Resolution of the 180° ambiguity for inverse horizontal magnetic field configurations

A well-known problem in solar physics is that solutions for the transverse magnetic field direction are ambiguous with respect to a 180° reversal in the field direction. In this paper we focus on three methods for the removal of the 180° ambiguity applied to three MHD models. These methods are (1) the reference field method, (2) the method of magnetic pressure gradient, and (3) the magnetic field divergence-free method. All three methods are noniterative, and methods 2 and 3 are analytical and fast. We apply these methods to three MHD equilibrium model fields: (1) an analytical solution of a nonlinear force-free magnetic field equilibrium from Low, (2) a simulation of an emerging twisted flux tube from Fan & Gibson, and (3) a pre-eruptive twisted magnetic flux rope equilibrium reached by relaxation from Amari et al. We measure the success of methods within "inverse horizontal field" regions in the boundary, which are mathematically defined by B ⊥ · ∇ ⊥ B _z> 0. When such regions overlap with the magnetic field neutral lines, they are known as "bald patches" (BPs) or inverse topology. Our most important conclusion is that the magnetic divergence-free method is far more successful than the other two methods within BPs. This method requires a second level of measurements of the vertical magnetic field. As high-quality multilevel magnetograms will come online in the near future, our work shows that multilayer magnetic field measurements will be highly desirable to objectively and successfully tackle the 180° ambiguity problem.