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Appendix A: Line properties at different line depression levels

Appendix A.1: Average values

Figures A.1 to A.3 show the average values of the line properties at different line depression levels but for the average bisector velocity of the 630.25 nm line. The average bisector velocity of the 630.15 nm line is similar to that of 630.25 nm in Fig. 11. The two near-IR lines (bottom row of Fig. A.1) sample only low layers in the solar atmosphere. For the observations, the curves thus correspond to those from 10% line depression up to roughly the minimal bisector velocity of the 630 nm lines at 30% line depression. The results derived from the HD-FR spectra show nearly straight bisectors for the near-IR lines. For both the 557.6 nm and 1082.7 nm line, the line properties close to the continuum (<40% line depression) suffer from the presence of line blends (557.6 nm) or ill-defined line depression levels (1082.7 nm) because of the extended line wings. For the latter line, the limited extension of the simulation box is also likely to play a role. The HD-SPAT-SPEC actually gives smoother curves for these lines than the observations themselves. The average intensities at different line depression levels (Fig. A.2) provide little information in themselves because they basically only measure the line depth. The observations and the HD-SPAT-SPEC match well in most cases, with nearly identical values for instance for the 557.6 nm or 1565.2 nm lines. The average line widths at different line depression levels (Fig. A.3) show again that the near-IR line only sample the lower range of the atmosphere, with their curves corresponding to those of the 630 nm lines up to the inflection point at about the 50% line depression. The observations and the (degraded) HD simulation match well in the general shape of the curves here, whereas the absolute values of the line width slightly differ (cf. the red and red-dashed curves in Fig. A.3). This mismatch in line width was already seen in the average profiles (Fig. 8).

	Fig. A.1 Average velocities at different line depression levels for all lines but 630.25 nm in the observations (solid lines), the HD-SPAT-SPEC (dashed lines) and the HD-FR (solid black line).
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Appendix A.2: Rms fluctuations

	Fig. A.2 Average intensity at different line depression levels in the observations (solid lines), the HD-SPAT-SPEC (dashed lines) and the HD-FR (solid black line).
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	Fig. A.3 Average line width at different line depression levels in the observations (solid lines), the HD-SPAT-SPEC (dashed lines) and the HD-FR (solid black line).
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	Fig. A.4 Rms fluctuations in the line properties at different line depression levels for all lines but 630.25 nm and 557.6 nm in the observations (solid lines), the HD-SPAT-SPEC (dashed lines) and the HD-FR (solid black line). Top two rows: velocity. Middle two rows: intensity. Bottom two rows: line width.
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The rms fluctuations in the line properties at different line depression levels for all but the 630.25 nm and 557.6 nm lines are shown in Fig. A.4. The curves are all to some extent similar to the corresponding ones of the 630.25 nm line that are described in Sect. 5.3. The most noteworthy feature is that the fluctuations in the HD-SPAT-SPEC never significantly exceed the observed fluctuations in any of the parameters, but rather tend to show slightly lower values. Some parameters show a quite close match between observations and the degraded HD simulation, e.g. the rms velocities for all lines or the intensity rms for the near-IR lines.

Appendix B: Line parameters of 557.6 nm

	Fig. B.1 Histograms of the line parameters for the 557.6 nm line. Black lines: observations. Red lines: degraded HD simulation.
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	Fig. B.2 Rms fluctuations in the line properties at different line depression levels for the 557.6 nm line in the observations (solid lines), the HD-SPAT-SPEC (dashed lines) and the HD-FR (solid black line). Top: bisector velocity. Middle: bisector intensity. Bottom: line width.
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Figure B.1 shows histograms of all line parameters of the Fe i line at 557.6 nm for completeness. The 557 nm data were intended to be used for an abundance determination and were therefore recorded even under bad seeing conditions. This quite limits their usefulness for deriving spatial variations of line parameters because all observed spectra already represent some large-scale spatial average. The line is the only one in the sample with a Landé factor of zero, i.e. not sensitive to Zeeman broadening. It thus only reacts to the thermodynamic properties of the atmosphere and not directly to the magnetic field. The line parameters (Fig. B.1) show some deviation between the observations and the HD-SPAT-SPEC, especially the FWHM and the equivalent width. This is most likely related more to the settings in the spectral synthesis, i.e. the method for the inclusion of line broadening, than the thermodynamics themselves. The rms fluctuations in the line properties at different line depression levels (Fig. B.2) in observations and the HD-SPAT-SPEC are more similar than the histograms of line parameters. They show again lower fluctuations in the HD-SPAT-SPEC than in the observations. The 557.6 nm line will be most important in the comparison of the thermodynamic characteristics between the field-free, purely HD and the MHD simulations of increasing average magnetic flux. In the present context, this line shows no prominent deviations from the other Zeeman-sensitive lines in its behaviour.

© ESO, 2013