| Abstract
| - Aims. We determined abundances of Mg and K in the atmospheres of 53 (Mg) and 75 (K) turn-off (TO) stars of the Galactic globular cluster 47 Tuc. The obtained abundances, together with those of Li, O, and Na that we had earlier determined for the same sample of stars, were used to search for possible relations between the abundances of K and other light elements, Li, O, Na, and Mg, as well as the connections between the chemical composition of TO stars and their kinematical properties. Methods. Abundances of Mg and K were determined using archival high resolution VLT FLAMES/GIRAFFE spectra, in combination with the one-dimensional (1D) non-local thermodynamic equilibrium (NLTE) spectral synthesis methodology. Spectral line profiles were computed with the MULTI code, using 1D hydrostatic ATLAS9 stellar model atmospheres. We also utilized three-dimensional (3D) hydrodynamical CO 5BOLD and 1D hydrostatic LHD model atmospheres for computing 3D-1D LTE abundance corrections for the spectral lines of Mg and K, in order to assess the influence of convection on their formation in the atmospheres of TO stars. Results. The determined average abundance-to-iron ratios and their root mean square variations due to star-to-star abundance spreads were 〈[Mg/Fe]〉 1D NLTE = 0.47 ± 0.12, and 〈[K/Fe]〉 1D NLTE = 0.39 ± 0.09. Although the data suggest the possible existence of a weak correlation in the [K/Fe]-[Na/Fe] plane, its statistical significance is low. No statistically significant relations between the abundance of K and other light elements were detected. Also, we did not find any significant correlations or anti-correlations between the [Mg/Fe] and [K/Fe] ratios and projected distance from the cluster center. Similarly, no relations between the absolute radial velocities of individual stars and abundances of Mg and K in their atmospheres were detected. The 3D-1D abundance corrections were found to be small (≤0.1 dex) for the lines of Mg and K used in this study, thus indicating that the influence of convection on their formation is small.
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