On the third dredge-up phenomenon in asymptotic giant branch stars

The third dredge-up phenomenon in asymptotic giant branch (AGB) stars is analyzed through evolutionary model calculations of a \mass{3}, solar metallicity star. The Schwarzschild criterion is used to test the stability of a given layer against convection, and the calculations are performed either with or without extra-mixing below the convective envelope. Based on these calculations, several questions are addressed regarding the occurrence of the third dredge-up in AGB star models, the laws governing that phenomenon, and some of its implications on the structural and chemical evolution of those stars.