Modelling of the post-asymptotic giant branch phase as a tool to understand asymptotic giant branch evolution and nucleosynthesis.

We study a sample of single Galactic post-asymptotic giant branch (post-AGB) stars with known surface chemical composition. Gaia   EDR3 and Gaia   DR3 parallaxes have enabled accurate determinations of the luminosities of these objects, thus making it possible to characterize them in terms of their initial masses, chemical compositions, and progenitor ages. We used extant evolutionary sequences of asymptotic giant branch (AGB) stars produced using the ATON stellar evolutionary code extended to the post-AGB phase, specifically for this study. The luminosity and surface carbon abundance together prove to be the most valuable indicator of the previous evolution and nucleosynthetic history of the star, particularly regarding the efficiency of mixing mechanisms and the growth of the core. This analysis allows us to place the post-AGB sample into classes based on their evolutionary history on the AGB. This includes low-mass objects that evolved as M-type stars without third dredge-up, carbon stars, and intermediate-mass AGB stars with hot bottom burning (HBB). Additionally, our analysis reveals that AGB nucleosynthesis is not homogeneous, even for stars with similar initial masses and metallicities. The approach of using observations of post-AGB stars to constrain AGB and post-AGB models shed new light on still debated issues related to the AGB evolution, such as the threshold mass required to become a C-star, the minimum mass for HBB and the amount of carbon that can be accumulated in the surface regions of the star during the AGB lifetime, as well as deep mixing experienced during the red giant branch phase. [ABSTRACT FROM AUTHOR]