Density Distribution of Photospheric Vertical Electric Currents in Flare-Active Regions of the Sun
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DENSITY DISTRIBUTION OF PHOTOSPHERIC VERTICAL ELECTRIC CURRENTS IN FLARE-ACTIVE REGIONS OF THE SUN
I. V. Zimovets,1 A. B. Nechaeva,1,2 I. N. Sharykin,1 and W. Q. Gan3 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
can be calculated in a first approximation by a model consisting of a folded normal distribu-
PDF j z
tion 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. Keywords: active regions of the sun: electric currents
(1) Space Research Institute (IKI), Russian Academy of Sciences, Russia; e-mail: [email protected], [email protected] (2) Moscow Institute of Physics and Technology (National Research University), Russia; e-mail: [email protected] (3) Purple Mountain Observatory, Chinese Academy of Sciences, China; e-mail: [email protected]
Original article submitted September 6, 2019; accepted for publication June 24, 2020. Astrofizika, Vol. 63, No. 3, pp. 463-477 (August 2020) 408
0571-7256/19/6303-0408 ©2020 Springer Science+Business Media, LLC
Translated from
1. Introduction
Magnetic fields determine the processes of solar activity, heating the corona, and acceleration of the solar wind. At present, magnetic fields are routinely measured at the level of the photosphere. It is clear that active regions are permeated by fields concentrated in magnetic flux tubes [1,2]. Based on Ampere’s law (the theorem of circulation of the magnetic field) it has been found that electric currents can flow in these tubes [3,4]. Since vector magnetograms are usually accessible only for a single narrow layer, most of the information is about the vertical compone
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