The Flare-energy Distributions Generated by Kink-unstable Ensembles of Zero-net-current Coronal Loops

It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release and so we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory, i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold

An investigation of the topology and structure of constant-α force-free fields

Coronal field structures corresponding to specified normal fields on the photosphere are investigated using a force-free model. The force-free parameter is insufficient to determine the field uniquely, and so a second parameter representing the contribution of the complementary Green's function is included. For isolated loops represented by a single source-sink pair, the influence of the two parameters on field structure is comparable. Effects on the topology (as measured by field line connectivity) of multiple source configurations are also found to be comparable. It is notable that some configurations are more stable than others to variation of either parameter. The results of this study are compared with previous magnetic charge topology studies involving only the force-free parameter

Coronal magnetic topologies in a spherical geometry I. Two bipolar flux sources

The evolution of the solar corona is dominated to a large extent by the hugely complicated magnetic field which threads it. Magnetic topology provides a tool to decipher the structure of this field and thus help to understand its behaviour. Usually, the magnetic topology of a potential field is calculated due to flux sources on a locally planar photospheric surface. We use a Green's function method to extend this theory to sources on a global spherical surface. The case of two bipolar flux-balanced source regions is studied in detail, with an emphasis on how the distribution and relative strengths of the source regions affect the resulting topological states. A new state with two spatially distinct separators connecting the same two magnetic null points, called the &quot;dual intersecting&quot; state, is discovered.</p