On the iron ionization balance of cool stars

High-resolution spectroscopic studies of solar-type stars have revealed higher iron abundances derived from singly ionized species compared to neutral, violating the ionization equilibrium under the assumption of local thermodynamic equilibrium. In this work, we investigate the overabundances of Fe ii lines reported in our previous work for a sample of 451 solar-type HARPS stars in the solar neighborhood. The spectroscopic surface gravities of this sample, which emerge from the ionization balance, appear underestimated for the K-type stars. In order to understand this behaviour, we search our Fe ii line list for unresolved blends and outliers. First, we use the Vienna Atomic Line Database to identify possible unresolved blends around our lines and calculate which ones are strong enough to cause overestimations in the equivalent width measurements. Second, for our sample we use reference parameters (effective temperature and metallicity) and the Gaia DR2 parallaxes to derive surface gravities (trigonometric gravities) and calculate the Fe i and Fe ii abundances from different line lists. We exclude the Fe ii lines which produce overabundances above 0.10 dex. The derived surface gravities from the clean line list are now in agreement with the trigonometric. Moreover, the difference between Fe i and Fe ii abundance does not show now a correlation with the effective temperature. Finally, we show that the ionization balance of Ti can provide better estimates of surface gravities than iron. With this analysis, we provide a solution to the ionization balance problem observed in the atmospheres of cool dwarfs.