2009A&A...495..297M

Non-local thermodynamical equilibrium (non-LTE) line formation for singly-ionized and doubly-ionized praseodymium is considered for a range of effective temperatures between 7250K and 9500K. We evaluate the influence of departures from LTE on Pr abundance determinations and determine a distribution of the Pr abundance in the atmosphere of the roAp star HD24712 from a non-LTE analysis of the PrII and PrIII lines. A comprehensive model atom for PrII/III is presented based on the measured and the predicted energy levels, in total, 6708 levels of PrII and PrIII and the ground state of PrIV. Calculations of the PrII energy levels and oscillator strengths for the transitions in PrII and PrIII are described. The dependence of non-LTE effects on the atmospheric parameters is discussed. At T_eff≥8000K, departures from LTE lead to the overionization of PrII and, therefore, to systematically depleted total absorption in the line and positive abundance corrections. At the lower temperatures, different lines of PrII may be either weakened or amplified depending on the line strength. The non-LTE effects strengthen the PrIII lines and lead to negative abundance corrections. Non-LTE corrections grow with effective temperature for the PrII lines, and, in contrast, they decline for the PrIII lines. The PrII/III model atom is applied to determine the Pr abundance in the atmosphere of the roAp star HD24712 from the lines of two ionization stages. In the chemically uniform atmosphere with [Pr/H]=3, the departures from LTE may explain only a small part (approximately 0.3dex) of the difference between the LTE abundances derived from the PrII and PrIII lines (≃2dex). We find that the lines of both ionization stages are fitted for the vertical distribution of praseodymium, where the Pr enriched layer with [Pr/H]≥4 exists in the outer atmosphere at logτ₅₀₀₀←4. The departures from LTE for PrII/III are strong in the stratified atmosphere and have the opposite sign for the PrII and PrIII lines. The praseodymium stratification analysis of roAp stars has to be performed based on non-LTE line formation. Using the revised partition function of PrII and experimental transition probabilities, we determine the solar non-LTE abundance to be log(Pr/H)_☉=-11.15±0.08.