| Abstract
| - Aims. Coronal heating through the explosive release of magnetic energy remains an open problem in solar physics. Recent hydrodynamical models attempt an investigation by placing swarms of “nanoflares” at random sites and times in modeled one-dimensional coronal loops. We investigate the problem in three dimensions, using extrapolated coronal magnetic fields of observed solar active regions. Methods. We applied a nonlinear force-free field extrapolation above an observed photospheric magnetogram of NOAA active region (AR) 11 158. We then determined the locations, energy contents, and volumes of “unstable” areas, namely areas prone to releasing magnetic energy due to locally accumulated electric current density. Statistical distributions of these volumes and their fractal dimension are inferred, investigating also their dependence on spatial resolution. Further adopting a simple resistivity model, we inferred the properties of the fractally distributed electric fields in these volumes. Next, we monitored the evolution of 10 5 particles (electrons and ions) obeying an initial Maxwellian distribution with a temperature of 10 eV, by following their trajectories and energization when subjected to the resulting electric fields. For computational convenience, the length element of the magnetic-field extrapolation is 1 arcsec, or ~725 km, much coarser than the particles’ collisional mean free path in the low corona ( 0.1−1 km). Results. The presence of collisions traps the bulk of the plasma around the unstable volumes, or current sheets (UCS), with only a tail of the distribution gaining substantial energy. Assuming that the distance between UCS is similar to the collisional mean free path we find that the low active-region corona is heated to 100−200 eV, corresponding to temperatures exceeding 2 MK, within tens of seconds for electrons and thousands of seconds for ions. Conclusions. Fractally distributed, nanoflare-triggening fragmented UCS in the active-region corona can heat electrons and ions with minor enhancements of the local resistivity. This statistical result is independent from the nature of the extrapolation and the spatial resolution of the modeled active-region corona. This finding should be coupled with a complete plasma treatment to determine whether a quasi-steady temperature similar to that of the ambient corona can be maintained, either via a kinetic or via a hybrid, kinetic and fluid, plasma treatment. The finding can also be extended to the quiet solar corona, provided that the currently undetected nanoflares are frequent enough to account for the lower (compared to active regions) energy losses in this case.
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