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Astron. Astrophys. 359, 729-742 (2000)

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6. Solar Fe line shifts

A major advantage with solar observations compared with corresponding stellar observations is the existence of high-quality spectral atlases given on an absolute velocity scale, which is possible since the differential radial velocity between the Sun and the Earth can be accurately corrected for (e.g. Kurucz et al. 1984; Brault & Neckel 1987; Neckel 1999). Furthermore, the well-determined solar mass and radius allow the solar gravitational redshift of 636 m s-1, or 633 m s-1 for light intercepted on Earth (Lindegren et al. 1999), to be estimated, leaving the remaining shifts to be attributed to convection as pressure shifts and similar line shifts are of much lesser importance (e.g. Allende Prieto 1998). Solar spectral lines show different line shifts depending on the typical depths of formation of the line cores. Unfortunately, the remaining uncertainties in the individual laboratory wavelengths and possible blends cause a scatter of about 100 m s-1 in the observed line shifts, in particular for the weaker lines.

Through the self-consistently calculated convective flows in the solar simulations the predicted line shifts can be directly compared with observations on an absolute wavelength scale. Figs. 11 and 12 show the calculated line shifts for Fe I and Fe II lines, respectively; we prefer to plot the shifts vs line strengths rather than vs line depths as Hamilton & Lester (1999), since due to saturation the latter method will not detect clearly the gravitional redshift plateau (Allende Prieto & García López 1998a). Weaker lines show as expected more prominent blueshifts and Fe II lines more so than Fe I lines due to their in general deeper layers of formation. The maximum predicted blueshift for Fe I lines is 550 m s-1 while it reaches 800 m s-1 for Fe II lines. A trend between line shift and excitation potential is present (Fig. 13) but much less pronounced due to the obscuration introduced by the [FORMULA]- and [FORMULA]-dependencies (cf. Figs. 3, 5 and Hamilton & Lester 1999).

[FIGURE] Fig. 11. Upper panel: The predicted (open circles) and observed (stars) line shifts for Fe I lines as a function of equivalent widths. The equivalent widths are taken from Blackwell et al. (1995), Holweger et al. (1995) and Moore et al. (1966), in this order of preference. Lower panel: The differences between predicted and observed line shifts. The gravitational red-shift of 633 m s-1 has been subtracted from the observed line shifts. The agreement is very good for weak and intermediate strong lines but becomes progressively worse for stronger lines. Most of the scatter for the weaker lines is probably due to uncertainties in laboratory wavelengths and blends

[FIGURE] Fig. 12. Same as Fig. 11 but for the 15 Fe II lines. The equivalent widths are taken from Hannaford et al. (1992)

[FIGURE] Fig. 13. Same as Fig. 11 but as a function of excitation potential of the lower level. In general high excitation lines are formed in deeper layers and thus have larger convective blueshifts. The trend is not as striking as in Fig. 11, since also e.g. the oscillator strength determines the line-formation depth

As clear from Figs. 11 and 12 the predicted line shifts agree well with observations for weak and intermediate strong lines. The average difference for weak ([FORMULA]pm) Fe I lines is [FORMULA] m s-1 ([FORMULA] km s-1), while when including also the intermediate strong lines ([FORMULA]pm) the corresponding difference increases to [FORMULA] m s-1; in these estimates we have not included the Fe I 666.8 nm line ([FORMULA]pm) as we suspect that it has an erroneous laboratory wavelength, since it is significantly more discrepant (300 m s-1) than other lines with similar strengths. The situation is slightly worse for the Fe II lines with a mean difference of [FORMULA] m s-1 for all 15 lines with [FORMULA]pm. However, the laboratory wavelengths for Fe II lines are likely of somewhat poorer quality than the Fe II lines and there are unfortunately only few available lines of the appropriate strengths.

As evident from Figs. 11 and 12, the correspondence between predictions and observations becomes progressively worse for stronger Fe I and Fe II lines; a trend with [FORMULA] in the line shift differences may also extend to weaker Fe II lines, according to Fig. 12. We attribute this effect predominantly to the influence of the outer boundary in the spectral line calculations but departures from LTE may also play a role. The cores of these strong lines have significant optical depths already at the uppermost depth layers where the average vertical velocity is directed downwards, as shown in Fig. 14. This follows from having on average no net mass flux, since the downward moving material in general has smaller densities and thus larger velocities in these layers. Since the temperature-velocity correlations present further in has essentially completely disappeared at these large heights, this results in convective redshifts, which do not seem to be present in the observational evidence (Allende Prieto & García López 1998a). The discrepancy was noticably larger in the simulations with smaller extension (maximum height of 0.6 Mm) and numerical resolution (Asplund et al. 2000a). We therefore consider the effect as a numerical artifact, which should be possible to further reduce by using an improved treatment of the outer boundary and higher numerical resolution. In spite of the remaining shortcomings, differential line shifts are very accurate; the main uncertainty is of observational (blends and laboratory rest wavelengths) nature.

[FIGURE] Fig. 14. The time averaged horizontal average (solid) and rms (dashed) vertical velocity in the solar simulations. Positive vertical velocities indicate downward motion. Note the upturn in [FORMULA] which reaches 400 m s-1 in the uppermost parts of the atmosphere. The horizontal part of the curves at the upper boundary is a consequence of the boundary formulation, which specifies the same vertical velocity in the two top layers

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© European Southern Observatory (ESO) 2000

Online publication: July 7, 2000
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