Since the convection zone reaches up to the optical surface in the Sun, convection directly influences the spectrum formation both by modifying the mean stratification and by introducing inhomogeneities and velocity fields in the photosphere. Traditionally, convection is incorporated in classical 1D theoretical model atmospheres through the rudimentary mixing length theory (Böhm-Vitense, 1958) or some close relative thereof (e.g., Canuto and Mazzitelli, 1991). These convection descriptions are local, 1D, time-independent and ignore crucial 3D energy exchange effects between the radiation field and the gas (see Section 3.12). Reality is very far from this simple-minded picture. It should not come as a surprise then that the predicted emergent spectrum based on such 1D model atmospheres may be hampered by significant systematic errors.
As an alternative to 1D theoretical model atmospheres solar physicists often prefer the use of semi-empirical model atmospheres such as the Holweger and Müller (1974), Vernazza et al. (1976) (better known as VAL3C) and Fontenla et al. (2007) models, in which the temperature structure is inferred from observations, notably continuum center-to-limb variation and strengths of various spectral lines; the first of these model atmospheres is based on an LTE inversion while the others account for departures from LTE. While the uncertainty in the temperature structure arising from convective motion is thus hopefully largely bypassed, such semi-empirical models are still 1D and, like all 1D models, predict insufficient line broadening that require the introduction of the fudge parameters micro- and macroturbulence (see Gray, 2005, for a general discussion). Such semi-empirical models are not easily constructed for stars other than the Sun due to the inability to observe center-to-limb variations on stars.
Going somewhat beyond the standard 1D modeling, it is possible to combine several 1D atmosphere models corresponding to, for example, typical up- and down-flows to construct multi-component models of solar/stellar granulation (Voigt, 1956; Schröter, 1957; Nordlund, 1976; Kaisig and Schröter, 1983; Dravins, 1990; Borrero and Bellot Rubio, 2002). Bar a few notable exceptions, little effort has been invested in studying the possible impact of multi-component models on solar/stellar abundance determinations (Lambert, 1978; Hermsen, 1982; Frutiger et al., 2000; Bellot Rubio and Borrero, 2002; Ayres et al., 2006).
A more ambitious approach is to make use of the multi-dimensional, time-dependent radiative-hydrodynamical simulations of solar surface convection that are described in this review. These simulations may then be employed as a 2D or 3D solar model atmosphere for spectral line formation purposes (e.g., Dravins et al., 1981; Nordlund, 1985a; Dravins and Nordlund, 1990a,b; Bruls and Rutten, 1992; Atroshchenko and Gadun, 1994; Gadun and Pavlenko, 1997; Gadun et al., 1997; Uitenbroek, 2000a; Asplund et al., 2000a,b,c; Asplund, 2000; Asplund et al., 2004; Asplund, 2004; Asplund et al., 2005a,b; Asplund, 2005; Allende Prieto et al., 2001, 2002; Steffen and Holweger, 2002; Scott et al., 2006; Ljung et al., 2006; Ludwig and Steffen, 2007; Caffau and Ludwig, 2007; Caffau et al., 2007a,b, 2008b,a; Mucciarelli et al., 2008; Centeno and Socas-Navarro, 2008; Ayres, 2008; Basu and Antia, 2008; Meléndez and Asplund, 2008). For computational reasons, most of the calculations have assumed LTE but some studies have braved going beyond this approximation, either in 1.5D2 (e.g., Shchukina and Trujillo Bueno, 2001) or in 3D (e.g., Nordlund, 1985b; Kiselman and Nordlund, 1995; Kiselman, 1997, 1998, 2001; Uitenbroek, 1998; Barklem et al., 2003; Asplund et al., 2003, 2004; Allende Prieto et al., 2004). A recent review on 3D spectral line formation is given in Asplund (2005).
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