On the Force-Freeness of Photospheric Magnetic Fields in Solar Active Regions: The Current Density Method

We introduce and apply a method to investigate the force-free character of the photospheric magnetic fields in solar active regions. The vertical current density, inferred from vector magnetograms, is decomposed into a helical (assumed field-aligned) component, and a component perpendicular to the magnetic field. Contrary to the classical method of calculating the integrated Lorentz forces, the current density method does not require balanced magnetic configurations, i.e. zero net flux, and it provides spatial information, i.e. maps of force-free vs. non-force-free areas. A revised force-free condition and a new expression for the twist parameter are also introduced. The new twist parameter is more accurate than the conventional one in that it discards contributions from currents that are non-field-aligned by definition. The current density method is applied on high-resolution (0.5′′) photospheric vector magnetograms of the emerging flux region NOAA 8844, acquired by the Flare Genesis Experiment. We find that the photospheric magnetic fields in our active region are not force-free, but they tend to become force-free ∼ 30 hr after our observations. We conclude that the degree of force-freeness is a function of the evolutionary stage of an active region, determined by the mean inclination of the magnetic field vector with respect to the photosphere. Non-force-free magnetic fields are due to the flux emergence process and the subsequent intense photospheric flows which, in turn, give rise to strong shear. Force-freeness is achieved by the completion of the flux emergence process. The non-force-free character of the magnetic fields is manifested by non-field-aligned, azimuthal, currents, that flow around flux tubes. These currents are stronger than field-aligned currents, in many cases. The azimuthal currents are associated with shear and they become detectable due to a low-lying magnetic canopy of inclined flux tubes, extending above the interspot area. Subject headings: Sun: atmosphere—Sun: magnetic fields—Sun: photosphere