Toward Improved Understanding of Magnetic Fields Participating in Solar Flares: Statistical Analysis of Magnetic Field within Flare Ribbons

Flares and coronal mass ejections are manifestations of magnetic evolution in the solar corona in which magnetic reconnection is believed to play key roles. While the properties of underlying, photospheric line-of-sight magnetic fields of active regions (ARs) as a whole have been analyzed in detail, properties of vector magnetic fields that participate in the reconnection process, highlighted by the flare ribbons, have not been described. Here we present a statistical analysis of vector magnetic field properties in 40 ARs associated with 33 eruptive and 7 confined flares, of GOES class C9.0 and greater. For every event in the database, we use a HMI/SDO vector magnetogram, and AIA 1600A images to calculate various properties of the photospheric vector magnetic field within the AR, flare ribbons and the polarity inversion line (PIL) areas: magnetic flux, reconnection flux fraction, magnetic shear, vertical electric current and current neutralization. We find that while the peak X-ray flux has a strong correlation with ribbon reconnection flux, it has only moderate correlation with the magnetic shear within ribbon- and PIL- areas and the degree of current neutralization. We find a new linear relationship between the amount of non-neutralized current within the AR (or ribbon) and the amount of shear at PIL. This scaling is consistent with earlier simulations and case studies, of net currents being formed as a result of any mechanism that could generate magnetic shear along PIL: flux emergence, twisting or shearing motions. Finally, we find that the CME speed has a much stronger correlation with the reconnection flux fraction than with any other active region property. We also find that for a fixed peak X-ray flux, eruptive events tend to have smaller PIL fluxes and larger magnetic shears than confined events. To summarize, our observational analysis, supported by MHD ARMS and magnetofrictional simulations, suggests that flare peak X-ray fluxes and CME speeds are most strongly guided by the total amount of magnetic flux that participates in the reconnection process and the amount of the flux in the overlying field, than by the amount of PIL shear or AR net current.