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

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3. Spectral line calculations and atomic data

From the full solar convection simulation, which covers two solar hours, a shorter sequence of 50 min with snapshots stored every 30 s was chosen for the subsequent spectral line calculations. The adopted snapshots have a temporally averaged effective temperature very close to the observed nominal [FORMULA]K for the Sun (Willson & Hudson 1988): [FORMULA] K where the quoted range is the standard deviation of the individual snapshots. For our present purposes the time coverage is sufficient to obtain statistically significant spatially and temporally averaged line profiles and shifts, as verified by test calculations after dividing the snapshots in various sub-groups. Even as short sequences as 10 min produced line asymmetries and shifts to within 50 m s-1 of the full calculations. In order to improve the vertical sampling, the simulation was interpolated to a finer depth scale with the same number of depth points but only extending down to layers with minimum continuum optical depths of [FORMULA] ([FORMULA] km below [FORMULA] rather than [FORMULA]Mm in the original simulation). Prior to the line transfer computations, the snapshots were also interpolated to a coarser grid of 50 x 50 x 82 but with the same horizontal dimension to save computing time; various tests assured that the procedure did not introduce any differences in the spatially averaged line shapes or asymmetries. The Doppler shifts introduced by the convective motions in the 3D model atmosphere were correctly accounted for in the solution of the 3D spectral line transfer. In most cases, intensity profiles at the center of the solar disk ([FORMULA]) were considered, which have been calculated for every column of the interpolated snapshots, before spatial and temporal averaging and normalization. A few lines where, however, computed under different viewing angles to allow a disk-integration for comparison with published solar flux atlases (Kurucz et al. 1984). The assumption of LTE in the ionization and excitation balances and for the source function in the line transfer calculations ([FORMULA]) have been made throughout in the present study. The background continuous opacities were calculated using the Uppsala opacity package (Gustafsson et al. 1975 and subsequent updates).

Fe lines are the most natural tools to study line shapes and asymmetries in stars: Fe is an abundant element with a complex atomic structure which ensures there are many useful lines of the appropriate strength; there exists accurate laboratory measurements for the necessary atomic data such as transition probabilities and wavelengths (e.g. Blackwell et al. 1995; Nave et al. 1994); the Fe nuclei have a large atomic mass which minimizes the thermal velocities; the influence from isotope and hyperfine splitting should be negligible (e.g. Kurucz 1993); and LTE is a reasonable approximation for Fe (e.g. Shchukina & Trujillo Bueno 2000), at least for 1D model atmospheres of solar-type stars (3D NLTE studies of Fe may, however, reveal larger departures from NLTE as speculated by e.g. Nordlund 1985 and Kostik et al. 1996). By studying a large sample of neutral and ionized Fe lines with different atomic data and therefore line strengths, the solar photospheric convection at varying atmospheric layers can be probed by analysing the resulting line shifts and asymmetries. The Fe lines and their atomic data are the same as described in detail in Paper II. In particular, accurate laboratory wavelengths for the Fe I and Fe II lines were taken from Nave et al. (1994) and Johansson (1998, private communication), respectively. The final profiles have been computed with the individual Fe abundances derived in Paper II.

For comparison with observations, the solar FTS disk-center intensity atlas by Brault & Neckel (1987) (see also Neckel 1999) has been used, due to its superior quality over the older Liege atlas by Delbouille et al. (1973) in terms of wavelength calibration (Allende Prieto & García López 1998a,b) and continuum tracement. For flux profiles the solar atlas by Kurucz et al. (1984) has been used, which is also based on FTS-spectra with a similar spectral resolution as the disk-center atlas. The wavelengths for the observed profiles have been adjusted to remove the effects of the solar gravitational redshift (633 m s-1). All spatially averaged theoretical profiles have been convolved with an instrumental profile to account for the finite spectral resolution of the observed atlas. Since the atlas was acquired with a Fourier Transform Spectrograph (FTS), the instrumental profile corresponds to a sinc-function with [FORMULA] in the visual rather than the normal Gaussian (e.g. Gray 1992). The additional instrumental broadening has only a minor (but not entirely negligible) effect on the resulting line asymmetries due to the high resolving power of the FTS.

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© European Southern Observatory (ESO) 2000

Online publication: July 7, 2000
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