Cyclic Variations in the Mean Recurrence Times of Solar Flares in Active Regions

Context.Large-scale solar eruptions significantly affect space weather and damage space-based human infrastructures. It is necessary to predict large-scale solar eruptions; it will enable us to protect the vulnerable infrastructures of our modern society.Aims.We investigate the difference between flaring and nonflaring active regions. We also investigate whether it is possible to forecast a solar flare.Methods.We used photospheric vector magnetogram data from the Solar Dynamic Observatory’s Helioseismic Magnetic Imager to study the time evolution of photospheric magnetic parameters on the solar surface. We built a database of flaring and nonflaring active regions observed on the solar surface from 2010 to 2017. We trained a machine-learning algorithm with the time evolution of these active region parameters. Finally, we estimated the performance obtained from the machine-learning algorithm.Results.The strength of some magnetic parameters such as the total unsigned magnetic flux, the total unsigned magnetic helicity, the total unsigned vertical current, and the total photospheric magnetic energy density in flaring active regions are much higher than those of the non-flaring regions. These magnetic parameters in a flaring active region evolve fast and are complex. We are able to obtain a good forecasting capability with a relatively high value of true skill statistic. We also find that time evolution of the total unsigned magnetic helicity and the total unsigned magnetic flux provides a very high ability of distinguishing flaring and nonflaring active regions.Conclusions.We can distinguish a flaring active region from a nonflaring region with good accuracy. We confirm that there is no single common parameter that can distinguish all flaring active regions from the nonflaring regions. However, the time evolution of the top two magnetic parameters, the total unsigned magnetic flux and the total unsigned magnetic helicity, have a very high distinguishing capability.

The initiation mechanism of coronal mass ejections and solar flares remains a central topic in solar physics. While it is widely accepted that magnetic reconnection plays a crucial role in these phenomena, the exact sequence of events leading to their onset is still debated. This study investigates the possibility of a current sheet (CS) formed prior to the X2.2 flare in solar active region (AR) 11158 on 2011 February 15. Using vector magnetograms from the Helioseismic and Magnetic Imager (HMI) and a magnetohydrodynamic relaxation model, we provide evidences for the existence of a pre-flare CS. Observations reveal thin, J-shaped ribbons of strong vertical current density (Jz) along the polarity inversion line before the flare, which we interpret as the photospheric footprints of a coronal CS. Numerical reconstruction of the coronal field constrained by the vector magnetogram confirms the presence of a CS in the corona, with its thickness converging to a true discontinuity at higher resolutions. The synthetic coronal emission from the simulated CS matches the observed sigmoidal structure in the Atmospheric Imaging Assembly (AIA) 131 Åchannel, further supporting the existence of a pre-flare CS. Our findings suggest that the X2.2 flare in AR 11158 was likely triggered by reconnection within a CS that formed gradually before the eruption, rather than by the ideal MHD instability of a pre-existing magnetic flux rope. This study provides new insights into the triggering mechanisms of solar eruptions and highlights the importance of pre-eruption CS formation in the initiation of major flares.

Observational precursors of large solar flares provide a basis for future operational systems for forecasting. Here, we study the evolution of the normalized emergence (EM), shearing (SH), and total (T) magnetic helicity flux components for 14 flaring (with at least one X-class flare) and 14 nonflaring (<M5-class flares) active regions (ARs) using the Space-weather Helioseismic Magnetic Imager Active Region Patches vector magnetic field data. Each of the selected ARs contain a δ-type spot. The three helicity components of these ARs were analyzed using wavelet analysis. Localized peaks of the wavelet power spectrum (WPS) were identified and statistically investigated. We find that (i) the probability density function of the identified WPS peaks for all the EM/SH/T profiles can be fitted with a set of Gaussian functions centered at distinct periods between ∼3 and 20 hr. (ii) There is a noticeable difference in the distribution of periods found in the EM profiles between the flaring and nonflaring ARs, while no significant difference is found in the SH and T profiles. (iii) In flaring ARs, the distributions of the shorter EM/SH/T periods (<10 hr) split up into two groups after flares, while the longer periods (>10 hr) do not change. (iv) When the EM periodicity does not contain harmonics, the ARs do not host a large energetic flare. (v) Finally, significant power at long periods (∼20 hr) in the T and EM components may serve as a precursor for large energetic flares.

