Are the photospheric sunspots magnetically force-free in nature?

Abstract

In a force-free magnetic field, there is no interaction of field and the plasma in the surrounding atmosphere i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of many magnetic parameters like magnetic energy, gradient of twist of sunspot magnetic fields (computed from the force-free parameter $\alpha$), including any kind of extrapolations heavily hinge on the force-free approximation of the photospheric magnetic fields. The force-free magnetic behaviour of the photospheric sunspot fields has been examined by \cite{metc95} and \cite{moon02} ending with inconsistent results. \cite{metc95} concluded that the photospheric magnetic fields are far from the force-free nature whereas \cite{moon02} found the that the photospheric magnetic fields are not so far from the force-free nature as conventionally regarded. The accurate photospheric vector field measurements with high resolution are needed to examine the force-free nature of sunspots. We use high resolution vector magnetograms obtained from the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard Hinode to inspect the force-free behaviour of the photospheric sunspot magnetic fields. Both the necessary and sufficient conditions for force-freeness are examined by checking global as well as as local nature of sunspot magnetic fields. We find that the sunspot magnetic fields are very close to the force-free approximation, although they are not completely force-free on the photosphere.