Empirical Scaling Relations for the Photospheric Magnetic Elements of the Flaring and Non-Flaring 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.

Magnetic elements of the solar surface are studied (using the 6173 A Fe i line) in magnetograms recorded with the high-resolution Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI). To extract some statistical and physical properties of these elements (e.g. filling factors, magnetic flux, size, and lifetimes), we employed the region-based method called Yet Another Feature Tracking Algorithm (YAFTA). An area of $400^{\prime\prime}\times400^{\prime\prime}$ was selected to investigate the magnetic characteristics in 2011. The correlation coefficient between filling factors of negative and positive polarities is 0.51. A broken power-law fit was applied to the frequency distribution of size and flux. Exponents of the power-law distributions for sizes smaller and greater than $16~\mbox{arcsec}^{2}$ were found to be −2.24 and −4.04, respectively. The exponents of power-law distributions for fluxes lower and greater than $2.63\times 10^{19}~\mbox{Mx}$ were found to be −2.11 and −2.51, respectively. The relationship between the size [ $S$ ] and flux [ $F$ ] of elements can be expressed by a power-law behavior of the form of $S\propto F^{0.69}$ . The lifetime and its relationship with the flux and size of quiet-Sun (QS) elements during three days were studied. The code detected patches with lifetimes of about 15 hours, which we call long-duration events. We found that more than 95% of the magnetic elements have lifetimes shorter than 100 minutes. About 0.05% of the elements had lifetimes of more than six hours. The relationships between size [ $S$ ], lifetime [ $T$ ], and flux [ $F$ ] for patches in the QS yield power-law relationships $S\propto T^{0.25}$ and $F\propto T^{0.38}$ , respectively. Executing a detrended-fluctuation analysis of the time series of new emerged magnetic elements, we found a Hurst exponent of 0.82, which implies a long-range temporal correlation in the system.

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 apply differential affine velocity estimator (DAVE) to the Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) 12-min line-of-sight magnetograms, and separately calculate the injected magnetic helicity for the leading and the following polarities of nine emerging bipolar active regions (ARs). Comparing magnetic helicity flux of the leading polarity with the following polarity, we find that six ARs studied in this paper have the following polarity that injected more magnetic helicity flux than that of the leading polarity. We also measure the mean area of each polarity in all the nine ARs, and find that the compact polarity tend to possess more magnetic helicity flux than the fragmented one. Our results confirm the previous studies on asymmetry of magnetic helicity that emerging bipolar ARs have a polarity preference in injecting magnetic helicity. Based on the changes of unsigned magnetic flux, we divide the emergence process into two evolutionary stages: (1) an increasing stage before the peak flux and (2) a constant or decreasing stage after the peak flux. Obvious changes on magnetic helicity flux can be seen during transition from one stage to another. Seven ARs have one or both polarity that changed the sign of magnetic helicity flux. Additionally, the prevailing polarity of the two ARs, which injects more magnetic helicity, changes form the following polarity to the leading one.

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.

We used full-disk line-of-sight magnetograms taken by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) to study the variation of coronal magnetic helicity in the Active Region (AR) NOAA 11429, where several GOES M- and X-class flares and coronal mass ejections (CMEs) occurred. The magnetic flux, total magnetic-helicity flux, and helicity accumulation over the period of interest, i.e. 6 to 11 March 2012, were measured and are discussed. We also evaluated the tilt-angle evolution within the standard polarity flux-weighted centroids approach. The AR displays a shearing motion of the magnetic structures along the polarity inversion line, reaching values of about 1.0 km s−1. The variations of magnetic helicity flux and the tilt-angle seem to be time-correlated, and both display three-phase evolutionary patterns. We also found that the flare/CME activity is higher during the first observation phase when the tilt-angle decreases and the negative magnetic helicity is accumulated. The main changes in the accumulated helicity curve are observed only after the onset of the two strongest flare/CME events. After the major event (GOES X5.4 class/CME of 7 March) there was a decrease in the occurrence of flares and CMEs. This phase is marked by a decrease of the flux of magnetic helicity from the convection zone to the corona and a change in the orientation of the tilt of the AR. This behavior suggests that the combination of these two quantities might be important in the description of the magnetic complexity accumulated by an AR during its lifetime.

