Relationships between photospheric vertical electric currents and hard X-ray footpoints in solar flares: statistical study for the 24th solar cycle

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). To answer this question, we carried out the first observational statistical study of the relationship between flare hard X-ray (HXR; 50-100 keV) footpoints observed by RHESSI and photospheric vertical ECs (PVECs) calculated using HMI/SDO vector magnetograms in a sample of 47 flares (from C3.0 to X3.1) observed on the solar disk by both instruments in 2010–2017. Particular attention was paid to determining the level of PVECs background in HMI/SDO data. The deviation of the probability density function (PDF) of PVECs density (jr), calculated for both quiet and active regions of the Sun, from the normal distribution is established. It is shown that the PDF in the region of low PVECs (jr < 6000 statamper/cm2) is described by the normal distribution (whose triple root-mean-square deviation determines the PVEC background), and by a power-law function in the region of higher jr. At least for some ARs, the jr PDF as a whole can be represented by the kappa distribution. It was found that in 42 events (89%) at least one HXR source was at the periphery of the region of strong (jr > 10^4 statamper/cm2) PVECs in the form of islands or ribbons, stretched mainly along the magnetic polarity inversion line (PIL). The values of the maximum PVEC density under the HXR sources in all the studied ARs were in the range (0.06–2) x 105 stamper/cm2. No significant correlation was found between the intensity of HXR sources and the density of PVECs below them. By comparing the post-flare and pre-flare maps of PVECs, no evidence was found of significant dissipation of PVECs in areas corresponding to the HXR sources. In some cases, an enhancement of PVECs was detected during a flare. The results confirm the findings of earlier case studies that the HXR sources tend to be located predominantly on the periphery of areas of strong PVECs and avoid their maxima. Taken together, the results do not support the concept of electron acceleration by a longitudinal electric field induced at the foot of the flare loops. The presence of ribbons and islands of supra-background PVECs indicates the presence of spatially concentrated bunches of free magnetic energy in ARs. The finding out of the specific role of these PVECs bunches in the processes of flare energy release and particle acceleration requires further research.