  There has been a long-lasting debate on the question of whether or not
electric currents in solar active regions are neutralized. That is, whether or
not the main (or direct) coronal currents connecting the active region
polarities are surrounded by shielding (or return) currents of equal total
value and opposite direction. Both theory and observations are not yet fully
conclusive regarding this question, and numerical simulations have,
surprisingly, barely been used to address it. Here we quantify the evolution of
electric currents during the formation of a bipolar active region by
considering a three-dimensional magnetohydrodynamic simulation of the emergence
of a sub-photospheric, current-neutralized magnetic flux rope into the solar
atmosphere. We find that a strong deviation from current neutralization
develops simultaneously with the onset of significant flux emergence into the
corona, accompanied by the development of substantial magnetic shear along the
active region's polarity inversion line. After the region has formed and flux
emergence has ceased, the strong magnetic fields in the region's center are
connected solely by direct currents, and the total direct current is several
times larger than the total return current. These results suggest that active
regions, the main sources of coronal mass ejections and flares, are born with
substantial net currents, in agreement with recent observations. Furthermore,
they support eruption models that employ pre-eruption magnetic fields
containing such currents.
