Helicity of the Solar Magnetic Field

Magnetic helicity is a physical quantity that measures the complexity in the field lines. It is given by a volume integral over scalar product of magnetic field and its vector potential. Direct computation of magnetic helicity in the solar atmosphere is not possible in want of observations to compute the volume integral. We have clarified the physical meaning of ¿ and its relation with the magnetic helicity. An analytical bipole was generated to study the effect of polarimetric noise on the estimation of various magnetic parameters. We then examined the fine structures of sunspots in terms of local current and ¿. The concept of signed shear angle (SSA) has been introduced. Spatially averaged SSA (SASSA) gives actual twist present in a sunspot at an observed height irrespective of force-free nature and shape of sunspots. We find that there is no net current in the sunspots even in the presence of significant twist which is consistent with fibril-bundle structure of sunspot magnetic fields. The SASSA holds promise to be very useful in predicting the severity of solar flares. A good correlation has been found among the signs of helicity at different heights in the solar atmosphere.