We test the reliability of helioseismic far-side active-region predictions, made using Dopplergrams from both the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) and the Global Oscillation Network Group (GONG), by comparison with far-side observation of solar activity from the Solar TErrestrial RElations Observatory (STEREO). Both GONG and HMI produce seismic Carrington maps that show strong magnetic-field regions, labeling predictions of far-side active regions that have a probability ≥ 70 %. By visual comparison of these prediction maps with STEREO extreme ultraviolet (EUV) Carrington maps, we determine whether or not solar activity, as evidenced as brightness in EUV, is observed at the predicted locations. We analyzed nine months of data from 2011 and 2012. For both GONG and HMI, we find that for approximately 90 % of the active-region predictions, activity/brightness is observed in EUV at the predicted location. We also investigated the success of GONG and HMI at predicting large active regions before they appear at the east limb as viewed from Earth. Of the 27 identified large east-limb active regions in the nine months of data analyzed, GONG predicted 15 (55 %) at least once within the week prior to Earth-side appearance and HMI predicted 13 (48 %). Based on the STEREO far-side EUV observations, we suggest that 9 of the 27 active regions were probably too weak to be predicted while on the far side. Overall, we conclude that HMI and GONG have similar reliability using the current data-processing procedures.

Extrapolation codes in Cartesian geometry for modelling the magnetic field in\nthe corona do not take the curvature of the Sun's surface into account and can\nonly be applied to relatively small areas, e.g., a single active region. We\ncompare the analysis of the photospheric magnetic field and subsequent\nforce-free modeling based on full-disk vector maps from Helioseismic and\nMagnetic Imager (HMI) on board solar dynamics observatory (SDO) and Vector\nSpectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of\nthe Sun (SOLIS). We use Helioseismic and Magnetic Imager and Vector\nSpectromagnetograph photospheric magnetic field measurements to model the\nforce-free coronal field above multiple solar active regions, assuming magnetic\nforces to dominate. We solve the nonlinear force-free field equations by\nminimizing a functional in spherical coordinates over a full disk excluding the\npoles. After searching for the optimum modeling parameters for the particular\ndata sets, we compare the resulting nonlinear force-free model fields. We\ncompare quantities like the total magnetic energy content and free magnetic\nenergy, the longitudinal distribution of the magnetic pressure and surface\nelectric current density using our spherical geometry extrapolation code. The\nmagnetic field lines obtained from nonlinear force-free extrapolation based on\nHelioseismic and Magnetic Imager and Vector Spectromagnetograph data have good\nagreement. However, the nonlinear force-free extrapolation based on\nHelioseismic and Magnetic Imager data have more contents of total magnetic\nenergy, free magnetic energy, the longitudinal distribution of the magnetic\npressure and surface electric current density compared to the one from Vector\nSpectromagnetograph data.\n

<p>The axial dipole moments of emerging active regions control the evolution of the axial dipole moment of the whole photospheric magnetic field and the strength of polar fields. Hale's and Joy's laws of polarity and tilt orientation affect the sign of the axial dipole moment of an active region, determining the normal sign for each solar cycle. If both laws are valid (or both violated), the sign of the axial moment is normal. However, for some active regions, only one of the two laws is violated, and the signs of these axial dipole moments are the opposite of normal. The opposite-sign axial dipole moments can potentially have a significant effect on the evolution of the photospheric magnetic field, including the polar fields.</p><p>We determine the axial dipole moments of active regions identified from magnetographic observations and study how the axial dipole moments of normal and opposite signs are distributed in time and latitude in solar cycles 21-24.We use active regions identified from the synoptic maps of the photospheric magnetic field measured at the National Solar Observatory (NSO) Kitt Peak (KP) observatory, the Synoptic Optical Long term Investigations of the Sun (SOLIS) vector spectromagnetograph (VSM), and the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO).</p><p>We find that, typically, some 30% of active regions have opposite-sign axial dipole moments in every cycle, often making more than 20% of the total axial dipole moment. Most opposite-signed moments are small, but occasional large moments, which can affect the evolution of polar fields on their own, are observed. Active regions with such a large opposite-sign moment may include only a moderate amount of total magnetic flux. We find that in cycles 21-23 the northern hemisphere activates first and shows emergence of magnetic flux over a wider latitude range, while the southern hemisphere activates later, and emergence is concentrated to lower latitudes. We also note that cycle 24 differs from cycles 21-23 in many ways. Cycle 24 is the only cycle where the northern butterfly wing includes more active regions than the southern wing, and where axial dipole moment of normal sign emerges on average later than opposite-signed axial dipole moment. The total axial dipole moment and even the average axial moment of active regions is smaller in cycle 24 than in previous cycles.</p>

