Aims. The statistical equilibrium of neutral and ionized silicon in the atmospheres of metal-poor stars is discussed. Non-local thermodynamic equilibrium effects are investigated and the silicon abundances in metal-poor stars determined. Methods. We have used high resolution, high signal to noise ratio spectra from the UVES spectragraph at the ESO VLT telescope. Line formation calculations of Si i and Si ii in the atmospheres of metal-poor stars are presented for atomic models of silicon including 174 terms and 1132 line transitions. Recent improved calculations of Si i and Si ii photoionization cross-sections are taken into account, and the influence of the free-free quasi-molecular absorption in the Ly alpha wing is investigated by comparing theoretical and observed fluxes of metal-poor stars. All abundance results are derived from LTE and NLTE statistical equilibrium calculations and spectrum synthesis methods. Results. It is found that the extreme ultraviolet radiation is very important for metal-poor stars, especially for the high temperature, very metal-poor stars. The radiative bound-free cross-sections also play a very important role for these stars. Conclusions. NLTE effects for Si are found to be important for metal-poor stars, in particular for warm metal-poor stars. It is found that these effects depend on the temperature. For warm metal-poor stars, the NLTE abundance correction reaches ~ 0.2 dex relative to standard LTE calculations. Our results indicate that Si is overabundant for metal-poor stars.
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