Oxygen and Sodium Abundances in M13 (NGC 6205) Giants: Linking Globular Cluster Formation Scenarios, Deep Mixing, and Post-RGB Evolution

We present O, Na, and Fe abundances, as well as radial velocities, for 113 red giant branch (RGB) and asymptotic giant branch (AGB) stars in the globular cluster M13. The abundances and velocities are based on spectra obtained with the WIYN-Hydra spectrograph, and the observations range in luminosity from the horizontal branch (HB) to RGB-tip. The results are examined in the context of recent globular cluster formation scenarios. We find that M13 exhibits many key characteristics that suggest its formation and chemical enrichment are well-described by current models. Some of these observations include: the central concentration of O-poor stars, the notable decrease in [O/Fe] (but small increase in [Na/Fe]) with increasing luminosity that affects primarily the "extreme" population, the small fraction of stars with halo-like composition, and the paucity of O-poor AGB stars. In agreement with recent work, we conclude that the most O-poor M13 giants are likely He-enriched and that most (all?) O-poor RGB stars evolve to become extreme HB and AGB-manqu\'e stars. In contrast, the "primordial" and "intermediate" population stars appear to experience standard HB and AGB evolution.