Approximations for non-grey radiative transfer in numerical simulations of the solar photosphere

Realistic simulations of solar (magneto-)convection require an accurate treatment of the non-grey character of the radiative energy transport. Owing to the large number of spectral lines in the solar atmosphere, statistical representations of the line opacities have to be used in order to keep the problem numerically tractable. We consider two statistical approaches, the opacity distribution function (ODF) concept and the multigroup (or opacity binning) method and provide a quantitative assessment of the errors that arise from the application of these methods in the context of 2D/3D simulations. In a first step, the ODF- and multigroup methods are applied to a 1 D model-atmosphere and the resulting radiative heating rates are compared. A number of 4-6 frequency bins is found to warrant a satisfactory modeling of the radiative energy exchange. Further tests in 2D model-atmospheres show the applicability of the multigroup method in realistic situations and underline the importance of a non-grey treatment. Furthermore, we address the question of an appropriate opacity average in multigroup calculations and discuss the significance of velocity gradients for the radiative heating rates.