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

The computationally demanding nature of radiative-hydrodynamical simulation s of stellar surface convection warrants an investigation of the sensitivit y of the convective structure and spectral synthesis to the numerical resol ution and dimension of the simulations, which is presented here. With too coarse a resolution the predicted spectral lines tend to be too na rrow, reflecting insufficient Doppler broadening from the convective motion s, while at the currently highest affordable resolution the line shapes hav e converged essentially perfectly to the observed profiles. Similar conclus ions are drawn from the line asymmetries and shifts. Due to the robustness of the pressure and temperature structures with respect to the numerical re solution, strong Fe lines with pronounced damping wings and HI lines are es sentially immune to resolution effects, and can therefore be used for impro ved T-eff and log g determinations even at very modest resolutions. In term s of abundances, weak Fe I and Fe rr lines show a very small dependence (si milar or equal to 0.02 dex) while for intermediate strong lines with signif icant non-thermal broadening the sensitivity increases (less than or simila r to 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 profile s tend to be too shallow and broad compared with the 3D calculations and ob servations, in particular for intermediate strong lines. In terms of abunda nces, the 2D results are systematically about 0.1 dex lower than for the 3D case for Fe I lines. Furthermore, the pre dieted line asymmetries and shif ts are much inferior in 2D with discrepancies amounting to similar to 200 m s(-1). Given these shortcomings and computing time considerations it is bet ter to use 3D simulations of even modest resolution than high-resolution 3D simulations.