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 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 mu(NP) = 15 degrees +/- 3 degrees. The resulting mean rotational twist angle is phi = 49 degrees +/- 11 degrees, which corresponds to N-twist = phi/360 degrees = 0.14 +/- 0.03 turns with respect to the untwisted PF, with an absolute upper limit of N-twist less than or similar to 0.5, which is far below the kink instability limit of vertical bar N-twist vertical bar greater than or similar to 1. 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 vertical bar N-link vertical bar >= 1) 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.