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We investigate the feasibility of representing a structured multi-dimensionalstellar atmosphere with a single one-dimensional average stratification for thepurpose of spectral diagnosis of the atmosphere's average spectrum. Inparticular we construct four different one-dimensional stratifications from asingle snapshot of a magneto-hydrodynamic simulation of solar convection: oneby averaging its properties over surfaces of constant height, and threedifferent ones by averaging over surfaces of constant optical depth at 500 nm.Using these models we calculate continuum, and atomic and molecular lineintensities and their center-to-limb variations. From analysis of the emergingspectra we identify three main reasons why these average representations areinadequate for accurate determination of stellar atmospheric properties throughspectroscopic analysis. These reasons are: non-linearity in the Planck functionwith temperature, which raises the average emergent intensity of aninhomogeneous atmosphere above that of an average-property atmosphere, even iftheir temperature-optical depth stratification is identical; non-linearities inmolecular formation with temperature and density, which raise the abundance ofmolecules of an inhomogeneous atmosphere over that in a one-dimensional modelwith the same average properties; the anisotropy of convective motions, whichstrongly affects the center-to-limb variation of line-core intensities. Weargue therefore that a one-dimensional atmospheric model that reproduces themean spectrum of an inhomogeneous atmosphere necessarily does not reflect theaverage physical properties of that atmosphere, and are therefore inherentlyunreliable.

Why one-dimensional models fail in the diagnosis of average spectra from inhomogeneous stellar atmospheres