Helicity of the solar magnetic field

Abstract: Helicity measures complexity in the field. Magnetic helicity is given by a volume integral over the scalar product of magnetic field {\bf B} and its vector potential {\bf A}. A direct computation of magnetic helicity in the solar atmosphere is not possible due to unavailability of the observations at different heights and also due to non-uniqueness of {\bf A}. The force-free parameter $\alpha$ has been used as a proxy of magnetic helicity for a long time. We have clarified the physical meaning of $\alpha$ and its relationship with the magnetic helicity. We have studied the effect of polarimetric noise on estimation of various magnetic parameters. Fine structures of sunspots in terms of vertical current ($J_z$) and $\alpha$ have been examined. We have introduced the concept of signed shear angle (SSA) for sunspots and established its importance for non force-free fields. We find that there is no net current in sunspots even in presence of a significant twist, showing consistency with their fibril-bundle nature. The finding of existence of a lower limit of SASSA for a given class of X-ray flare will be very useful for space weather forecasting. A good correlation is found between the sign of helicity in the sunspots and the chirality of the associated chromospheric and coronal features. We find that a large number of sunspots observed in the declining phase of solar cycle 23 do not follow the hemispheric helicity rule whereas most of the sunspots observed in the beginning of new solar cycle 24 do follow. This indicates a long term behaviour of the hemispheric helicity patterns in the Sun. The above sums up my PhD thesis.