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We study the abundances of Na, Mg, and K in the atmospheres of 32 RGB starsin the Galactic globular cluster (GGC) 47 Tuc, with the goal to investigate thepossible existence of Na-K and Mg-K correlations/anti-correlations, similar tothose that were recently discovered in two other GGCs, NGC 2419 and 2808. Theabundances of K, Na, and Mg were determined using high-resolution 2df spectraobtained with the AAT. The 1D NLTE abundance estimates were obtained using 1Dhydrostatic ATLAS9 model atmospheres and spectral line profiles synthesizedwith the MULTI package. We also used 3D hydrodynamical CO5BOLD and 1Dhydrostatic LHD model atmospheres to compute 3D-1D LTE abundance corrections,$\Delta_{\rm 3D-1D~LTE}$, for the spectral lines of Na, Mg, and K used in ourstudy. These abundance corrections were used to understand the role ofconvection in the formation of spectral lines, as well as to estimate thedifferences in the abundances obtained with the 3D hydrodynamical and 1Dhydrostatic model atmospheres. The average element-to-iron abundance ratios andtheir RMS variations due to star-to-star abundance spreads determined in oursample of RGB stars were $\langle{\rm [Na/Fe]}\rangle^{\rm1D~NLTE}=0.42\pm0.13$, $\langle{\rm [Mg/Fe]}\rangle^{\rm 1D~NLTE}=0.41\pm0.11$,and $\langle{\rm [K/Fe]}\rangle^{\rm 1D~NLTE}=0.05\pm0.14$. We found nostatistically significant relations between the abundances of the threeelements studied here. Also, there were no abundance trends with the distancefrom the cluster center, nor any statistically significant relations betweenthe abundance/abundance ratios and absolute radial velocities of individualstars. All these facts suggest the similarity of K abundance in stars thatbelong to different generations in 47 Tuc which, in turn, may hint thatevolution of K in this particular cluster was unrelated to the nucleosynthesisof Na and/or Mg.

Abundances of Na, Mg, and K in the atmospheres of red giant branch stars of Galactic globular cluster 47 Tucanae