Context. Although oxygen is an important tracer of Galactic chemical evolution, measurements of its abundance in the atmospheres of the oldest Galactic stars are still scarce and rather imprecise. At the lowest end of the metallicity scale, oxygen can only be measured in giant stars and in most of cases such measurements rely on a single forbidden [O I] 630 nm line that is very weak and frequently blended with telluric lines. Although molecular OH lines located in the ultraviolet and infrared could also be used for the diagnostics, oxygen abundances obtained from the OH lines and the [O I] 630 nm line are usually discrepant to a level of ~0.3-0.4 dex. Aims. We study the influence of convection on the formation of the infrared (IR) OH lines and the forbidden [O I] 630 nm line in the atmospheres of extremely metal-poor (EMP) red giant stars. Methods. We used high-resolution and high signal-to-noise ratio spectra of four EMP red giant stars obtained with the VLT CRIRES spectrograph. For each EMP star, 4-14 IR OH vibrational-rotational lines located in the spectral range of 1514-1548 and 1595-1632 nm were used to determine oxygen abundances by employing standard 1D LTE abundance analysis methodology. We then corrected the 1D LTE abundances obtained from each individual OH line for the 3D hydrodynamical effects. Results. We find that the influence of convection on the formation of [O I] 630 nm line in the atmospheres of EMP giants studied here is minor, which leads to very small 3D-1D abundance corrections (< -0.01 dex). On the contrary, IR OH lines are strongly affected by convection and thus the abundance corrections for these lines are significant, 3D-1D ~ -0.2 ... -0.3 dex. These abundance corrections do indeed bring the 1D LTE oxygen abundances of EMP red giants obtained using IR OH lines into better agreement with those determined from the [O I] 630 nm line.
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