Solving the Paradox of the Solar Sodium $D_1$ Line Polarization

Twenty-five years ago, enigmatic linear polarization signals were discovered in the core of the sodium $D_1$ line. The only explanation that could be found implied that the solar chromosphere is practically unmagnetized, in contradiction with other evidences. This opened a paradox that has challenged physicists for many years. Here we present its solution, demonstrating that these polarization signals can be properly explained in the presence of magnetic fields in the gauss range. This result opens a novel diagnostic window for exploring the elusive magnetism of the solar chromosphere.

Figure 1

(a) Grotrian diagram of the considered atomic model of sodium. The diagram shows the upper and lower terms of the sodium doublet, as well as the fine structure and hyperfine structure (HFS) levels (energy splittings not to scale). The fine structure transitions corresponding to the $D_1$ and $D_2$ lines are also indicated, as well as the allowed transitions between HFS $F$ levels. The quantum number $I$ indicates the nuclear spin. (b) Theoretical intensity profiles (normalized to the continuum) of the $D_2$ and $D_1$ lines. Calculations were carried out in a one-dimensional semiempirical model of the solar atmosphere [17] for a line of sight with $\mu =\cos \theta =0.1$ (with $\theta$ the heliocentric angle). The dashed and dotted vertical lines show the wavelength positions of the various HFS components of the $D_1$ and $D_2$ lines, indicated in the Grotrian diagram (a).

Figure 2

Fractional linear polarization ($Q/I$) pattern of the Na i doublet. The black solid curves represent spectropolarimetric observations performed using ZIMPOL-3 [27] in quiet regions close to the solar limb. The measurement shown in the upper panel was taken for a spectral interval containing both $D_1$ and $D_2$, and had a spectral sampling of 8.38 mÅ/pixel. The one shown in the lower panel included only $D_1$, but had a better spectral sampling, of 4.60 mÅ/pixel. In both panels, the red dotted curves and the blue solid curves show the results of radiative transfer calculations in a semiempirical one-dimensional atmospheric model of the quiet solar atmosphere [17]. The red colored profiles were obtained in the absence of a magnetic field, whereas the blue colored ones were obtained including a volume-filling tangled magnetic field of 15 G throughout the entire atmosphere (see the Supplemental Material [26]). The theoretical Stokes profiles were calculated for a line of sight with $\mu =0.1$ for the top panel, and $\mu =0.125$ for the bottom one, in accordance with the observation to which they are compared. The reference direction for positive Stokes $Q$ is taken parallel to the nearest solar limb.