  Flares and coronal mass ejections are powered by magnetic energy stored in
coronal electric currents. Here, we explore the nature of coronal currents in
observed and model active region (ARs) by studying manifestations of these
currents in photospheric vector magnetograms. We employ Gauss's separation
method, recently introduced to the solar physics literature, to partition the
photospheric field into three distinct components, each arising from a separate
source: (i) currents passing through the photosphere, (ii) currents flowing
below it, and (iii) currents flowing above it. We refer to component (iii) as
the photospheric imprint of coronal currents. In both AR 10930 and AR 11158,
photospheric imprints exhibit large-scale, spatially coherent structures along
these regions' central, sheared polarity inversion lines (PILs) that are
consistent with coronal currents flowing horizontally above these PILs, similar
to recent findings in AR 12673 by Schuck et al. (2022). We find similar
photospheric imprints in a simple model of a non-potential AR with known
currents. We find that flare-associated changes in photospheric imprints in AR
11158 accord with earlier reports that near-PIL fields become more horizontal,
consistent with the "implosion" scenario. We hypothesize that this evolution
effectively shortens, in an overall sense, current-carrying coronal fields,
leading to decreased inductive energy (DIE) in the coronal field. We further
hypothesize that, in the hours prior to flares, parts of the coronal field
slowly expand, in a process we deem coronal inflation (CI) -- essentially, the
inverse of the implosion process. Both of these hypotheses are testable with
non-potential coronal field extrapolations.
