Galactic planetary nebulae with precise nebular abundances as a tool to understand the evolution of asymptotic giant branch stars

We present nucleosynthesis predictions (HeCNOCl) from asymptotic giant branch (AGB) models, with diffusive overshooting from all the convective borders, in the metallicity range Z/4 < Z < 2Zsun. They are compared to recent precise nebular abundances in a sample of Galactic planetary nebulae (PNe) that is divided among double-dust chemistry (DC) and oxygen-dust chemistry (OC) according to the infrared dust features. Unlike the similar subsample of Galactic carbon-dust chemistry PNe recently analysed by us, here the individual abundance errors, the higher metallicity spread, and the uncertain dust types/subtypes in some PNe do not allow a clear determination of the AGB progenitor masses (and formation epochs) for both PNe samples; the comparison is thus more focussed on a object-by-object basis. The lowest metallicity OC PNe evolve from low-mass (~1 Msun) O-rich AGBs, while the higher metallicity ones (all with uncertain dust classifications) display a chemical pattern similar to the DC PNe. In agreement with recent literature, the DC PNe mostly descend from high-mass (M > 3.5 Msun) solar/supersolar metallicity AGBs that experience hot bottom burning (HBB), but other formation channels in low-mass AGBs like extra mixing, stellar rotation, binary interaction, or He pre-enrichment cannot be disregarded until more accurate C/O ratios would be obtained. Two objects among the DC PNe show the imprint of advanced CNO processing and deep second dredge-up, suggesting progenitors masses close to the limit to evolve as core collapse supernovae (above 6 Msun). Their actual C/O ratio, if confirmed, indicate contamination from the third dredge-up, rejecting the hypothesis that the chemical composition of such high-metallicity massive AGBs is modified exclusively by HBB.