The abundance evolution of oxygen, sodium, and magnesium in extremely metal poor intermediate-mass stars: Implications for the self-pollution scenario in globular clusters

We present full stellar evolution and parametric models of the surface abundance evolution of O-16, Ne-22, Na-23 and the magnesium isotopes in an extremely metal poor intermediate- mass star (M-ZAMS = 5 M., where ZAMS stands for the zero- age main sequence, and Z = 0.0001). O-16 and Ne-22 and are injected into the envelope by the third dredge-up following thermal pulses on the asymptotic giant branch. These species and the initially present Mg-24 are depleted by hot bottom burning (HBB) during the interpulse phase. As a result, Na-23, Mg-25, and Mg-26 are enhanced. If the HBB temperatures are sufficiently high for this process to deplete oxygen efficiently, Na-23 is first produced and then depleted during the interpulse phase. Although the simultaneous depletion of O-16 and enhancement of Na-23 is possible, the required fine-tuning of the dredge-up and HBB casts some doubt on the robustness of this process as the origin of the O-Na anticorrelation observed in globular cluster stars. However, a very robust prediction of our models are low Mg-24/Mg-25 and Mg-24/Mg-26 ratios whenever significant O-16 depletion can be achieved. This seems to be in stark contrast to recent observations of the magnesium isotopic ratios in the globular cluster NGC 6752.