THE RISE OF KINK-UNSTABLE MAGNETIC FLUX TUBES AND THE ORIGIN OF d-CONFIGURATION SUNSPOTS

We perform three-dimensional simulations of the rise of twisted magnetic Ñux tubes in an adiabatically stratiÐed model solar convection zone. The initial Ñux tube in our simulations is a uniformly twisted, buoyant, horizontal tube located near the bottom of the stratiÐed layer. The twist of the initial Ñux tube is described by a parameter a, which is deÐned as the angular rate of Ðeld-line rotation about the tube axis per unit length of the tube. We study the nonlinear evolution of the helical kink instability of the Ñux tube as it rises through the stratiÐed layer. We Ðnd from our simulations that in order for the tube to develop signiÐcant kinking during its rise, the initial twist of the tube needs to be close to or greater than the critical limit for the onset of the kink instability. If the initial twist is signiÐcantly below the (a c ) critical limit (a below about 50% of we Ðnd essentially no kink development and the evolution is a c ), similar to the results from previous two-dimensional simulations of the rise of twisted, horizontal Ñux tubes. On the other hand, if the initial twist is sufficiently greater than the critical limit such that the e-folding period of the fastest growing kink mode is small compared to the rise time of the tube, we Ðnd sharp bending and distortion of the tube as a result of the nonlinear evolution of the kink instability. In this case, we Ðnd that due to the e†ect of gravitational stratiÐcation, the kinked Ñux tube arches upward and evolves into a buckled loop with a local change of tube orientation at the loop apex that exceeds 90¡ from the original direction of the tube. The emergence of this buckled loop can give rise to a compact magnetic bipole with polarity order inverted from the Hale polarity law, similar to the conÐguration often seen in d spots. Furthermore, our simulations show that the writhing of the tube axis as a result of the kink instability stretches the Ñux tube and increases its buoyancy. Hence, the development of the kink instability can speed up the overall rise of the Ñux tube. Subject headings : MHD È Sun: magnetic Ðelds È sunspots