Density distribution of photospheric vertical electric currents in flare active regions of the Sun

Abstract

Solar active regions contain electric currents. Information on the distribution of currents is important for understanding the processes of energy release on the surface of the Sun and in the overlying layers. The paper presents an analysis of the probability density function (PDF) of the absolute value of the photospheric vertical electric current density (|j z |) in 48 active regions before and after flares in 2010-2017. Calculation of |j z | is performed by applying the differential form of Ampere's circuital law to photospheric vector magnetograms obtained from observations of the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). It has been established that for the studied active regions PDF(|j z |) is described by the Gauss function in the low-|j z | region (|j z | < 10110 ± 1321 statampere/cm 2 ) and the decaying power-law function in the region of higher |j z | values. Also, for some active regions PDF(|j z |) can be described by the special kappa-function. The distributions of the parameters of the approximating functions are obtained using the least squares method. The average absolute value of the power-law function index is 3.69 ± 0.51, and 3.99 ± 0.51 of the kappa-function. No systematic changes in parameters during the flares are detected. An explicit connection between the parameters and the flare X-ray class, as well as with the Hale magnetic class of the active regions, is not found. Arguments are presented in favor of the suggestion that the Gaussian distribution in the low-value region of PDF(|j z |) represents noise in the data, while the power-law "tail" reflects the nature of electric currents in the solar active regions.

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

“…To determine the noise level, for each SHARP data set we selected a 'background box' in a quiet Sun region without significant magnetic fields, constructed and plotted the distribution of |j r | for this 'background box'. As shown in Zimovets et al (2019), for all the considered 48 active regions the j r -distribution below the threshold value of j thr r ≈ 10 4 statampere cm −2 can be well approximated by a Gaussian function, while it has a powerlaw shape above this threshold. It was argued that the Gaussian part of j r -distribution represent data noise, but the power-law part can contain physically meaningful information.…”

“…The choice of this specific value of j thr r is determined by the shape of j r -distributions obtained with the SHARP data series. As it was shown inZimovets et al (2019), the j r -distributions below j thr r have a Gaussian shape and can be composed mainly from data noise. Above this threshold value, the j r -distributions have a power-law shape, which can be physically meaningful, representing some real processes of formation and distribution of PVECs in active regions.…”