Three-dimensional hydrodynamical CO5BOLD model atmospheres of red giant stars III. Line formation in the atmospheres of giants located close to the base of the red giant branch

Aims. We utilize state-of-the-art three-dimensional (3D) hydrodynamical and classical 1D stellar model atmospheres to study the influence of convection on the formation properties of various atomic and molecular spectral lines in the atmospheres of four red giant stars, located close to the base of the red giant branch, RGB (T-eff approximate to 5000 K, log g = 2.5), and characterized by four different metallicities, [M/H] = 0.0, -1.0, -2.0, -3.0. Methods. The role of convection in the spectral line formation is assessed with the aid of abundance corrections, i. e., the differences in abundances predicted for a given equivalent width of a particular spectral line with the 3D and 1D model atmospheres. The 3D hydrodynamical and classical ID model atmospheres used in this study were calculated with the (COBOLD)-B-5 and 1D LHD codes, respectively. Identical atmospheric parameters, chemical composition, equation of state, and opacities were used with both codes, therefore allowing a strictly differential analysis of the line formation properties in the 3D and 1D models. Results. We find that for lines of certain neutral atoms, such as Mg I, Ti I, Fe I, and Ni, the abundance corrections strongly depend both on the metallicity of a given model atmosphere and the line excitation potential, chi. While abundance corrections for all lines of both neutral and ionized elements tend to be small at solar metallicity (<=+/- 0.1 dex), for lines of neutral elements with low ionization potential and low-to-intermediate X they quickly increase with decreasing metallicity, reaching in their extremes -0.6 to -0.8 dex. In all such cases the large abundance corrections are due to horizontal temperature fluctuations in the 3D hydrodynamical models. Lines of neutral elements with higher ionization potentials (E-ion greater than or similar to 10 eV) generally behave very similarly to lines of ionized elements characterized by low ionization potentials (E-ion less than or similar to 6 eV). In the latter case, the abundance corrections are small (generally, <=+/- 10.1 dex) and are caused by approximately equal contributions from the horizontal temperature fluctuations and differences between the temperature profiles in the 3D and ID model atmospheres. Abundance corrections of molecular lines are very sensitive to the metallicity of the underlying model atmosphere and may be larger (in absolute value) than similar to-0.5 dex at [M/H] = -3.0 (similar to-1.5 dex in the case of CO). At fixed metallicity and excitation potential, the abundance corrections show little variation within the wavelength range studied here, 400-1600 nm. We also find that an approximate treatment of scattering in the 3D model calculations (i. e., ignoring the scattering opacity in the outer, optically thin, atmosphere) leads to abundance corrections that are altered by less than similar to 0.1 dex, both for atomic and molecular (CO) lines, with respect to the model where scattering is treated as true absorption throughout the entire atmosphere, with the largest differences for the resonance and low-excitation lines.