A non-LTE study of neutral and singly-ionized calcium in late-type stars
  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. Departures from LTE significantly affect the profiles of Ca I lines over the whole range of stellar parameters considered. However, at [Ca/H] >= -2, NLTE abundance correction of individual lines may be small in 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 4226 at [Ca/H] = -4.9. In contrast, 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. For the IR lines of multiplet 3d - 4p, they grow in absolute value with decreasing Ca abundance exceeding 0.4 dex in metal-poor stars with [Fe/H] <= -3. Ca abundances are determined for the Sun, Procyon, 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 $\eps{Ca,\odot}$ = 6.38+-0.01. For Procyon, the mean Ca abundance from Ca I lines is markedly subsolar, [Ca/H] = -0.14+-0.03. The W(Ca I 4226)/W(Ca II 8498) 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). 
L. Mashonkina, A.J. Korn, N. Przybilla