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Using non-linear force free field (NLFFF) extrapolation, 3D magnetic fields were modeled from the 12-min cadence Solar Dynamics Observatory Helioseismic and Magnetic Imager (HMI) photospheric vector magnetograms, spanning a time period of 1 hour before through 1 hour after the start of 18 X-class and 12 M-class solar flares. Several magnetic field parameters were calculated from the modeled fields directly, as well as from the power spectrum of surface maps generated by summing the fields along the vertical axis, for two different regions: areas with photospheric |B_z|≥ 300 G (active region—AR) and areas above the photosphere with the magnitude of the non-potential field (B_NP) greater than three standard deviations above $\overline{\left|{\mathit{B}}_{\mathit{N}\mathit{P}}\right|}$of the AR field and either the unsigned twist number |T_w| ≥ 1 turn or the shear angle Ψ ≥ 80° (non-potential region—NPR). Superposed epoch (SPE) plots of the magnetic field parameters were analyzed to investigate the evolution of the 3D solar field during the solar flare events and discern consistent trends across all solar flare events in the dataset, as well as across subsets of flare events categorized by their magnetic and sunspot classifications. The relationship between different flare properties and the magnetic field parameters was quantitatively described by the Spearman ranking correlation coefficient, r_s. The parameters that showed the most consistent and discernable trends among the flare events, particularly for the hour leading up to the eruption, were the total unsigned fluxϕ), free magnetic energy (E_Free), total unsigned magnetic twist (τ_Tot), and total unsigned free magnetic twist (ρ_Tot). Strong (|r_s| ∈ [0.6, 0.8)) to very strong (|r_s| ∈ [0.8, 1.0]) correlations were found between the magnetic field parameters and the following flare properties: peak X-ray flux, duration, rise time, decay time, impulsiveness, and integrated flux; the strongest correlation coefficient calculated for each flare property was 0.62, 0.85, 0.73, 0.82, −0.81, and 0.82, respectively. 

The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface | B z |≥ 300 G, areas of flare brightening seen in SDO Atmospheric Imaging Assembly imagery, and areas with surface | B | ≥ 1000 G and high twist. Time series of the magnetic field parameters were analyzed to investigate the evolution of the coronal field during the solar flare event and discern pre-eruptive signatures. The data shows that areas with | B | ≥ 1000 G and | T w |≥ 1.5 align well with areas of initial flare brightening during the pre-flare phase and at the beginning of the eruptive phase of the flare, suggesting that measurements of the photospheric magnetic field strength and twist can be used to predict the flare location within an active region if triggered. Additionally, the evolution of seven investigated magnetic field parameters indicated a destabilizing magnetic field structure that could likely erupt. 

ABSTRACT We analysed line-of-sight magnetic fields and magnetic power spectra of an undisturbed photosphere using magnetograms acquired by the Helioseismic and Magnetic Imager (HMI) on-board the Solar Dynamic Observatory and the Near InfraRed Imaging Spectrapolarimeter (NIRIS) operating at the Goode Solar Telescope of the Big Bear Solar Observatory. In the NIRIS data, we revealed thin flux tubes of 200–400 km in diameter and of 1000–2000 G field strength. The HMI power spectra determined for a coronal hole, a quiet sun, and a plage areas exhibit the same spectral index of −1 on a broad range of spatial scales from 10–20 Mm down to 2.4 Mm. This implies that the same mechanism(s) of magnetic field generation operate everywhere in the undisturbed photosphere. The most plausible one is the local turbulent dynamo. When compared to the HMI spectra, the −1.2 slope of the NIRIS spectrum appears to be more extended into the short spatial range until the cut-off at 0.8–0.9 Mm, after which it continues with a steeper slope of −2.2. Comparison of the observed and Kolmogorov-type spectra allowed us to infer that the Kolmogorov turbulent cascade cannot account for more than 35 per cent of the total magnetic energy observed in the scale range of 3.5–0.3 Mm. The energy excess can be attributed to other mechanisms of field generation such as the local turbulent dynamo and magnetic superdiffusivity observed in an undisturbed photosphere that can slow down the rate of the Kolmogorov cascade leading to a shallower resulting spectrum.