Relationship between Hard X-Ray Footpoint Sources and Photospheric Electric Currents in Solar Flares: a Statistical Study

It is believed that solar flares are a result of release of free magnetic energy contained in electric currents (ECs) flowing in active regions (ARs). However, there are still debates whether the primary energy release and acceleration of electrons take place in coronal current sheets or in chromospheric footpoints of current-carrying magnetic flux tubes (loops). We present results of an observational statistical study of spatial relationship between hard X-ray (HXR; EHXR≥50keV) footpoint sources detected by RHESSI and vertical photospheric ECs calculated using vector magnetograms obtained from the SDO/HMI data. We found that for a sample of 47 flares (from C3.0 to X3.1 class) observed on the solar disk by both instruments in 2010-2016, at least one HXR source was in a region of strong (within 20% of the maximum EC density in the corresponding ARs) vertical ECs having the form of a ribbon (79%) or an island (21%). The total vertical ECs in such HXR sources are in the range of 1010-1013 A. The EC density is in the range of 0.01-1.0 A/m2. We found no correlation between intensity of the HXR sources and the EC density. By comparing pre-flare and post-flare EC maps we did not find evidences of significant dissipation of vertical ECs in the regions corresponding to the HXR sources. In some cases, we found amplification of ECs during flares. We discuss effects of sensitivity and angular resolution of RHESSI and SDO/HMI. In general, the results indicate that there is a link between the flare HXR footpoint sources and enhanced vertical ECs in the photosphere. However, the results do not support a concept of electron acceleration by the electric field excited in footpoints of current-carrying loops due to some (e.g. Rayleigh-Taylor) instabilities (Zaitsev et al., 2016), since strong correlation between the HXR intensity and the EC density is expected in such concept.