Titanium abundances in late-type stars

II. Grid of departure coefficients and application to a sample of 70 000 stars

¹ Department of Astronomy, Stockholm University, AlbaNova University Centre, Roslagstullsbacken, 106 91 Stockholm, Sweden
e-mail: jack.mallinson@astro.su.se
² Theoretical Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516 751 20 Uppsala, Sweden

Received: 10 August 2023
Accepted: 20 February 2024

Abstract

Context. Rapidly growing datasets from stellar spectroscopic surveys are providing unprecedented opportunities to analyse the chemical evolution history of our Galaxy. However, spectral analysis requires accurate modelling of synthetic stellar spectra for late-type stars, for which the assumption of local thermodynamic equilibrium (LTE) has been shown to be insufficient in many cases. Errors associated with LTE can be particularly large for Ti I, which is susceptible to over-ionisation, particularly in metal-poor stars.

Aims. The aims of this work are to study and quantify the 1D non-LTE effects on titanium abundances across the Hertzsprung-Russell diagram for a large sample of stars.

Methods. A large grid of departure coefficients, β_ν, were computed on standard MARCS model atmospheres. The grid extends from 3000 K to 8000 K in T_eff, −0.5 dex to +5.5 dex in log g, and −5.0 to +1.0 in [Fe/H], with non-LTE effects in this grid reaching up to 0.4 dex. This was used to compute abundance corrections that were subsequently applied to the LTE abundances of over 70 000 stars selected from the GALAH survey in addition to a smaller sample of literature Keck data for metal-poor dwarfs.

Results. The non-LTE effects grow towards lower [Fe/H], lower log g, and higher T_eff, with a minimum and maximum ΔA(Ti)_Ti I of 0.02 and 0.19 in the GALAH sample. For metal-poor giants, the non-LTE modelling reduces the average ionisation imbalance (Δ_I−II) from −0.11 dex to −0.01 dex at [Fe/H] = −1.7, and the enhancement in titanium abundances from Ti I lines results in a [Ti/Fe] versus [Fe/H] trend that more closely resembles the behaviour of Ti II at low metallicities. At higher metallicities, the results are limited by the precision of the GALAH DR3 LTE abundances and the effects are within the errors. For the most metal-poor dwarfs from the Keck sample, the average ionisation imbalance increases from −0.1 dex to +0.2 dex, a shortcoming that is consistent with previous 1D non-LTE studies and which we speculate could be related to 3D effects.

Conclusions. Non-LTE effects on titanium abundances are significant. Neglecting them may alter our understanding of Galactic chemical evolution. We have made our grid of departure coefficients publicly available, with the caveat that the Ti abundances of metal-poor dwarfs need further study in 3D non-LTE.