Multifractal Analysis Of Solar Magnetograms

As solar observational techniques improve, fine small-scale structures observed on the solar surface become more pronounced. Complex filigree structures of solar granulation, sunspots, photospheric magnetic and velocity fields cannot be described adequately by a single parameter (e.g., filling factor, fractal dimension, or power-law index). Methods which incorporate parameters that are a function of scale (multiscale methods) to describe the complexity of a field under study, should be involved. The multifractal approach offers such a possibility. In this paper the scaling of structure functions is proposed in order to analyze multifractality. Application of the approach to SOHO/MDI high-resolution magnetograms of active regions show that the structure functions differ for all active regions studied. For a given active region, the functions may maintain their shape during several hours; however, they can significantly change during a day. Flare-quiet active regions tend to possess a lower degree of multifractality than flaring active regions do. The increase in multifractality is a signal that a magnetic structure is driven to a critical state, thus gaining tangential discontinuities of various length scales.     

Topological changes of the photospheric magnetic field inside active regions: A prelude to flares?

The detection of magnetic field variations as a signature of flaring activity is one of the main goals in solar physics. Past efforts gave apparently no unambiguous observations of systematic changes. In the present study, we discuss recent results from observations that scaling laws of turbulent current helicity inside a given flaring active region change in response to large flares in that active region. Such changes can be related to the evolution of current structures by a simple geometrical argument, which has been tested using high Reynolds number direct numerical simulations of the MHD equations. Interpretation of the observed data within this picture indicates that the change in scaling behavior of the current helicity seems to be associated with a topological reorganization of the footpoint of the magnetic field loops, namely with the dissipation of small scales structures in turbulent media.     

Contributions from Different-Type Active Regions Into the Total Solar Unsigned Magnetic Flux

Geomagnetism and Aeronomy - Data set acquired by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) during 2010–2017 allowed us to classify active regions...     

Statistical Assessment of Photospheric Magnetic Features in Imminent Solar Flare Predictions

In this study we use the ordinal logistic regression method to establish a prediction model, which estimates the probability for each solar active region to produce X-, M-, or C-class flares during the next 1-day time period. The three predictive parameters are (1) the total unsigned magnetic flux T _flux, which is a measure of an active region’s size, (2) the length of the strong-gradient neutral line L _gnl, which describes the global nonpotentiality of an active region, and (3) the total magnetic dissipation E _diss, which is another proxy of an active region’s nonpotentiality. These parameters are all derived from SOHO MDI magnetograms. The ordinal response variable is the different level of solar flare magnitude. By analyzing 174 active regions, L _gnl is proven to be the most powerful predictor, if only one predictor is chosen. Compared with the current prediction methods used by the Solar Monitor at the Solar Data Analysis Center (SDAC) and NOAA’s Space Weather Prediction Center (SWPC), the ordinal logistic model using L _gnl, T _flux, and E _diss as predictors demonstrated its automatic functionality, simplicity, and fairly high prediction accuracy. To our knowledge, this is the first time the ordinal logistic regression model has been used in solar physics to predict solar flares.     

Solar MHD turbulence in regions with various levels of flare activity

The paper continues investigations of MHD turbulence in active solar regions. The statistical distributions of the increments (structure functions) of the turbulent field are studied analytically in the context of a refined Kolmogorov theory of turbulence. Since photospheric transport of the B _z component of the magnetic field is quite similar to that of a scalar field in a turbulent flow, the theory of transport of a passive scalar can be applied. This approach enables us to show that the structure functions are determined by the competition between the dissipation of the magnetic and kinetic energies and to obtain a number of relations between the structure-function parameters and energy characteristics of the MHD turbulence. Taking into account general conclusions that can be drawn on the basis of the refined Kolmogorov turbulence theory, the structure functions of the B _z field are calculated for eight active regions (from measurements of SOHO/MDI and the Huairou Solar Observing Station, China). These calculations show that the behavior of the structure functions is different for the B _z field of each active region. The energy-dissipation index of the fluctuation spectrum (which is uniquely determined by the structure functions) is closely related to the level of flare activity: the more activity, the less steep the dissipation spectrum for a given active region. This provides a means to test and, consequently, forecast the flare activity of active regions.     

Pre-flare changes in the turbulence regime for the photospheric magnetic field in a solar active region

Observations of the total magnetic field in the active region NOAA 6757 have been used to study the turbulence regime from 2.5 h before the onset of a 2B/X1.5 flare until two minutes after its maximum. The curvature of the exponent ζ(q) for the structure functions of the B _z field increases monotonically before the flare (i.e., the multifractal character of the B _z field becomes more complex) but straightens at the flare maximum and coincides with a linear Kolmogorov dependence (implying a monofractal structure for the B _z field). The observed deviations of ζ(q) from a Kolmogorov line can be used for short-term forecasting of strong flares. Analysis of the power spectra of the B _z field and the dissipation of magnetic-energy fluctuations shows that the beginning of the flare is associated with the onset of a new turbulence regime, which is closer to a classical Kolmogorov regime. The scaling parameter (cancellation index) of the current helicity of the magnetic field, k _h , remains at a high level right up until the last recording of the field just before the flare but decreases considerably at the flare maximum. The variations detected in the statistical characteristics of the turbulence can be explained by the formation and amplification of small-scale flux tubes with strong fields before the flare. The dissipation of magnetic energy before the flare is primarily due to reconnection at tangential discontinuities of the field, while the dissipation after the flare maximum is due to the anomalous plasma resistance. Thus, the flare represents an avalanche dissipation of tangential discontinuities.     

Self-Organized Criticality of Solar Magnetism

Geomagnetism and Aeronomy - Self-organization is a property of any nonlinear, dynamic, dissipative system that evolves under the influence of external forces and positive feedback....     

Sign-Singularity of the Current Helicity in Solar Active Regions

On the basis of vector magnetograms of 20 active regions we analyzed the scaling behavior of the current helicity H_c in the photosphere. We show that H_c possesses well pronounced sign-singularity in the range of scales from more than 10⁴ km up to the resolution limit of observations.