Sodium abundances of AGB and RGB stars in galactic globular clusters I. Analysis and results of NGC 2808

Galactic globular clusters (GC) are known to have multiple stellar populations and be characterised by similar chemical features, e.g. O-Na anti-correlation. While second-population stars, identified by their Na overabundance, have been found from the main sequence turn-off up to the tip of the red giant branch in various Galactic GCs, asymptotic giant branch (AGB) stars have rarely been targeted. The recent finding that NGC 6752 lacks an Na-rich AGB star has thus triggered new studies on AGB stars in GCs, since this result questions our basic understanding of GC formation and stellar evolution theory. In order to compare the Na abundance distributions of AGB and RGB stars in Galactic GCs and investigate whether the presence of Na-rich stars on the AGB is metallicity-dependent, we obtained the high-resolution spectra with the multi-object high-resolution spectrograph FLAMES on ESO/VLT for a sample of AGB and RGB stars in the Galactic GC NGC 2808. The accurate Na abundances were derived for 31 AGB and 40 RGB stars. We find that NGC 2808 has a mean metallicity of -1.11 $\pm$ 0.08 dex, in good agreement with earlier analyses. Comparable Na abundance dispersions are derived for our AGB and RGB samples, with the AGB stars being slightly more concentrated than the RGB stars. The ratios of Na-poor first-population to Na-rich second-population stars are 45:55 in the AGB sample and 48:52 in the RGB sample. NGC 2808 has Na-rich second-population AGB stars, which turn out to be even more numerous - in relative terms - than their Na-poor AGB counterparts and the Na-rich stars on the RGB. Our findings are well reproduced by the fast rotating massive stars scenario and they do not contradict the recent results that there is not an Na-rich AGB star in NGC 6752. NGC 2808 thus joins the larger group of Galactic GCs for which Na-rich second-population stars on the AGB have recently been found.