5 Spectral Line Formation

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 (1974Jump To The Next Citation Point), 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, 2005Jump To The Next Citation Point, 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, 1956Schröter, 1957Nordlund, 1976Kaisig and Schröter, 1983Dravins, 1990Borrero 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, 1978Jump To The Next Citation PointHermsen, 1982Frutiger et al., 2000Bellot Rubio and Borrero, 2002Ayres et al., 2006Jump To The Next Citation Point).

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., 1981Jump To The Next Citation PointNordlund, 1985aDravins and Nordlund, 1990aJump To The Next Citation Point,bJump To The Next Citation PointBruls and Rutten, 1992Atroshchenko and Gadun, 1994Gadun and Pavlenko, 1997Gadun et al., 1997Uitenbroek, 2000aJump To The Next Citation PointAsplund et al., 2000aJump To The Next Citation Point,bJump To The Next Citation Point,cJump To The Next Citation PointAsplund, 2000Jump To The Next Citation PointAsplund et al., 2004Jump To The Next Citation PointAsplund, 2004Jump To The Next Citation PointAsplund et al., 2005aJump To The Next Citation Point,bJump To The Next Citation PointAsplund, 2005Jump To The Next Citation PointAllende Prieto et al., 2001Jump To The Next Citation Point2002Jump To The Next Citation PointSteffen and Holweger, 2002Jump To The Next Citation PointScott et al., 2006Jump To The Next Citation PointLjung et al., 2006Jump To The Next Citation PointLudwig and Steffen, 2007Jump To The Next Citation PointCaffau and Ludwig, 2007Jump To The Next Citation PointCaffau et al., 2007aJump To The Next Citation Point,bJump To The Next Citation Point2008bJump To The Next Citation Point,aJump To The Next Citation PointMucciarelli et al., 2008Jump To The Next Citation PointCenteno and Socas-Navarro, 2008Jump To The Next Citation PointAyres, 2008Jump To The Next Citation PointBasu and Antia, 2008Jump To The Next Citation PointMeléndez and Asplund, 2008Jump To The Next Citation Point). 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, 2001Jump To The Next Citation Point) or in 3D (e.g., Nordlund, 1985bKiselman and Nordlund, 1995Jump To The Next Citation PointKiselman, 19971998Jump To The Next Citation Point2001Uitenbroek, 1998Barklem et al., 2003Asplund et al., 2003Jump To The Next Citation Point2004Jump To The Next Citation PointAllende Prieto et al., 2004Jump To The Next Citation Point). A recent review on 3D spectral line formation is given in Asplund (2005Jump To The Next Citation Point).

 5.1 Spatially resolved lines
 5.2 Spatially averaged lines
 5.3 Solar abundance analysis
  5.3.1 Carbon
  5.3.2 Nitrogen
  5.3.3 Oxygen
  5.3.4 Fe
  5.3.5 Other elements
  5.3.6 Implications and reliability of the new solar abundances

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