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

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5. Solar Fe line shapes

The Doppler shifts introduced by the convective flow velocities in the photosphere cause significant line broadening beyond the thermal, radiative and collisional broadening. Fig. 8 shows a few examples of spatially and temporally averaged Fe I and Fe II lines at disk-center calculated using the 3D solar simulation together with the corresponding observed intensity profiles; additional examples are given in Paper II. Clearly the agreement is very satisfactory for unblended Fe I and Fe II lines with almost a perfect match. In contrast, theoretical 1D profiles are clearly discrepant in spite of the presence of both a micro- and macroturbulence (as exemplified by the Fe I 621.9 nm line which is shown in the middle panel of Fig. 8). The residual intensities amount to only [FORMULA], which is accomplished without any micro- or macroturbulent broadening. The FWHM of the Fe lines typically agree to within 1%. Fig. 9 shows the disk-integrated flux profiles of two Fe I lines as compared with the solar flux atlas of Kurucz et al. (1984) and again the agreement is very encouraging. In fact, given the good agreement in general for both intensity and flux profiles, blending lines, which may otherwise have gone undetected in a 1D analysis, are easily identified.

[FIGURE] Fig. 8. Some examples of spatially and temporally averaged disk-center Fe I and Fe II lines (diamonds) compared with the observed solar atlas (solid lines, Brault & Neckel 1987). Also shown are the residual intensities (observed - predicted) to emphasize the remaining minor differences; minor blends not included in the spectral synthesis are clearly seen in some of the line wings. The predicted profiles have been convolved with a sinc-function to account for the finite spectral resolution of the solar atlas. Minor corrections to the observed wavelengths ([FORMULA] m s-1) and continuum level ([FORMULA]) have been allowed to improve the fits. The Fe lines are almost perfectly matched by the theoretical profiles, which implies that the rms velocity amplitudes in the simulations are very close to the real values in the solar photosphere. For comparison the best fit 1D profile for the Fe I 621.9 nm line is also shown (thin solid line in the middle right panel), which has been computed with the Holweger-Müller (1974) model atmosphere, log[FORMULA] (to achieve the same equivalent width as the 3D profile), [FORMULA] km s-1 and convolved with a Gaussian macroturbulence of 1.6 km s-1 to have the correct line depth (radial-tangential macroturbulence is not applicable for intensity profiles, Gray 1992); clearly the agreement is much inferior in spite of the adjustable broadening parameters due to the neglect of convective velocities and spatial inhomogeneities

[FIGURE] Fig. 9. The predicted flux profiles of the Fe I 608.2 and 621.9 nm lines (diamonds) compared with the solar flux atlas (solid lines, Kurucz et al. 1984). The theoretical lines have been disk-integrated using a solar rotational velocity of [FORMULA] km s-1 and convolved with sinc-function to account for the finite spectral resolution of the FTS-atlas

Although the overall agreement is very satisfactory, it is clear from a closer inspection of Figs. 8 and 9 that there are systematic discrepancies in the line profiles which are appearent in most intensity and flux profiles, in particular the weaker lines. The cores of the predicted lines tend to be slightly too shallow while the near line wings are somewhat too broad, which suggests a slightly over-estimated rms vertical velocity amplitude in the solar simulation. The slightly problematic line cores may also signal departures from LTE (cf. Rutten & Kostik 1982), which is more likely to affect the cores than the wings. Furthermore, the cores of intermediate strong lines tend to be displaced compared with observations; the latter feature will be discussed further in Sects. 6 and 7. It should not come as a surprise that the cores of the stronger lines show discrepancies, since the highest atmospheric layers are likely the least realistic due to still missing ingredients in the simulations and spectral synthesis in terms of e.g. departures from LTE and the inexact line blanketing treatment in the actual convection simulation.

The minor disagreements shown by the Fe lines are very important, since they point to how the simulations can be improved further. Prior to the convection simulations used here, we have carried out several similar solar simulations which differed from the present ones, most notably in terms of equation-of-state and opacities (Gustafsson et al. 1975 with subsequent updates vs. Mihalas et al. 1988 and Kurucz 1993), height extension ([FORMULA] vs. -1.0 Mm) and numerical resolution (100 x 100 x 82, 50 x 50 x 82 and 50 x 50 x 63 vs. 200 x 200 x 82). In all cases they suffered from more pronounced problems in terms of line asymmetries, which were subsequently addressed with the more refined and improved simulations. However, it is noteworthy that the overall shapes of weak Fe lines illustrated in Figs. 8 and 9 were even better described with the previous equation-of-state and line opacities (Gustafsson et al. 1975 with subsequent updates), as seen Fig. 10, although with a slightly smaller Fe abundance. One may speculate that the older equation-of-state better describes the conditions typical of the line-forming layers than the more recent version (Mihalas et al. 1988) which has been optimized for stellar interiors. But it may also be coincidental, since the differences in line profiles are relatively small and there are also additional differences in terms of resolution (253 x 253 x 163) and [FORMULA] (-0.6 Mm) between the two simulations. A further investigation into the matter would, however, be interesting.

[FIGURE] Fig. 10. The predicted spatially and temporally averaged profile of the Fe I 608.2 line (diamonds) using a solar simulation based on a previous equation-of-state and line opacities (Gustafsson et al. 1975 with subsequent updates instead of Mihalas et al. 1988 and Kurucz 1993) compared with the solar disk-center intensity atlas (solid lines, Brault & Neckel 1987). The agreement is even better than the corresponding profile shown in Fig. 8

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Online publication: July 7, 2000