Force‐Freeness of Solar Magnetic Fields in the Photosphere

It is widely believed that solar magnetic fields are force-free in the solar corona but not in the solar photosphere at all. In order to examine the force-freeness of active region magnetic fields at the photospheric level, we have calculated the integrated magnetic forces for 12 vector magnetograms of three flare-productive active regions. The magnetic field vectors are derived from simultaneous Stokes profiles of the Fe I doublet λλ6301.5 and 6302.5 obtained by the Haleakala Stokes Polarimeter of Mees Solar Observatory, with a nonlinear least-squares method adopted for field calibration. The resulting vertical Lorentz force normalized to the total magnetic pressure force |Fz/Fp| ranges from 0.06 to 0.32 with a median value of 0.13, which is smaller than the values (~0.4) obtained by Metcalf et al., who applied a weak field derivative method to the Stokes profiles of Na I λ5896. Our results indicate that the photospheric magnetic fields are not so far from force-free as conventionally regarded. As a good example of a linear force-free field, NOAA Active Region 5747 is examined. By applying three different methods (a most probable value method, a least-squares fitting method, and comparison with linear force-free solutions), we have derived relatively consistent linear force-free coefficients for NOAA AR 5747. It is found that the scaled downward Lorentz force (|Fz/Fp|) in the solar photosphere decreases with increasing |α|. Our results also show that the force-freeness of photospheric magnetic fields depends not only on the character of the active region but also on its evolutionary status.