Vertical Lorentz Force and Cross‐Field Currents in the Photospheric Magnetic Fields of Solar Active Regions

Abstract

We demonstrate that the vertical Lorentz force and a corresponding lower limit of the cross-field electric current density can be calculated from vector magnetograms of solar active regions obtained at a single height in the solar atmosphere, provided that the vertical gradient of the magnetic field strength is known at this height. We use a predicted vertical magnetic field gradient derived from a previous analysis. By testing various force-free solutions, we find that the numerical accuracy of our method is satisfactory. Applying the method to active region photospheric vector magnetograms, we find vertical Lorentz forces ranging from several hundredths to a few tenths of the typical photospheric gravitational force, and typical cross-field current densities up to several times 10 mA m-2. The typical vertical current density is found to be 2-3 times smaller, on the order of 10-15 mA m-2. These differences are above the associated uncertainties. The values of the cross-field currents decrease in an averaged vector magnetogram, but the ratio of the cross-field to the vertical current density increases, also above the uncertainties. We conclude that the photospheric active region magnetic fields are not force-free, contrary to the conjectures of some recent studies.