A Statistical Study on Force-Freeness of Solar Magnetic Fields in the Photosphere

It is an indisputable fact that solar magnetic fields are force-free in the corona, where force free fields means that current and magnetic fields are parallel and there is no Lorentz force in the fields. While the force-free extent of photospheric magnetic fields remains open. In this paper, the statistical results about it is given. The vector magnetograms (namely, $B_{x}$, $B_{y}$ and $B_{z}$ in heliocentric coordinates) are employed, which are deduced and calibrated from Stokes spectra, observed by Solar Magnetic Field Telescope (SMFT) at Huairou Solar Observing Station (HSOS) are used. We study and calibrated 925 magnetograms calibrated by two sets of calibration coefficients, that indicate the relations between magnetic fields and the strength of Stokes spectrum and can be calculated either theoretically or empirically. The statistical results show that the majority of active region magnetic fields are not consistent with the force-free model.