Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops

Coronal loops in active regions are often characterized by quasi-circular and helically twisted (sigmoidal) geometries, which are consistent with dipolar potential field (PF) models in the former case, and with nonlinear force-free field models with vertical currents in the latter case. Alternatively, Parker-type nanoflare models of the solar corona hypothesize that a braiding mechanism operates between unresolved loop strands, which is a more complex topological model. In this study we use the vertical-current approximation of a nonpotential magnetic field solution (that fulfils the divergence-free and force-free conditions) to characterize the number of helical turns Ntwist in twisted coronal loops. We measure the helical twist in 15 active regions observed with Atmospheric Imaging Assembly and Helioseismic and Magnetic Imager/SDO (Solar Dynamic Observatory) and find a mean nonpotentiality angle (between the potential and nonpotential field directions) of NP = 15° 3°. The resulting mean rotational twist angle is = 49° 11°, which corresponds to Ntwist = /360° = 0.14 0.03 turns with respect to the untwisted PF, with an absolute upper limit of Ntwist 0.5, which is far below the kink instability limit of . The number of twist turns Ntwist corresponds to the Gauss linkage number Nlink in braiding topologies. We conclude that any braided topology (with ) cannot explain the observed stability of loops in a force-free corona, nor the observed low twist number. Parker-type nanoflaring can thus occur in non-force-free environments only, such as in the chromosphere and transition region.