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Non-LTE line formation for Si I-II-III in A-B stars and the origin of Si II emission lines in iota Her

A comprehensive model atom was developed for Si I-II-III using the most up-to-date atomic data available so far. Based on the non-local thermodynamic equilibrium (non-LTE = NLTE) line formation for Si I, Si II, and Si III and high-resolution observed spectra, we determined the NLTE abundances for a sample of nine unevolved A9 to B3-type stars with well determined atmospheric parameters. For each star, NLTE reduces substantially the line-to-line scatter for Si II compared with the LTE case and leads to consistent mean abundances from lines of different ionisation stages. In the hottest star of our sample, $ι$ Her, Si II is subject to overionisation that drives emission in the lines arising from the high-excitation (above 12.5 eV) doublet levels. Our NLTE calculations reproduced 10 emission lines of Si II observed in $ι$ Her. The same overionisation effect leads to greatly weakened Si II lines, which are observed in absorption in $ι$ Her. Large positive NLTE abundance corrections (up to 0.98 dex for 5055 A) were useful for achieving consistent mean abundances from lines of the two ionisation stages, Si II and Si III. It was found that the NLTE effects are overestimated for the Si II 6347, 6371 A doublet in $ι$ Her, while the new model atom works well for the cooler stars. At this stage, we failed to understand this problem. We computed for a grid of the NLTE abundance corrections for lines of Si I, Si II, and Si III in the model atmospheres with effective temperatures and surface gravities characteristic of unevolved A-B type stars.