Carbon and oxygen are key tracers of the Galactic chemical evolution ; in particular , a reported upturn in \mathrm { \left [ C / O \right ] } towards decreasing \mathrm { \left [ O / H \right ] } in metal-poor halo stars could be a signature of nucleosynthesis by massive Population III stars .
We reanalyse carbon , oxygen , and iron abundances in 39 metal-poor turn-off stars .
For the first time , we take into account 3D hydrodynamic effects together with departures from local thermodynamic equilibrium ( LTE ) when determining both the stellar parameters and the elemental abundances , by deriving effective temperatures from 3D non-LTE \mathrm { H \upbeta } profiles , surface gravities from Gaia parallaxes , iron abundances from 3D LTE Fe II equivalent widths , and carbon and oxygen abundances from 3D non-LTE C I and O I equivalent widths .
We find that \mathrm { \left [ C / Fe \right ] } stays flat with \mathrm { \left [ Fe / H \right ] } , whereas \mathrm { \left [ O / Fe \right ] } increases linearly up to 0.75 \mathrm { dex } with decreasing \mathrm { \left [ Fe / H \right ] } down to -3.0 \mathrm { dex } .
Therefore \mathrm { \left [ C / O \right ] } monotonically decreases towards decreasing \mathrm { \left [ O / H \right ] } , in contrast to previous findings , mainly because the non-LTE effects for O I at low \mathrm { \left [ Fe / H \right ] } are weaker with our improved calculations .