We present an analysis of the magnetic mechanism of an X6.4-class confined flare in NOAA Active Region (AR) 13590 on 2024 February 22. Despite a pre-existing magnetic flux rope (MFR) embedded within a null-point topology, the flare produced only a localized jet without an associated coronal mass ejection. Using data from the Solar Dynamics Observatory and nonlinear force-free field extrapolations, we traced the formation and evolution of the MFR, which developed under photospheric shearing motions but remained weakly twisted (with twist number being lower than 1.3) and below the thresholds for kink instability. Meanwhile, the MFR is located at heights where the decay index (n ≤ 1.0) of the overlying field was insufficient to trigger torus instability. Furthermore, we calculated two important parameters measuring the non-potentiality of the AR, one is the ratio of the free energy to the potential-field energy, and the other is the ratio of the non-potential helicity to the square of the magnetic flux. Both the two parameters were significantly lower than critical values for eruptive flares. These factors, combined with the stabilizing influence of the strong overlying field, confined the MFR and limited the eruption to a jet. Our findings highlight the importance of both local magnetic properties and global energy constraints in determining the eruptive potential of solar flares.

Intermittent magnetohydrodynamical turbulence is most likely at work in the magnetized solar atmosphere. As a result, an array of scaling and multi-scaling image-processing techniques can be used to measure the expected self-organization of solar magnetic fields. While these techniques advance our understanding of the physical system at work, it is unclear whether they can be used to predict solar eruptions, thus obtaining a practical significance for space weather. We address part of this problem by focusing on solar active regions and by investigating the usefulness of scaling and multi-scaling image-processing techniques in solar flare prediction. Since solar flares exhibit spatial and temporal intermittency, we suggest that they are the products of instabilities subject to a critical threshold in a turbulent magnetic configuration. The identification of this threshold in scaling and multi-scaling spectra would then contribute meaningfully to the prediction of solar flares. We find that the fractal dimension of solar magnetic fields and their multi-fractal spectrum of generalized correlation dimensions do not have significant predictive ability. The respective multi-fractal structure functions and their inertial-range scaling exponents, however, probably provide some statistical distinguishing features between flaring and non-flaring active regions. More importantly, the temporal evolution of the above scaling exponents in flaring active regions probably shows a distinct behavior starting a few hours prior to a flare and therefore this temporal behavior may be practically useful in flare prediction. The results of this study need to be validated by more comprehensive works over a large number of solar active regions.

The evolution of magnetic helicity has a close relationship with solar eruptions and is of interest as a predictive diagnostic. In this case study, we analyze the evolution of the normalized emergence, shearing, and total magnetic helicity components in the case of three flaring and three non-flaring active regions (ARs) using Spaceweather Helioseismic Magnetic Imager Active Region Patches vector magnetic field data. The evolution of the three magnetic helicity components is analyzed with wavelet transforms, revealing significant common periodicities of the normalized emergence, shearing, and total helicity fluxes before flares in the flaring ARs. The three non-flaring ARs do not show such common periodic behavior. This case study suggests that the presence of significant periodicities in the power spectrum of magnetic helicity components could serve as a valuable precursor for flares.

There appear indications of more global activity on the Sun which is larger, much beyond the scale of solar active regions (ARs). These indications include formation, flaring and eruption of the trans-equatorial loops seen in EUV and X-rays, formation and eruption of trans-equatorial filaments, global magnetic connectivity in EUV dimming associated with halo-coronal mass ejections, wide spread of radio burst sources in meter wavelength in the solar corona, and quasi-simultaneous magnetic flux emergence in both hemispheres seen during some major solar events. With examples of a few major events in the last solar cycle we discuss the possibility that there is large or global-scale activity on the Sun. Its spatial scale is many times larger than that of AR and temporal scale is over 10 hours. The exemplified trans-equatorial loops are anchored in ARs and their activity is temporally associated with flares in ARs too. In some sense the flares in ARs appear either as a part of or a precursor of the more global activity. It is likely that the combination of the flares in ARs and the associated global activity is responsible to the major solar-terrestrial events. More efforts in understanding the global activity are undertaken.

