  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. 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.
A large grid of departure coefficients, $\beta_\nu$, were computed on standard
MARCS model atmospheres. The grid extends from 3000K to 8000K in
T$_{\mathrm{eff}}$, -0.5 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 and additional
metal-poor dwarfs. The non-LTE effects grow towards lower [Fe/H], lower log(g),
and higher T$_{\mathrm{eff}}$, with a minimum and maximum $\Delta$A(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 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. 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.
