The primordial and evolutionary abundance variations in globular-cluster stars: a problem with two unknowns

We demonstrate that among the potential sources of the primordial abundance variations of the proton-capture elements in globular-cluster stars proposed so far, such as the hot-bottom burning in massive AGB stars and H burning in the convective cores of supermassive and fast-rotating massive MS stars, only the supermassive MS stars with M > 10,000 Msun can explain all the observed abundance correlations without any fine-tuning of model parameters. We use our assumed chemical composition for the pristine gas in M13 (NGC6205) and its mixtures with 50% and 90% of the material partially processed in H burning in the 60,000 Msun MS model star as the initial compositions for the normal, intermediate and extreme populations of low-mass stars in this globular cluster, as suggested by its O-Na anti-correlation. We evolve these stars from the zero-age MS to the RGB tip with the thermohaline and parametric prescriptions for the RGB extra mixing. We find that the 3He-driven thermohaline convection cannot explain the evolutionary decline of [C/Fe] in M13 RGB stars, which, on the other hand, is well reproduced with the universal values for the mixing depth and rate calibrated using the observed decrease of [C/Fe] with MV in the globular cluster NGC5466 that does not have the primordial abundance variations.