An evolutionary feature of the magnetic field related to flares in active regions - Incorporation of the Magnetic Flux of the Same Polarity (IMFSP) was studied in this paper. The statistics show that IMFSP related to a major X-ray flare (I ≥M) needs to have a stronger magnetic strength and gradient: (1) Two or more magnetic fluxes of the same polarity located near a magnetic area of the opposite polarity split or push away the flux of the opposite polarity and merge together. The maximum magnetic strength among them is not less than 320 G, and the minimum magnetic strength is not less than 80 G. (2) The new polarity inversion line is formed after the merger. The maximum gradient of the longitudinal field near the new polarity inversion line is not less than 0.12 G km−1. The statistics also show that IMFSP is a rare phenomenon, 92% of them are accompanied by major X-flares. IMFSP is likely induced by two effects at least: (1) the horizontal motion of the matter beneath the photospheric surface moves the magnetic flux; (2) the magnetic flux emerges and grows continuously. The physical reasons that IMFSP results in the flare are discussed.

In the framework of a refined Kolmogorov hypothesis, the scaling behavior of the Bz-component of the photospheric magnetic field is analyzed and compared with flaring activity in solar active regions. We use Solar and Heliospheric Observatory Michelson Doppler Imager, Huairou (China), and Big Bear measurements of the Bz-component in the photosphere for nine active regions. We show that there is no universal behavior in the scaling of the Bz-structure functions for different active regions. Our previous study has shown that scaling for a given active region is caused by intermittency in the field, (B)(), describing the magnetic energy dissipation. When intermittency is weak, the Bz field behaves as a passive scalar in the turbulent flow, and the energy dissipation is largely determined by the dissipation of kinetic energy in the active regions with low flare productivity. However, when the field (B)() is highly intermittent, the structure functions behave as transverse structure functions of a fully developed turbulent vector field, and the scaling of the energy dissipation is mostly determined by the dissipation of the magnetic energy (active regions with strong flaring productivity). Based on this recent result, we find that the dissipation spectrum of the Bz-component is strongly related to the level of flare productivity in a solar active region. When the flare productivity is high, the corresponding spectrum is less steep. We also find that during the evolution of NOAA Active Region 9393, the Bz dissipation spectrum becomes less steep as the active region's flare activity increases. Our results suggest that the reorganization of the magnetic field at small scales is also relevant to flaring: the relative fraction of small-scale fluctuations of magnetic energy dissipation increases as an active region becomes prone to producing strong flares. Since these small-scale changes seem to begin long before the start of a solar flare, we suggest that the relation between scaling exponents, calculated by using only measurements of the Bz-component, and flare productivity of an active region can be used to monitor and forecast flare activity.

The physical relations among matter motion, evolution of currents and eruption of flares in active regions

Search for predictors of strong flare produced in solar active region (AR) is important application of solar physics. Here we consider the sequence of magnetogram (LOS SDO/HMI instrument) for AR 2034, 2035 and 2036 (April 2014). All three AR were observed on the Sun at about the same time, characterized by low probability of flare events according to official forecasts of NOAA, but 2036 still produced X1-flare near the center of solar disc (April 18). We propose that Generalized Laplacian is a descriptor which could help predict this and similar events. The Laplacian is associated with the flow of Ricci curvature and with topological invariants of the observed field - Betti numbers for compact manifolds. Using discrete version of Morse theory, we consider each pixel of energy flux (B2) image as a simplex and calculate its combinatorial Bochner Laplacian. It was found that maximum of Laplacian is located near AR polarity inversion line. Evolution of total spatial variation of the Laplacian has a number of maxima in time for each of examined AR. However, the maxima in AR 2035 and AR 2034 have relatively low amplitude, while the highest maximum prefaced X1 flare in AR 2036 by about 29 hours.

