Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops

Abstract

Abstract 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 N twist 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 μ NP = 15° ± 3°. The resulting mean rotational twist angle is φ = 49° ± 11°, which corresponds to N twist = φ/360° = 0.14 ± 0.03 turns with respect to the untwisted PF, with an absolute upper limit of N twist ≲ 0.5, which is far below the kink instability limit of . The number of twist turns N twist corresponds to the Gauss linkage number N link 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.