Non-local thermodynamic equilibrium effects of Ti I in M dwarfs and giants

We present detailed NLTE Ti I calculations in model atmospheres of cool dwarf and giant stars. A fully self-consistent NLTE treatment for a Ti I model atom with 395 levels and 5279 primary bound-bound transitions is included, and we discuss the implication of departures from LTE in this atom for the strengths of Ti I lines and TiO molecular bands in cool star spectra. We show that in the atmospheric parameter range investigated, LTE is a poor approximation to Ti I line formation, as expected from the low collisional rates in cool stars. The secondary effects of Ti I overionization on the TiO number density and the TiO molecular opacities, however, are found to be negligible in the molecular line-forming region for the relatively small parameter range studied in this paper.