Evolution and surface abundances of red giants experiencing deep mixing

We have calculated the evolution of low metallicity red giant stars under the assumption of deep mixing between the convective envelope and the hydrogen burning shell. We find that the extent of the observed abundance anomalies, and in particular the universal O-Na anticorrelation, can be totally explained by mixing which does not lead to significant helium enrichment of the envelope. On the other hand, models with extremely deep mixing and strong helium enrichment predict anomalies of sodium and oxygen, which are much larger than the observed ones. This latter result depends solely on the nucleosynthesis inside the hydrogen burning shell, but not on the details of the mixing descriptions. These, however, influence the evolution of surface abundances with brightness, which we compare with the limited observational material available. Our models allow, nevertheless, to infer details on the depth and speed of the mixing process in several clusters. Models with strong helium enrichment evolve to high luminosities and show an increased mass loss. However, under peculiar assumptions, red giants reach very high luminosities even without extreme helium mixing. Due to the consequently increased mass loss, such models could be candidates for blue horizontal branch stars, and, at the same time, would be consistent with the observed abundance anomalies.