Global Twist of Sunspot Magnetic Fields Obtained from High Resolution Vector Magnetograms

The presence of fine structures in the sunspot vector magnetic fields has been confirmed from Hinode as well as other earlier observations. We studied 43 sunspots based on the data sets taken from ASP/DLSP, Hinode (SOT/SP) and SVM (USO). In this \emph{Letter}, (i) We introduce the concept of signed shear angle (SSA) for sunspots and establish its importance for non force-free fields. (ii) We find that the sign of global $\alpha$ (force-free parameter) is well correlated with the global SSA and the photospheric chirality of sunspots. (iii) Local $\alpha$ patches of opposite signs are present in the umbra of each sunspot. The amplitude of the spatial variation of local $\alpha$ in the umbra is typically of the order of the global $\alpha$ of the sunspot. (iv) We find that the local $\alpha$ is distributed as alternately positive and negative filaments in the penumbra. The amplitude of azimuthal variation of the local $\alpha$ in the penumbra is approximately an order of magnitude larger than that in the umbra. The contributions of the local positive and negative currents and $\alpha$ in the penumbra cancel each other giving almost no contribution for their global values for whole sunspot. (v) Arc-like structures (partial rings) with a sign opposite to that of the dominant sign of $\alpha$ of the umbral region are seen at the umbral-penumbral boundaries of some sunspots. (vi) Most of the sunspots studied, belong to the minimum epoch of the 23$^{rd}$ solar cycle and do not follow the so-called hemispheric helicity rule.