Density Distribution of Photospheric Vertical Electric Currents in Flare-Active Regions of the Sun

Electric currents flow in active regions of the sun. Information on the distribution of the currents is important for understanding energy release processes on the sun’s surface and in overlying layers. This is an analysis of the probability density function (PDF) of the absolute value of the density of photospheric vertical electric currents | j_z | in 48 active regions from 2010 through 2015 at times before and after flares. | j_z | is calculated by applying a differential form of the magnetic field circulation theorem (Ampere’s law) to photospheric vector magnetograms from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). It is shown that for the active regions studied here PDF (| j_z |) can be calculated in a first approximation by a model consisting of a folded normal distribution at low values (| j_z |≲ 9·10³ statampere/cm²) and a falling power law function at higher values. A least squares method yields the model parameters for all regions, histograms of their distributions are plotted, and the mathematical expectations and mean square deviations are calculated. No systematic changes in the model parameters over the time of a flare were observed. Neither an explicit relation of the parameters to the class of a flare, nor to the Hale magnetic class was found in terms of the approach used for the limited sample of flares and active regions examined here. Arguments are presented in favor of the proposition that a folded normal distribution at low values represents noise in the data, while a power-law “tail” may reflect the nature of the processes that generate the currents in active regions of the sun.