Simulations of the solar near-surface layers with the CO5BOLD, MURaM, and Stagger codes

Context. Radiative hydrodynamic simulations of solar and stellar surface convection have become an important tool for exploring the structure and gas dynamics in the envelopes and atmospheres of late-type stars and for improving our understanding of the formation of stellar spectra. Aims. We quantitatively compare results from three-dimensional, radiative hydrodynamic simulations of convection near the solar surface generated with three numerical codes ((COBOLD)-B-5, MURaM, and Stagger) and different simulation setups in order to investigate the level of similarity and to cross-validate the simulations. Methods. For all three simulations, we considered the average stratifications of various quantities (temperature, pressure, flow velocity, etc.) on surfaces of constant geometrical or optical depth, as well as their temporal and spatial fluctuations. We also compared observables, such as the spatially resolved patterns of the emerging intensity and of the vertical velocity at the solar optical surface as well as the center-to-limb variation of the continuum intensity at various wavelengths. Results. The depth profiles of the thermodynamical quantities and of the convective velocities as well as their spatial fluctuations agree quite well. Slight deviations can be understood in terms of differences in box size, spatial resolution and in the treatment of non-gray radiative transfer between the simulations. Conclusions. The results give confidence in the reliability of the results from comprehensive radiative hydrodynamic simulations.