A non-LTE study of neutral and singly-ionized calcium in late-type stars

Aims. Non-local thermodynamical equilibrium (NLTE) line formation for neutral and singly-ionized calcium is considered through a range of spectral types when the Ca abundance varies from the solar value down to [Ca/H] = -5. We evaluate the influence of departures from LTE on Ca abundance determinations and inspect the possibility of using Ca I/Ca II line-strength ratios as indicators of surface gravity for extremely metal-poor stars. Methods. A comprehensive model atom for Ca I and Ca II is presented. Accurate radiative and electron collisional atomic data are incorporated. The role of inelastic collisions with hydrogen atoms in the statistical equilibrium of Ca I/II is estimated empirically from inspection of their different influences on the Ca I and Ca II lines in selected stars with well determined stellar parameters and high-quality observed spectra. Results. The dependence of NLTE effects on the atmospheric parameters is discussed. Departures from LTE significantly affect the profiles of Ca I lines over the whole range of stellar parameters being considered. However, at [Ca/H] = -2, NLTE abundance correction of individual lines have a low absolute value due to the different influence of NLTE effects on line wings and the line core. At lower Ca abundances, NLTE leads to systematically depleted total absorption in the line and positive abundance corrections, exceeding +0.5 dex for Ca I lambda 4226 at [Ca/H] = -4.9. In contrast, the NLTE effects strengthen the Ca II lines and lead to negative abundance corrections. NLTE corrections are small, <= 0.02 dex, for the Ca II resonance lines, and they grow in absolute value with decreasing Ca abundance for the IR lines of multiplet 3d-4p, exceeding 0.4 dex in the metal-poor models with [Fe/H] = -3. As a test and first application of the Ca I/II model atom, Ca abundances are determined on the basis of plane-parallel LTE model atmospheres for the Sun, Procyon (F IV-V), and seven metal-poor stars, using high S/ N and high-resolution spectra at visual and near-IR wavelengths. Lines of Ca I and Ca II give consistent abundances for all objects (except Procyon) when collisions with hydrogen atoms are taken into account. The derived absolute solar Ca abundance (from Ca I and Ca II lines) is log epsilon(Ca,circle dot) = 6.38 +/- 0.06. For Procyon, the mean Ca abundance from Ca I lines is markedly subsolar, [Ca/H] = -0.14 +/- 0.03. All metal-poor stars within our sample show an overabundance of calcium relative to iron with [Ca/Fe] abundance ratios of 0.26 to 0.46 that are typical of the halo population. The W(Ca I4226)/W(Ca II8498) equivalent width ratio is predicted to be sensitive to surface gravity for extremely metal-poor stars, while this is not the case for the ratio involving the Ca II resonance line(s).