Influence of inelastic collisions with hydrogen atoms on the non-LTE modelling of Ca i and Ca ii lines in late-type stars

We performed the non-local thermodynamic equilibrium (non-LTE, NLTE) calculations for Ca i-ii with the updated model atom that includes new quantum-mechanical rate coefficients for Ca i + H i collisions from two recent studies and investigated the accuracy of calcium abundance determinations using the Sun, Procyon, and five metal-poor (MP, −2.6 ≤ [Fe/H] ≤−1.3) stars with well-determined stellar parameters. Including H i collisions substantially reduces over-ionisation of Ca i in the line formation layers compared with the case of pure electronic collisions and thus the NLTE effects on abundances derived from Ca i lines. We show that both collisional recipes lead to very similar NLTE results. As for Ca ii, the classical Drawinian rates scaled by SH = 0.1 are still applied. When using the subordinate lines of Ca i and the high-excitation lines of Ca ii, NLTE provides the smaller line-to-line scatter compared with the LTE case for each star. For Procyon, NLTE removes a steep trend with line strength among strong Ca i lines seen in LTE and leads to consistent [Ca/H] abundances from the two ionisation stages. In the MP stars, the NLTE abundance from Ca ii 8498 Å agrees well with the abundance from the Ca i subordinate lines, in contrast to LTE, where the abundance difference grows towards lower metallicity and reaches 0.46 dex in BD −13°3442 ([Fe/H] = −2.62). NLTE largely removes abundance discrepancies between the high-excitation lines of Ca ii and Ca ii 8498 Å obtained for our four [Fe/H] < −2 stars under the LTE assumption. We investigated the formation of the Ca i resonance line in the [Fe/H] < −2 stars. When the calcium abundance varies between [Ca/H] ≃ −1.8 and −2.3, photon loss in the resonance line itself in the uppermost atmospheric layers drives the strengthening of the line core compared with the LTE case, and this effect prevails over the weakening of the line wings, resulting in negative NLTE abundance correction and underestimation of the abundance derived from Ca i 4226 Å compared with that from the subordinate lines, by 0.08 to 0.32 dex. This problem may be related to the use of classical homogeneous (1D) model atmospheres. The situation is improved when the calcium abundance decreases and the Ca i 4226 Å line formation depths are shifted into deep atmospheric layers that are dominated by over-ionisation of Ca i. However, the departures from LTE are still underestimated for Ca i 4226 Å at [Ca/H] ≃ −4.4 (HE 0557-4840). Consistent NLTE abundances from the Ca i resonance line and the Ca ii lines are found for HE 0107-5240 and HE 1327-2326 with [Ca/H] ≤−5. Thus, the Ca i/Ca ii ionisation equilibrium method can successfully be applied to determine surface gravities of [Ca/H] ≾ −5 stars. We provide the NLTE abundance corrections for 28 lines of Ca i in a grid of model atmospheres with 5000 K ≤ Teff ≤ 6500 K, 2.5 ≤ log g ≤ 4.5, −4 ≤ [Fe/H] ≤ 0, which is suitable for abundance analysis of FGK-type dwarfs and subgiants.

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