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Twist, Writhe & Helicity in the inner penumbra of a sunspot

The aim of this work is the determination of the twist, writhe, and self magnetic helicity of penumbral filaments located in an inner Sunspot penumbra. To this extent, we inverted data taken with the spectropolarimeter (SP) aboard Hinode with the SIR (Stokes Inversion based on Response function) code. For the construction of a 3D geometrical model we applied a genetic algorithm minimizing the divergence of the magnetic field vector and the net magnetohydrodynamic force, consequently a force-free solution would be reached if possible. We estimated two proxies to the magnetic helicity frequently used in literature: the force-free parameter and the current helicity term. We show that both proxies are only qualitative indicators of the local twist as the magnetic field in the area under study significantly departures from a force-free configuration. The local twist shows significant values only at the borders of bright penumbral filaments with opposite signs on each side. These locations are precisely correlated to large electric currents. The average twist (and writhe) of penumbral structures is very small. The spines (dark filaments in the background) show a nearly zero writhe. The writhe per unit length of the intraspines diminishes with increasing length of the tube axes. Thus, the axes of tubes related to intraspines are less wrung when the tubes are more horizontal. As the writhe of the spines is very small, we can conclude that the writhe reaches only significant values when the tube includes the border of a intraspine.