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 asymptotic giant branch stars and H burning in the convective cores of supermassive and fast-rotating massive main-sequence (MS) stars, only the supermassive MS stars with M > 104 M-circle dot 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 (NGC 6205) and its mixtures with 50 and 90 per cent of the material partially processed in H burning in the 6 x 10(4) M-circle dot 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 anticorrelation. We evolve these stars from the zero-age MS to the red giant branch (RGB) tip with the thermohaline and parametric prescriptions for the RGB extra mixing. We find that the He-3-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 M-V in the globular cluster NGC5466 that does not have the primordial abundance variations.