Possibilities for Estimating Horizontal Electrical Currents in Active Regions on the Sun

Part of the “free” magnetic energy associated with electrical current systems in the active region (AR) is released during solar flares. This proposition is widely accepted and it has stimulated interest in detecting electrical currents in active regions. The vertical component of an electric current in the photosphere can be found by observing the transverse magnetic field. At present, however, there are no direct methods for calculating transverse electric currents based on these observations. These calculations require information on the field vector measured simultaneously at several levels in the photosphere, which has not yet been done with solar instrumentation. In this paper we examine an approach to calculating the structure of the square of the density of a transverse electrical current based on a magnetogram of the vertical component of the magnetic field in the AR. Data obtained with the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO) for the AR of NOAA AR 11283 are used. It is shown that (1) the observed variations in the magnetic field of a sunspot and the proposed estimate of the density of an annular horizontal current around the spot are consistent with Faraday’s law and (2) the resulting estimates of the magnitude of the square of the density of the horizontal current ${j}_{\perp}^2$= (0.002− 0.004) A²/m⁴ are consistent with previously obtained values of the density of a vertical current in the photosphere. Thus, the proposed estimate is physically significant and this method can be used to estimate the density and structure of transverse electrical currents in the photosphere.