tokens: steps; we therefore estimate the above convergence to be sufficient. Convergence is however not fully reached in the line wings within the allocated computing time. Development of efficient acceleration methods would be desirable for future work. Fig. 2. Convergence of the linear polarization rate Q / I , for the D 2 line ( left ) and for the D 1 line ( right ) at line center ( upper row ) and in the line far wing ( lower row ). Fig. 3. Convergence of the emerging linear polarization Q / I : evolution of the step increment Δ( Q / I ) as a function of the step number N . The aim is to show that the step increment decreases more rapidly than the inverse of the step number 1/ N (as for a Riemann series). In this respect, their ratio is the upper plot and the logarithm of their ratio is the lower plot, which also includes linear fits and their equations. The two terms of the Q / I ratio, namely the Stokes parameters Q and I , each nevertheless converge much less quickly, in such a way that they are not at all converged within the 166 iteration steps. However, the behavior of the ratio Q / I appears to be different, because some simplifications certainly occur when forming the ratio. 4. Concluding discussion Although the calculation seems reasonably converged in the line wings, the agreement between the observed and computed profiles remains only qualitative. As described below, we investigated the different possible causes of this difference. We questioned the accuracy of collision rate calculations, in particular those with hydrogen neutral atoms that determine the coherent scattering weight in PRD, and therefore in the far wings. We artificially varied these rates, but the Na I D 2 wing profile was not improved with respect to observations. We questioned the model electron density, whose determination is very indirect from observations, and in light of the recent investigation by Bommier (2020) , who suggests that the electron density at the solar surface would be much higher than in present models, and similar to the neutral hydrogen atom density. We artificially varied the model electron density, but again the Na I D 2 wing profile was not improved with respect to observations. We questioned the accuracy of our model of Rayleigh scattering on neutral hydrogen atoms, which is responsible for the continuum below spectral lines, which is of more relative importance in their wings. Our model is taken from the MALIP code for computing the Stokes parameter profiles of magnetoactive Fraunhofer lines by Landi Degl’Innocenti (1976) , and we did not try to modify it. We questioned the very rough HOLMUL approximation ( Holweger Mueller 1974 ) we applied to our atmosphere model. This approximation consists in not considering atmosphere higher than the temperature minimum. The temperature reversal there may be responsible for a central bump in the line profile, following a well-known result for a two-level atom in LTE. As our model considers only the
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