On the Resolution of the Azimuthal Ambiguity in Vector Magnetograms of Solar Active Regions

Abstract

We introduce a "structure minimization" technique to resolve the azimuthal ambiguity of 180°, intrinsic in solar vector magnetic field measurements. We resolve the 180° ambiguity by minimizing the inhomogeneities of the magnetic field strength perpendicular to the magnetic field vector. This relates to a minimization of the sheath currents that envelope the solar magnetic flux tubes, thus allowing for more space-filling and less complex magnetic fields. Structure minimization proceeds in two steps: First, it derives a local solution analytically, by means of a structure minimization function. Second, it reaches a global solution numerically, assuming smoothness of the magnetic field vector. Structure minimization (i) is disentangled from any use of potential or linear force-free extrapolations and (ii) eliminates pixel-to-pixel dependencies, thus reducing exponentially the required computations. We apply structure minimization to four active regions, located at various distances from disk center. The minimum structure solution for each case is compared with the "minimum energy" solution obtained by the slower simulated annealing algorithm. We find correlation coefficients ranging from significant to excellent. Moreover, structure minimization provides an ambiguity-free vertical gradient of the magnetic field strength that reveals the variation of the magnetic field with height. The simplicity and speed of the method allow a near real-time processing of solar vector magnetograms. This task was not possible in the past and may be of interest to both existing and future solar missions and ground-based magnetographs.