Analysis of Magnetic Knots in δ-Sunspots

Delta (δ)-spots are active regions (ARs) in which positive and negative umbrae share a penumbra. They are known to be the source of strong flares. We use a quantity, the degree of δ, to measure the fraction of umbral flux participating in the δ-configuration and to isolate the dynamics of the magnetic knot, i.e. adjacent umbrae in the δ-configuration. Using HMI/SDO data, we analyze 19 δ-spots and 11 β-spots in detail, and 120 δ-spots in less detail. We find that δ-regions are not in a δ-configuration for the entire time but spend 55% of their observed time as δ-spots. On average, the magnetic knots rotate 17 degrees per day while the β-spots rotate 2 degrees per day. Approximately 72% of the magnetic knots present anti-Hale or anti-Joy tilts, contrasting starkly with only 9% of the β-spots. 84% of the δ-spots are formed by single flux emergence events and 58% have a quadrupolar magnetic configuration. The δ-spot characteristics are consistent with the formation mechanism signatures as follows: 42% with the kink instability or Σ-effect, 32% with multi-segment buoyancy, 16% with collisions and two active regions that are unclassified but consistent with a rising O-ring. In order to better distinguish between a kink instability and the Σ-effect as formation mechanisms, we study active regions NOAA 11158, 11267, and 11476 as observed with data from the Solar Dynamic Observatory (SDO) Helioseismic and Magnetic Imager (HMI) and find that the current helicity H^c_z, a proxy for twist (α_z), and a proxy for writhe (change in tilt angle) are the same sign for each magnetic knot as predicted in simulations of the kink instability acting on highly twisted flux tubes. Each magnetic footpoint contains a single sign of the vertical current, J_z, which suggests that we are observing the core of the flux rope without return currents, i.e., we are not observing a neutralized region with net zero current. While our observations support the formation mechanism of these three magnetic knots being a kink instability, a much larger sample is needed to confidently determine the prevalence of the kink instability as the cause of flux tube deformation.