The effects of numerical resolution on hydrodynamical surface convection simulations and spectral line formation

The computationally demanding nature of radiative-hydrodynamical simulations of stellar surface convection warrants an investigation of the sensitivity of the convective structure and spectral synthesis to the numerical resolution and dimension of the simulations, which is presented here. With too coarse a resolution the predicted spectral lines tend to be too narrow, reflecting insufficient Doppler broadening from the convective motions, while at the currently highest affordable resolution the line shapes have converged essentially perfectly to the observed profiles. Similar conclusions are drawn from the line asymmetries and shifts. Due to the robustness of the pressure and temperature structures with respect to the numerical resolution, strong Fe lines with pronounced damping wings and H lines are essentially immune to resolution effects, and can therefore be used for improved Teff and log g determinations even at very modest resolutions. In terms of abundances, weak Fe I and Fe II lines show a very small dependence (≃ 0.02 dex) while for intermediate strong lines with significant non-thermal broadening the sensitivity increases (<∼ 0.10 dex). Problems arise when using 2D convection simulations to describe an inherent 3D phenomenon, which translates to inaccurate atmospheric velocity fields and temperature and pressure structures. In 2D the theoretical line profiles tend to be too shallow and broad compared with the 3D calculations and observations, in particular for intermediate strong lines. In terms of abundances, the 2D results are systematically about 0.1 dex lower than for the 3D case for Fe I lines. Furthermore, the predicted line asymmetries and shifts are much inferior in 2D with discrepancies amounting to ∼ 200m s. Given these shortcomings and computing time considerations it is better to use 3D simulations of even modest resolution than high-resolution 2D simulations.