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The physical conditions of the solar photosphere change on very small spatialscales both horizontally and vertically. Such a complexity may pose a seriousobstacle to the accurate determination of solar magnetic fields. We examine theapplicability of Milne-Eddington (ME) inversions to high spatial resolutionobservations of the quiet Sun. Our aim is to understand the connection betweenthe ME inferences and the actual stratifications of the atmospheric parameters.We use magnetoconvection simulations of the solar surface to synthesizeasymmetric Stokes profiles such as those observed in the quiet Sun. We theninvert the profiles with the ME approximation. We perform an empirical analysisof the heights of formation of ME measurements and analyze the uncertaintiesbrought about by the ME approximation. We also investigate the quality of thefits and their relationship with the model stratifications. The atmosphericparameters derived from ME inversions of high-spatial resolution profiles arereasonably accurate and can be used for statistical analyses of solar magneticfields, even if the fit is not always good. We also show that the ME inferencescannot be assigned to a specific atmospheric layer: different parameters sampledifferent ranges of optical depths, and even the same parameter may tracedifferent layers depending on the physical conditions of the atmosphere.Despite this variability, ME inversions tend to probe deeper layers in granulesas compared with intergranular lanes.

Applicability of Milne-Eddington inversions to high spatial resolution observations of the quiet Sun