Non-LTE line formation for heavy elements in four very metal-poor stars

Aims. Stellar parameters and abundances of Na, Mg, Al, K, Ca, Sr, Ba, and Eu are determined for four very metal-poor (VMP) stars (-2.15 >= [Fe/H] >= -2.66). For two of them, HD84937 and HD 122563, the fraction of the odd isotopes of Ba derived for the first time. Methods. Determination of an effective temperature, surface gravity, and element abundances was based on non-local thermodynamic equilibrium (non-LTE) line formation and analysis of high-resolution (R similar to 60 000 and 90 000) high signal-to-noise (S/N >= 200) observed spectra. A model atom for HI is presented. An effective temperature was obtained from the Balmer H-alpha and H-beta line wing fits. The surface gravity was calculated from the Hipparcos parallax if available and the non-LTE ionization balance between Ca I and Ca II. Based on the hyperfine structure affecting the Ba II resonance line lambda 4554, the fractional abundance of the odd isotopes of Ba was derived from a requirement that Ba abundances from the resonance line and subordinate lines of Ba II must be equal. Results. For each star, non-LTE leads to a consistency of T-eff from two Balmer lines and to a higher temperature compared to the LTE case, by up to 60 K. Non-LTE effects are important in spectroscopic determination of surface gravity from the ionization balance between Ca I and Ca II. For each star with a known trigonometric surface gravity, non-LTE abundances from the lines of two ionization stages, Ca I and Ca II, agree within the error bars, while a difference in the LTE abundances consists of 0.23 dex to 0.40 dex for different stars. Departures from LTE are found to be significant for all investigated atoms, and they strongly depend on stellar parameters. For HD84937, the Eu/Ba ratio is consistent with the relative solar system r-process abundances, and the fraction of the odd isotopes of Ba, f(odd), equals 0.43 +/- 0.14. The latter can serve as an observational constraint on r-process models. The lower Eu/Ba ratio and f(odd) = 0.22 +/- 0.15 found for HD 122563 suggest that the s-process or the unknown process has contributed significantly to the Ba abundance in this star.