Kinetic equilibrium of iron in the atmospheres of cool stars - III. The ionization equilibrium of selected reference stars

Non-LTE line formation calculations of Fe I are performed for a small number of reference stars to investigate and quantify the efficiency of neutral hydrogen collisions. Using the atomic model that was described in previous publications, the final discrimination with respect to hydrogen collisions is based on the condition that the surface gravities as determined by the Fe I/Fe II ionization equilibria are in agreement with their astrometric counterparts obtained from HIPPARCOS parallaxes. High signal-to-noise, high-resolution echelle spectra are analysed to determine individual profile fits and differential abundances of iron lines. Depending on the choice of the hydrogen collision scaling factor S(H), we find deviations from LTE in Fe I ranging from 0.00 (S(H) = infinity) to 0.46 dex (S(H) = 0 for HD 140283) in the logarithmic abundances while Fe II follows LTE. With the exception of Procyon, for which a mild temperature correction is needed to fulfil the ionization balance, excellent consistency is obtained for the metal-poor reference stars if Balmer profile temperatures are combined with S(H) = 3. This value is much higher than what is found for simple atoms like Li or Ca, both from laboratory measurements and inference of stellar analyses. The correct choice of collisional damping parameters ("van-der-Waals" constants) is found to be generally more important for these little evolved metal-poor stars than considering departures from LTE. For the Sun the calibrated value for S(H) leads to average Fe I non-LTE corrections of 0.02 dex and a mean abundance from Fe I lines of log epsilon(Fe) = 7.49 +/- 0.08. We confront the deduced stellar parameters with comparable spectroscopic analyses by other authors which also rely on the iron ionization equilibrium as a gravity indicator. On the basis of the HIPPARCOS astrometry our results are shown to be an order of magnitude more precise than published data sets, both in terms of offset and star-to-star scatter.