bright points are discussed, especially for understanding the physical processes of solar magnetic energy transferred from the photosphere to the corona.
Three nonlinear analysis techniques, including cross-recurrence plot, line of synchronization, and cross-wavelet transform, are proposed to estimate the coherent phase vibrations of nonlinear and non-stationary time series. The case study utilizes the monthly averages of sunspot areas during the time interval from May 1874 to August 2014. The following prominent results are found: (1) the phase-leading hemisphere of long-term sunspot areas has changed twice in the past 140 years, indicating that the hemispheric imbalances and apparent phase differences on both hemispheres are a prevalent behavior and are not anomalous; (2) the alternating regularity of hemispheric asynchronism exhibits a cyclical pattern of 4.5+3.5 cycles, and the magnetic flux excess in a certain hemisphere during the ascending branch of a cycle can be taken as an indication of the phase-leading hemisphere in this cycle. We firmly believe that powerful nonlinear approaches are more advanced than classical linear methods when they are combined to determine the dynamic complexity of nonlinear physical systems.
Two relatively advanced and powerful analysis methods, i.e. coherence-wavelet transform and cross-recurrence plot, which are used to probe the nonlinear interrelation between different time series, have been applied to non-stationary time series in this paper. The case study uses the chaotic time series of astronomical observational data for the time interval from January 1966 to December 2010. We examined the phase dynamical properties between two data sets and found that the availability of a physically meaningful phase definition depends crucially on the appropriate choice of the reference frequencies. Furthermore, their phase shift is not only time-dependent but also frequency-dependent. We conclude that advanced nonlinear analysis approaches are more powerful than traditional linear methods when they are applied to analyze nonlinear and non-stationary dynamical behavior of complex physical systems.
Cross-wavelet transforms analysis is proposed to investigate the phase relationship between sunspot group numbers and sunspot numbers during the period of1874 May to 2010 December. Their phase relationship is not only time-dependent but also frequency-dependent, which implies that their phase asynchrony is not a simple linear relationship, although they are highly correlated with each other. This study shows that cross-wavelet transforms technique for the phase analysis between different time series of solar activity is fairly useful.