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Abstract

The treatment of convective boundaries remains an important source of uncertainty within stellar evolution, with drastic implications for the thermally pulsing stars on the asymptotic giant branch (AGB). Various sources are taken as motivation for the incorporation of convective boundary mixing (CBM) during this phase, from s-process nucleosynthesis to hydrodynamical models. In spite of the considerable evidence in favour of the existence of CBM on the pre-AGB evolution, this mixing is not universally included in models of TP-AGB stars. The aim of this investigation is to ascertain the extent of CBM, which is compatible with observations when considering full evolutionary models. Additionally, we investigate a theoretical argument that has been made that momentum-driven overshooting at the base of the pulse-driven convection zone should be negligible. We show that, while the argument holds, it would similarly limit mixing from the base of the convective envelope. On the other hand, estimations based on the picture of turbulent entrainment suggest that mixing is possible at both convective boundaries. We demonstrate that additional mixing at convective boundaries during core-burning phases prior to the thermally pulsing AGB has an impact on the later evolution, changing the mass range at which the third dredge-up and hot-bottom burning occur, and thus also the final surface composition. In addition, an effort has been made to constrain the efficiency of CBM at the different convective boundaries, using observational constraints. Our study suggests a strong tension between different constraints that makes it impossible to reproduce all observables simultaneously within the framework of an exponentially decaying overshooting. This result calls for a reassessment of both the models of CBM and the observational constraints.