Abstract. We are presenting a semi-classical theory of the impact polarization due to a quadrupolar electric excitation, which is the case of this forbidden line. In addition, this line is also radiatively forbidden being a triplet-singlet transition. This last feature is overcome by scaling the semi-classical result to a full quantum calculation at a single energy value. The cross-section and impact polarization are thus obtained as a function of energy, in agreement with the quantum calculations that exist only for the cross-section. The behavior of the impact polarization is found to be quite different than that of the usual dipolar electric interaction. Let us denote as radial the polarization parallel to the incident beam or magnetic field, and as tangential the perpendicular polarization. In the case of the dipolar electric interaction (permitted lines), the polarization is radial at low energy, and tangential at high energy, and it vanishes at energy about twelve times the threshold energy. In the case of the quadrupolar electric interaction, we observe quite different behavior, with the polarization vanishing point much closer to the threshold energy. This leads us to reanalyze the auroral red line polarization observation by Lilensten et al. (2008). From polarization observations made at Svalbard, they conclude to a rather strong tangential polarization observed during a 4-h recording including two auroral events. The existence of tangential polarization is questioned by our new theory, which leads to reconsidering the contribution of scattered parasitic light from a neighboring city that was mentioned but discarded by the authors. Finally, we conclude that the line is only weakly radially polarized by electron impact, and only during the auroral events. The weak polarization level leads to taking the competing depolarization by collisions with the neighboring O atoms into account, and by the competing isotropical (thus depolarizing) processes for populating the line upper level: the dissociative recombination of O2+ colliding with thermal electrons, and above all the reaction N(2D)+O2. The final diagnostic could be a density determination by depolarization, but it may be rather complicated because it involves several species.
The theoretical impact polarization of the O I 6300 Å red line of Earth aurorae
