Analysis of modeled 3D solar magnetic field during 30 X/M-class solar flares

Abstract

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 |Bz|≥ 300 G (active region—AR) and areas above the photosphere with the magnitude of the non-potential field (BNP) greater than three standard deviations above |BNP|̄ of the AR field and either the unsigned twist number |Tw| ≥ 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, rs. 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 flux ϕ), free magnetic energy (EFree), total unsigned magnetic twist (τTot), and total unsigned free magnetic twist (ρTot). Strong (|rs| ∈ [0.6, 0.8)) to very strong (|rs| ∈ [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.