Fe II emission lines in Be stars. I. Empirical diagnostic of physical conditions in the circumstellar discs

Aims. The Fe ii emission lines formed in the circumstellar envelopes (CE) of classical Be stars are studied in order to determine whether they are optically thin or optically thick. We also aim at deriving both average Fe ii line excitation temperatures and the extent of their formation region in the CE. Methods. We simultaneously observed several series of Fe ii emission lines in the $\lambda\lambda4230{-}7712$ A wavelength interval and the first members of the hydrogen Balmer series of 18 southern classical Be stars. The optical depth regime that controls the formation of the observed Fe ii lines and the physical parameters of their CE formation region were studied using the empirical self-aborption-curve (SAC) method. Results. Our calculations give an average value of $\tau_{\rm o}=2.4\pm0.9$ for the optical depth of the studied Fe ii lines, which implies that these lines are optically thick in the CE of Be stars. Qualitative indications that Fe ii emission lines should be formed in circumstellar regions close to the central star are inferred from the correlations between Fe ii emission line widths and $V\sin i$. The application of the SAC method to Fe ii emission lines confirms this result, which gives $R_{\rm e}=2.0R_*\pm0.8$ for the extension of the line-forming region. The proximity of the line-forming region to the central star is also supported by the behavior of the source function of Fe ii lines, which rapidly decreases with radii. This prevents the lines from being formed over extended regions and/or far from the star. Finally, the correlations of the central depression in the Balmer emission lines with $V\sin i$ are consistent with the flattened geometrical shapes of CEs.