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

Abstract

We investigate the feasibility of representing a structured multi-dimensional stellar atmosphere with a single one-dimensional average stratification for the purpose of spectral diagnosis of the atmosphere's average spectrum. In particular we construct four different one-dimensional stratifications from a single snapshot of a magneto-hydrodynamic simulation of solar convection: one by averaging its properties over surfaces of constant height, and three different ones by averaging over surfaces of constant optical depth at 500 nm. Using these models we calculate continuum, and atomic and molecular line intensities and their center-to-limb variations. From analysis of the emerging spectra we identify three main reasons why these average representations are inadequate for accurate determination of stellar atmospheric properties through spectroscopic analysis. These reasons are: non-linearity in the Planck function with temperature, which raises the average emergent intensity of an inhomogeneous atmosphere above that of an average-property atmosphere, even if their temperature-optical depth stratification is identical; non-linearities in molecular formation with temperature and density, which raise the abundance of molecules of an inhomogeneous atmosphere over that in a one-dimensional model with the same average properties; the anisotropy of convective motions, which strongly affects the center-to-limb variation of line-core intensities. We argue therefore that a one-dimensional atmospheric model that reproduces the mean spectrum of an inhomogeneous atmosphere necessarily does not reflect the average physical properties of that atmosphere, and are therefore inherently unreliable.