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

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1. Introduction

A proper understanding of convection has for a long time been one of the greatest challenges for stellar astrophysics. Since convection can strongly influence both the stellar evolution and the emergent stellar spectra, this uncertainty also carries over to other fields of astrophysics, such as galactic evolution and cosmology. Convection also plays a dominant role in various processes besides energy transport and stellar evolution, perhaps most notably mixing of nuclear-processed material, magnetic activity, chromospheric heating and stellar pulsations. Convection is furthermore of relevance in searches for extra-solar planets by introducing differential spectral line shifts that are likely to change periodically with solar-like cycles, and may then affect the measurements of periodic variations induced by orbiting companions.

The convection zone in late-type stars extends to the visible surface layers and thereby influences the emergent spectrum, from which virtually all information about the stars is deduced. For the Sun, the directly observable manifestation is granulation: an evolving pattern of brighter (warmer) rising material with darker (cooler) sinking gas in between, driven by the radiative cooling in a thin surface layer. Convection also leaves distinct signatures in the spectral lines in the form of line shifts and asymmetries (e.g. Gray 1980; Dravins et al. 1981; Dravins 1982; Dravins & Nordlund 1990a,b). For late-type stars, the bisectors of unblended lines have a characteristic [FORMULA]-shape, which results from the differences in line strength, continuum level, area coverage and Doppler shift between up- (granules) and downflows (intergranular lanes). Weak lines normally only show the upper part of the [FORMULA]-shape and have convective blueshifts (after removing the effects of the gravitational redshift). The cores of stronger lines are formed in or above the convective overshoot layers and therefore have smaller or non-existent blueshifts (Allende Prieto & García López 1998a,b). Solar transition region and coronal emission lines can, however, show significant redshifts of several km s-1 (Doschek et al. 1976).

The possibility to obtain spectra of the Sun on an absolute wavelength scale (i.e. corrected for the radial velocity of the Sun relative to the spectrograph) with exceptionally high spectral resolution, signal-to-noise ratio (S/N) and wavelength coverage, makes the Sun an ideal testbench to study the physical conditions in the upper parts of the convection zone. For other stars one has previously been restricted to only a few spectral lines and poorer quality observations. Fortunately the situation has recently improved significantly (e.g. Allende Prieto et al. 1999, 2000), most notably concerning resolution, S/N and the use of carefully wavelength-calibrated spectra covering a large portion of the visual region.

In order to draw the correct conclusions from the observed stellar spectrum it is necessary to have a proper understanding of how convection modifies the atmospheric structure and the spectral line formation. Up to the present, theoretical models of stellar atmospheres have been based on several unrealistic assumptions, such as restriction to a 1-dimensional (1D) stratification in hydrostatic equilibrium with only a rudimentary parametrisation of convection through e.g. the mixing length theory (Böhm-Vitense 1958) or some close relative thereof (Canuto & Mazzitelli 1991). Such models therefore miss entirely the very nature of convection as an inhomogeneous, non-local and time-dependent phenomenon, which is driven by the radiative cooling at the surface. Furthermore, spectral synthesis using classical 1D model atmospheres show poor resemblance with observed spectra. In particular, the predicted line broadening is much too weak (of course, with no knowledge about the convective motions and Doppler shifts, all lines are also perfectly symmetric). To partly cure the problem, two artificial fudge parameters are introduced which the theoretical spectrum is convolved with to mimic the missing broadening: micro- and macroturbulence. In this situation, systematic errors arising from modeling inadequacies in e.g. chemical analyses of stars are far larger than the measuring errors alone. An improved theoretical foundation for the interpretation of stellar spectra is therefore highly desirable, to complement the impressive recent observational advances in terms of S/N, spectral resolution and limiting magnitudes following the new generation of large-aperture telescopes, like the ESO VLT and McDonald HET, and detectors.

With the advent of modern supercomputers, self-consistent 3D radiative hydrodynamical simulations of the surface convection in stars have now become tractable (e.g. Nordlund & Dravins 1990; Stein & Nordlund 1989, 1998; Asplund et al. 1999; Trampedach et al. 1999). These simulations invoke no free parameters like mixing length parameters except the numerical viscosity for stability purposes, yet succeed in reproducing key observational diagnostics such as granulation topology and statistics (Stein & Nordlund 1989, 1998), and helioseismic properties (Rosenthal et al. 1999). In the present paper we present a detailed study of the spectral line formation of Fe lines using such solar surface convection simulations as 3D model atmospheres. The resulting line shapes, shifts and asymmetries are found to compare very satisfactory with the observations, lending strong support to the realism of the simulations. The derived solar Fe abundances from weak and strong Fe I and Fe II lines are presented in an accompanying article (Asplund et al. 2000b, hereafter Paper II). Subsequent papers in the series will deal with Si lines (Asplund 2000, hereafter Paper III) and observed and predicted spatially resolved solar lines (Kiselman & Asplund, in preparation, hereafter Paper IV). Additionally, hydrogen line formation will be the topic of a following article (Asplund et al., in preparation, hereafter Paper V).

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© European Southern Observatory (ESO) 2000

Online publication: July 7, 2000