Identifying the quasi-regular and stochastic components of solar cyclicity and their properties

We have averaged over every Carrington semi-rotation (C.s.-r.), the daily Wolf numbers (RW), total areas of sunspot groups (SA), the 10.7-cm radio flux (F _10.7), and the modulus of the mean magnetic field (|SMMF|). The fractal method of scaling the variance of time series was used to separate the regular and stochastic components. The manifestation of chaotic and stochastic properties of these components was investigated by testing with the methods of chaotic dynamics, as well as with two new methods: (1) close return maps; and (2) multivariate scaling analysis. Results: (1) by separating time series of global indices of solar activity, it is possible to identify the quasi-regular (the quasi-regularity is caused not by the absolute smoothness of the function) component on time scales longer than two years, and the irregular component on time scales shorter than two years; (2) the regular component has the properties of a nonlinear quasi-periodic oscillator; (3) the irregular component is a random one and has the properties of chromatic noise; and (4) by investigating the nonlinear connection of the solar activity indices under consideration it was found that such a connection is strong between F _10.7and RW. A nonlinear correlation between the attractors RW–|SMMF| and F _10.7–|SMMF| was also revealed.     

Dynamics of the magnetic field and velocity field in an emerging active region

The dynamics of the magnetic field and velocity field during the birth and an early development stage of a major active region is studied. SOHO MDI longitudinal-component magnetograms, Dopplergrams, and continuum images are used. The presence of an enhanced material upflow in the photosphere during the passing of the top of the magnetic flux loop, forming the active region, is revealed. The maximum upflow velosity is 2 km/s and the maximum size of the upflow area exceeds 20000 km. The lifetime of the upflow is about two hours. The undulating form of the magnetic flux tubes crossing the photosphere is confirmed. A structural-analysis technique is used to show that the trailing polarity field at the formation stage of the active region is more highly structured than the leading polarity field.     

Fractal properties of active regions

The dynamics of active regions have been investigated using multi-fractal analysis methods, based on magnetograms of the full solar disk in the 630.2 nm line obtained with the SOLIS vector spectromagnetograph of Kitt Peak Observatory (USA) during 2006?C2007 and January 1, 2009?CApril 12, 2010. The applied method of multi-fractal segmentation reveals the appearance of new magnetic fluxes on the Sun disk. A comparison of these fluxes with flare activity shows that the flares are generated in areas of interaction of emerging fluxes with existing structures.     

The Topology of Background Magnetic Fields and Solar Flare Activity

We investigate the topological properties and evolution of background magnetic fields on synoptic maps from Wilcox Solar Observatory using mathematical morphology methods in terms of the Minkowski functionals. The total length of the neutral line, the total areas occupied by positive and negative polarities, and the Euler characteristics of background magnetic fields vary over an eleven-year cycle. Changes in the length of the neutral line that separates the polarities of the background magnetic field correlate well with flare activity. A time–longitude analysis of solar flare activity revealed a complicated organization and rotation of the entire flare ensemble. On the time–longitude diagram, flare activity is organized into the patterns which follow the rearrangements in background magnetic field and exhibit coexisting and alternating modes of rigid rotation. The character of rotation of the entire flare ensemble is similar to the rotation of background magnetic fields. The emergence of background magnetic fields and changes in their topology and rotation are often accompanied by enhancements in flare activity. A comparative analysis of the topological changes in background magnetic fields and flare activity reveals their causal relation.     

Variations in fractal characteristics of active regions and flares

A multifractal analysis of the Hα images for an active region has been performed; the singularity spectra and segmented images for a narrow range of fractal dimensions have been computed for them. The segmented images show the presence of singular areas where the singularity index takes on maximum values. These areas mark the active sites of flares.     

A Fractal Structure of the Time Series of Global Indices of Solar Activity

The structure of time series of daily global indices of solar activity is investigated: the sunspot numbers for the time interval between the years 1854 and 1996, the Greenwich total sunspot area for 1874–1983, the radio-flux at 10.7 cm (F10.7) for 1964–1996, and the Stanford mean solar magnetic field for 1975–1996. The fractal dimensions are determined by two fractal and spectral methods. The identified three time-scale ranges, 2 days–2 months, 2 months–2 years, 2 years–8 and more years, with the fractal dimensions 1.4–1.6, 2, 1.2–1.6, respectively, show perhaps some fractal structure of time series of global indices. The first time-scale range may correspond to ordinary brownian noise and the second to flicker noise. The solar rotation influence of the value of the fractal dimensions at the time range close to the rotational period is studied.     

Fractal properties of active region and flare

A fractal analysis of narrowband images of the chromosphere and transition layer has been performed in order to study regimes of turbulence and their variations during time-varying processes in active regions. The NOAA 10039 and 10050 activity complexes on July 31, 2002, were observed at Baikal astrophysical observatory of ISZF SO RAN in the H-α line using a chromospheric telescope equipped with a Halle birefringent filter (BF) with a passband of 0.5 Å. Images of the same activity complexes in the spectral band centered at the FeXI 171 Å line, obtained at TRACE space observatory, have been processed using the same technique. The method of structure functions has been used to compute the time series of the scaling parameters. The power spectra of two-dimensional images have been used to compute the time variations in the fractal dimension of the considered activity complex. It has been indicated that the parameters of a multifractal structure (intermittent turbulence) demonstrate jump-like and quasiperiodic time variations correlating with flares. These variations were detected in the H-α and FeXI 171 Å lines of the transition zone, using the ground-based and onboard measurements, which demonstrates that they are of the solar origin.