We apply discriminant analysis to 1023 active regions and their subsurface-flow parameters, such as vorticity and kinetic helicity density, with the goal of distinguishing between flaring and non-flaring active regions. We derive synoptic subsurface flows by analyzing GONG high-resolution Doppler data with ring-diagram analysis. We include magnetic-flux values in the discriminant analysis derived from NSO Kitt Peak and SOLIS synoptic maps binned to the same spatial scale as the helioseismic analysis. For each active region, we determine the flare information from GOES and include all flares within 60° central meridian distance to match the coverage of the ring-diagram analysis. The subsurface-flow characteristics improve the ability to distinguish between flaring and non-flaring active regions. For the C- and M-class flare category, the most important subsurface parameter is the so-called structure vorticity, which estimates the horizontal gradient of the horizontal-vorticity components. The no-event skill score, which measures the improvement over predicting that no events occur, reaches 0.48 for C-class flares and 0.32 for M-class flares, when the structure vorticity at three depths combined with total magnetic flux are used. The contributions come mainly from shallow layers within about 2 Mm of the surface and layers deeper than about 7 Mm.

We explore the relation between surface magnetic flux of the sun and subsurface flow vorticity for flaring and nonflaring solar active regions. For this purpose, we use a data set consisting of 1009 active regions, including the vorticity measurements of their subsurface flows derived from high‐resolution global oscillation network group (GONG) helioseismology data and the corresponding X‐ray flare data from the geostationary operation environmental satellite (GOES). Using quantities averaged over the disk passage of active regions, we find that, while there is a considerable spread of the flux and vorticity values, they are more or less linearly related. We distinguish the level of flare activity by X‐ray flare class and find that large flux or large vorticity values are sufficient for an active region to produce low‐intensity C‐class flares. Active regions that produce high‐intensity X‐class flares are characterized by large values of both flux and vorticity. Active regions that produce M‐class flares of intermediate intensity are characterized by large vorticity values. The inclusion of solar subsurface vorticity thus helps to distinguish between flaring and nonflaring active regions.

We analyzed temporal and periodic behavior of sunspot counts (SSCs) in flaring (C, M, or X class flares), and non-flaring active regions (ARs) for the almost two solar cycles (1996 through 2016). Our main findings are as follows: i) The temporal variation of monthly means of daily total SSCs in flaring and non-flaring ARs are different and these differences are also varying from cycle to cycle; temporal profile of non-flaring ARs are wider than the flaring ones during the solar cycle 23, while they are almost the same during the current cycle 24. The second peak (second maximum) of flaring ARs are strongly dominate during current cycle 24, while this difference is not such a remarkable during cycle 23. The amplitude of SSCs in the non-flaring ARs are comparable during the first and second peaks (maxima) of the current solar cycle, while the first peak is almost not existent in case of the flaring ARs. ii) Periodic variations observed in SSCs of flaring and non-flaring ARs are quite different in both MTM spectrum and wavelet scalograms and these variations are also different from one cycle to another; the largest detected period in the flaring ARs is 113 days, while there are much higher periodicities (327, 312, and 256 days) in non-flaring ARs. There are no meaningful periodicities in MTM spectrum of flaring ARs exceeding 45 days during solar cycle 24, while a 113 days periodicity detected from flaring ARs of solar cycle 23. For the non-flaring ARs the largest period is 72 days during solar cycle 24, while the largest period is 327 days during current cycle.

We attempt to forecast M-and X-class solar flares using a machine-learning algorithm, called Support Vector Machine (SVM), and four years of data from the Solar Dynamics Observatory's Helioseismic and Magnetic Imager, the first instrument to continuously map the full-disk photospheric vector magnetic field from space. Most flare forecasting efforts described in the literature use either line-of-sight magnetograms or a relatively small number of ground-based vector magnetograms. This is the first time a large dataset of vector magnetograms has been used to forecast solar flares. We build a catalog of flaring and non-flaring active regions sampled from a database of 2,071 active regions, comprised of 1.5 million active region patches of vector magnetic field data, and characterize each active region by 25 parameters. We then train and test the machine-learning algorithm and we estimate its performances using forecast verification metrics with an emphasis on the True Skill Statistic (TSS). We obtain relatively high TSS scores and overall predictive abilities. We surmise that this is partly due to fine-tuning the SVM for this purpose and also to an advantageous set of features that can only be calculated from vector magnetic field data. We also apply a feature selection algorithm to determine which of our 25 features are useful for discriminating between flaring and non-flaring active regions and conclude that only a handful are needed for good predictive abilities.