Magnetometry: Solving the fundamental ambiguity from line pair inversion

Context. All magnetic field vector measurements lead to ambiguous results. Aims. We demonstrate that carrying out observations in two different lines belonging to the same multiplet, but with different absorption coefficients (and thus formed at two different depths, e.g., Fe I 6302.5 Å and 6301.5 Å) allow for the azimuth ambiguity remaining from the Zeeman signal interpretation to be resolved. Methods. The measurement based on an interpretation of the Zeeman effect relates to the magnetic field, H , and not the divergence-free magnetic induction, B . We analyzed how the anisotropy of the photosphere, which is strongly stratified due to gravity and density at the star surface, affects the estimation of div H . We also considered how the ambiguity resolution ought to be performed in these conditions. Results. We obtained two ambiguity-resolved field vector maps at two different, but nonetheless close altitudes. This allowed us to derive the current density full vector via curl H = J . The process revealed the horizontal component of the current density, which is generally found to be markedly larger than the better known vertical one. We observed some systematical trends and present some examples in this paper, such as circular currents wrapping spots clockwise about a positive polarity spot and counterclockwise about a negative polarity spot. We also detail the strong horizontal current components crossing active region neutral lines. Conclusions. Finally, we remark that the Na I D1 and D2 lines form another such line pair. We propose them as a way to access the low chromosphere where they are formed. However, a better spatial resolution for both observations and analysis would likely be necessary in such a medium.