Context. The axial dipole moments of emerging active regions control the evolution of the axial dipole moment of the whole photospheric magnetic field and the strength of polar fields. Hale’s and Joy’s laws of polarity and tilt orientation affect the sign of the axial dipole moment of an active region. If both laws are valid (or both violated), the sign of the axial moment is normal. However, for some active regions, only one of the two laws is violated, and the signs of these axial dipole moments are the opposite of normal. Those opposite-sign active regions can have a significant effect, for example, on the development of polar fields. Aims. Our aim is to determine the axial dipole moments of active regions identified from magnetographic observations and study how the axial dipole moments of normal and opposite signs are distributed in time and latitude in solar cycles 21−24. Methods. We identified active regions in the synoptic maps of the photospheric magnetic field measured at the National Solar Observatory (NSO) Kitt Peak (KP) observatory, the Synoptic Optical Long term Investigations of the Sun (SOLIS) vector spectromagnetograph (VSM), and the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO), and determined their axial dipole moments. Results. We find that, typically, some 30% of active regions have opposite-sign axial moments in every cycle, often making more than 20% of the total axial dipole moment. Most opposite-signed moments are small, but occasional large moments, which can affect the evolution of polar fields on their own, are observed. Active regions with such a large opposite-sign moment may include only a moderate amount of total magnetic flux. We find that in cycles 21−23 the northern hemisphere activates first and shows emergence of magnetic flux over a wider latitude range, while the southern hemisphere activates later, and emergence is concentrated to lower latitudes. Cycle 24 differs from cycles 21−23 in many ways. Cycle 24 is the only cycle where the northern butterfly wing includes more active regions than the southern wing, and where axial dipole moment of normal sign emerges on average later than opposite-signed axial dipole moment. The total axial dipole moment and even the average axial moment of active regions is smaller in cycle 24 than in previous cycles.

\n Context. The magnetic field plays a dominant role in the solar irradiance variability. Determining the contribution of various magnetic features to this variability is important in the context of heliospheric studies and Sun-Earth connection.\n Aims. We studied the solar irradiance variability and its association with the underlying magnetic field for a period of five years (January 2011–January 2016). We used observations from the Large Yield Radiometer (LYRA), the Sun Watcher with Active Pixel System detector and Image Processing (SWAP) on board PROBA2, the Atmospheric Imaging Assembly (AIA), and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO).\n Methods. The Spatial Possibilistic Clustering Algorithm (SPoCA) is applied to the extreme ultraviolet (EUV) observations obtained from the AIA to segregate coronal features by creating segmentation maps of active regions (ARs), coronal holes (CHs) and the quiet sun (QS). Further, these maps are applied to the full-disk SWAP intensity images and the full-disk (FD) HMI line-of-sight (LOS) magnetograms to isolate the SWAP coronal features and photospheric magnetic counterparts, respectively. We then computed full-disk and feature-wise averages of EUV intensity and line of sight (LOS) magnetic flux density over ARs/CHs/QS/FD. The variability in these quantities is compared with that of LYRA irradiance values.\n Results. Variations in the quantities resulting from the segmentation, namely the integrated intensity and the total magnetic flux density of ARs/CHs/QS/FD regions, are compared with the LYRA irradiance variations. We find that the EUV intensity over ARs/CHs/QS/FD is well correlated with the underlying magnetic field. In addition, variations in the full-disk integrated intensity and magnetic flux density values are correlated with the LYRA irradiance variations.\n Conclusions. Using the segmented coronal features observed in the EUV wavelengths as proxies to isolate the underlying magnetic structures is demonstrated in this study. Sophisticated feature identification and segmentation tools are important in providing more insights into the role of various magnetic features in both the short- and long-term changes in the solar irradiance.\n

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.

