摘要：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 105 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.
关键词：Sun: corona;Sun: activity;Sun: magnetic fields
