Observations of Twist, Current Helicity, and Writhe in the Magnetic Knots of δ-sunspots Consistent with the Kink Instability of a Highly Twisted Flux Rope

We measure current helicity ( H r c ) as well as proxies for twist ( α r ) and writhe ( W ) in the isolated magnetic knots of three delta ( δ )-sunspots and report that the observations are consistent with a kink instability acting on a highly twisted flux tube. δ -spots are active regions (ARs) in which positive and negative umbrae share a penumbra. We identify and isolate “magnetic knots,” i.e., opposite polarity umbrae that are in close proximity and forming the δ -configuration, in ARs NOAA 11158, 11267, and 11476 as observed with data from the Solar Dynamic Observatory Helioseismic and Magnetic Imager. We find that H r c , α r , and W have the same sign for each magnetic knot, as predicted in simulations of a kink instability acting on highly twisted flux tubes. The deformed flux tube causing the δ -formation, the magnetic knot, is only a portion of the entire AR and demonstrates the potential for the kink instability to act on a smaller spatial scale within the AR. Each magnetic footpoint contains a single sign of the radial current, J r , which suggests that we are observing the core of the flux rope without return currents. As a counterexample, we analyze one β -spot that shows H r c and α r have the opposite signs of W . While our observations support the formation mechanism of the magnetic knots in δ -spots being the kink instability, a much larger sample is needed to determine confidently the prevalence of the kink instability as the cause of flux tube deformation.