Relationships between Photospheric Vertical Electric Currents and Hard X-Ray Sources in Solar Flares: Statistical Study

There are still debates over whether particle acceleration in solar flares may occur due to interruption of electric currents flowing along magnetic loops. To contribute to this debate, we performed the first statistical study of relationships between flare hard X-ray (HXR; 50-100 keV) sources observed by the Ramaty High-Energy Solar Spectroscopic Imager and photospheric vertical electric currents (PVECs, j _r) calculated using vector magnetograms obtained with the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. We analyzed a sample of 48 flares from the C3.0 to X3.1 class and were observed in the central part of the solar disk by both instruments in 2010-2015. We found that ≈70% of all HXR sources overlapped with islands or ribbons of enhanced (statampere cm^-2) PVECs. However, less than ≈40% of the HXR sources overlapped with PVEC maxima, with an accuracy of ±3″. In more than half of the flares, there were HXR sources outside of regions of enhanced PVECs. We found no correlation between the intensity of the HXR sources and PVEC density or total PVEC under them. No systematic dissipation of PVECs under the HXR sources was found during the flares. Collectively, the results do not support the current-interruption flare models. However, the results indicate the importance of the presence of longitudinal currents in flare regions. To understand their specific role in the processes of energy release, plasma heating, and acceleration of particles requires further investigation.