Formation of Zr I and II lines under non-LTE conditions of stellar   atmospheres
  The non-local thermodynaic equilibrium (non-LTE) line formation for the two ions of zirconium is considered through a range of spectral types when the Zr abundance varies from the solar value down to [Zr/H] = -3. The model atom was built using 148 energy levels of Zr I, 772 levels of Zr II, and the ground state of Zr III. It was shown that the main non-LTE mechnism for the minority species Zr I is ultraviolet overionization. Non-LTE leads to systematically depleted total absorption in the Zr I lines and positive abundance corrections, reaching to 0.33 dex for the solar metallicity models. The excited levels of Zr II are overpopulated relative to their thermodynamic equilibrium populations in the line formation layers due to radiative pumping from the low-excitation levels. As a result, the line source function exceeds the Planck function leading to weakening the Zr II lines and positive non-LTE abundance corrections. Such corrections grow towards lower metallicity and lower surface gravity and reach to 0.34 dex for Teff = 5500 K, log g = 2.0, [M/H] = -2. As a test and first application of the Zr I-Zr II model atom, Zr abundance was determined for the Sun on the basis of 1D LTE model atmosphere. Lines of Zr I and Zr II give consistent within the error bars non-LTE abundances, while the difference in LTE abundances amounts to 0.28 dex. The solar abundance of zirconium obtained with the MAFAGS solar model atmosphere is log eps(Zr) = 2.63+-0.07. 
A. Velichko, L. Mashonkina, H. Nilsson
astro-ph.SR