The rise of kink-unstable magnetic flux tubes and the origin of delta-configuration sunspots

We perform three-dimensional simulations of the rise of twisted magnetic fl ux tubes in an adiabatically stratified model solar convection zone. The in itial flux tube in our simulations is a uniformly twisted, buoyant, horizon tal tube located near the bottom of the stratified layer. The twist of the initial Bur tube is described by a parameter alpha, which is defined as the angular rate of field-line rotation about the tube axis per unit length of the tube. We study the nonlinear evolution of the helical kink instability of the flux tube as it rises through the stratified layer. We find from. o ur simulations that in order for the tube to develop significant kinking du ring its rise, the initial twist of the tube needs to be close to or greate r than the critical limit (alpha(c)) for the onset of the kink instability. If the initial twist is significantly below the critical limit (alpha belo w about 50% of alpha(c)), we find essentially no kink development and the e volution is similar to the results from previous two-dimensional simulation s of the rise of twisted, horizontal flux 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 find sharp bending and distortion of the tube as a result of the nonlinear evolution of the kink instability. In this case, we find that due to the effect of gravitational stratification, the kinked flux tube arches upward and evolves into a buckled loop with a local chang e of tube orientation at the loop apex that exceeds 90 degrees from the ori ginal direction of the tube. The emergence of this buckled loop can give ri se to a compact magnetic bipole with polarity order inverted from the Hale polarity law, similar to the configuration often seen in delta spots. Furth ermore, our simulations show that the writhing of the tube axis as a result of the kink instability stretches the flux tube and increases its buoyancy . Hence, the development of the kink instability can speed up the overall r ise of the Bur tube.