Three-dimensional surface convection simulations of metal-poor stars: The effect of scattering on the photospheric temperature stratification

Context: Three-dimensional (3D) radiative hydrodynamic model atmospheres of metal-poor late-type stars are characterized by cooler upper photospheric layers than their one-dimensional counterparts. This property of 3D model atmospheres can dramatically affect the determination of elemental abundances from temperature-sensitive spectral features, with profound consequences on galactic chemical evolution studies. Aims. We investigate whether the cool surface temperatures predicted by 3D model atmospheres of metal-poor stars can be ascribed to approximations in the treatment of scattering during the modelling phase. Methods. We use the Bifrost code to construct 3D model atmospheres of metal-poor stars and test three different ways to handle scattering in the radiative transfer equation. As a first approach, we solve iteratively the radiative transfer equation for the general case of a source function with a coherent scattering term, treating scattering in a correct and consistent way. As a second approach, we solve the radiative transfer equation in local thermodynamic equilibrium approximation, neglecting altogether the contribution of continuum scattering to extinction in the optically thin layers; this has been the default mode in our previous 3D modelling as well as in present Stagger-Code models. As our third and final approach, we treat continuum scattering as pure absorption everywhere, which is the standard case in the 3D modelling by the CO⁵BOLD collaboration. Results. For all simulations, we find that the second approach produces temperature structures with cool upper photospheric layers very similar to the case in which scattering is treated correctly. In contrast, treating scattering as pure absorption leads instead to significantly hotter and shallower temperature stratifications. The main differences in temperature structure between our published models computed with the Stagger- and Bifrost codes and those generated with the CO ⁵BOLD code can be traced to the different treatments of scattering. Conclusions. Neglecting the contribution of continuum scattering to extinction in optically thin layers provides a good approximation to the full, iterative solution of the radiative transfer equation in metal-poor stellar surface convection simulations, and at a much lower computational cost. Our results also demonstrate that the cool temperature stratifications predicted for metal-poor late-type stars by previous models by our collaboration are not an artifact of the approximated treatment of scattering.