The physical origin of the scattering polarization of the Na I D lines in the presence of weak magnetic fields

We demonstrate that the atomic alignment of the hyperfine-structure components of the ground-level S_1/2 of Na I and of the upper-level P_1/2 of the D₁ line are practically negligible for magnetic strengths B > 10 G and virtually zero for B ≥ 100 G. This occurs independently of the magnetic field inclination on the stellar surface (also, in particular, for vertical fields). Consequently, the characteristic antisymmetric linear polarization signature of the scattered light in the D ₁ line is practically suppressed in the presence of magnetic fields larger than 10 G, regardless of their inclination. Remarkably, we find that the scattering polarization amplitude of the D₂ line increases steadily with the magnetic strength, for vertical fields above 10 G, while the contribution of the alignment to the polarization of the D₁ line rapidly decreases. Therefore, we suggest that spectropolarimetric observations of the "quiet" solar chromosphere showing significant linear polarization peaks in both D₁ and D₂ cannot be interpreted in terms of one-component magnetic field models, implying that the magnetic structuring of the solar chromosphere could be substantially more complex than previously thought.