Relationship of the multimode kink instability to δ-spot formation

We study the current-driven kink instability with a three-dimensional MHD spectral code, under conditions appropriate for the convection zone of the Sun. Our goal is to determine whether the kink instability can explain the unusual morphology of certain "delta-spot" active regions. The characteristics of these delta-spots are unusually large tilt upon emergence, subsequent rotation, compactness during their lifetime, magnetic shear that develops along the neutral line of their vertical magnetic field, and unusually high hare activity. We find that highly twisted tubes perturbed with a single unstable kink mode evolve to a new helical equilibrium with finite amplitude. This kink would produce an active region that emerged tilted and then rotated and so is suggestive of delta-spot behavior. It would not, however, produce other characteristics of delta-spots such as compactness and shear. We then investigate the kink instability in tubes perturbed simultaneously with several unstable modes at different wavelengths. These tubes develop a concentrated kink at the point at which the modes interact constructively. We show that such a concentrated kink would first emerge highly tilted, rotate during its subsequent emergence while remaining compact, and develop strong shear along its magnetic neutral line, in agreement with delta-spot observations. In addition we find that very strong concentrated kinks develop a current sheet at which the magnetic field reconnects, causing field lines near the center of the tube to become knotted. This reconnection could be related to the high flare activity of delta-spots.