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.