The Helioseismic and Magnetic Imager (HMI) began near-continuous full-disk solar measurements on 1 May 2010 from the Solar Dynamics Observatory (SDO). An automated processing pipeline keeps pace with observations to produce observable quantities, including the photospheric vector magnetic field, from sequences of filtergrams. The basic vector-field frame list cadence is 135 seconds, but to reduce noise the filtergrams are combined to derive data products every 720 seconds. The primary 720 s observables were released in mid-2010, including Stokes polarization parameters measured at six wavelengths, as well as intensity, Doppler velocity, and the line-of-sight magnetic field. More advanced products, including the full vector magnetic field, are now available. Automatically identified HMI Active Region Patches (HARPs) track the location and shape of magnetic regions throughout their lifetime.The vector field is computed using the Very Fast Inversion of the Stokes Vector (VFISV) code optimized for the HMI pipeline; the remaining 180∘ azimuth ambiguity is resolved with the Minimum Energy (ME0) code. The Milne–Eddington inversion is performed on all full-disk HMI observations. The disambiguation, until recently run only on HARP regions, is now implemented for the full disk. Vector and scalar quantities in the patches are used to derive active region indices potentially useful for forecasting; the data maps and indices are collected in the SHARP data series, hmi.sharp_720s. Definitive SHARP processing is completed only after the region rotates off the visible disk; quick-look products are produced in near real time. Patches are provided in both CCD and heliographic coordinates.HMI provides continuous coverage of the vector field, but has modest spatial, spectral, and temporal resolution. Coupled with limitations of the analysis and interpretation techniques, effects of the orbital velocity, and instrument performance, the resulting measurements have a certain dynamic range and sensitivity and are subject to systematic errors and uncertainties that are characterized in this report.

We study properties of waves of frequencies above the photospheric acoustic cut-off of $\approx$5.3 mHz, around four active regions, through spatial maps of their power estimated using data from Helioseismic and Magnetic Imager (HMI) and Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO). The wavelength channels 1600 {\AA} and 1700 {\AA} from AIA are now known to capture clear oscillation signals due to helioseismic p modes as well as waves propagating up through to the chromosphere. Here we study in detail, in comparison with HMI Doppler data, properties of the power maps, especially the so called 'acoustic halos' seen around active regions, as a function of wave frequencies, inclination and strength of magnetic field (derived from the vector field observations by HMI) and observation height. We infer possible signatures of (magneto-)acoustic wave refraction from the observation height dependent changes, and hence due to changing magnetic strength and geometry, in the dependences of power maps on the photospheric magnetic quantities. We discuss the implications for theories of p mode absorption and mode conversions by the magnetic field.

The solar active region NOAA 11719 produced a large two-ribbon flare on 2013 April 11. We have investigated sudden variations in the photospheric magnetic fields in this active region during the flare by employing magnetograms obtained in the spectral line Fe I 6173 Å acquired by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) spacecraft. The analysis of the line-of-sight magnetograms from HMI show sudden and persistent magnetic field changes at different locations of the active region before the onset of the flare and during the flare. The vector magnetic field observations available from HMI also show coincident variations in the total magnetic field strength and its inclination angle at these locations. Using the simultaneous Dopplergrams obtained from HMI, we observe perturbations in the photospheric Doppler signals following the sudden changes in the magnetic fields in the aforementioned locations. The power spectrum analysis of these velocity signals shows enhanced acoustic power in these affected locations during the flare as compared to the pre-flare condition. Accompanying these observations, we have also used nearly simultaneous chromospheric observations obtained in the spectral line Hα 6562.8 Å by the Global Oscillation Network Group (GONG) to study the evolution of flare-ribbons and intensity oscillations in this active region. The Hα intensity oscillations also show enhanced oscillatory power during the flare in the aforementioned locations. These results indicate that the transient Lorentz force associated with sudden changes in the magnetic fields could drive localized photospheric and chromospheric oscillations, like the flare-induced oscillations in the solar atmosphere.