Nucleosynthetic yields of intermediate-mass primordial to extremely metal-poor stars

Abridged. We aim to better characterise the evolution and fates, and determine updated nucleosynthetic yields of intermediate-mass stars between primordial and EMP metallicity (Z=1e-10, 1e-8, 1e-7, 1e-6 and 1e-5). We also probed uncertainties in the nucleosynthesis of the oldest intermediate-mass stars during the asymptotic giant branch (AGB) phase. We analysed the evolution of models from their main sequence, through the thermally pulsing AGB (TP-AGB), to the latest stages of their evolution, using the Monash-Mount Stromlo stellar evolution code MONSTAR. The results were post-processed with the code MONSOON, which allowed for the determination of the nucleosynthetic yields of 77 species up to 62Ni. As reported in former works, we identified proton ingestion episodes (PIEs) in our lowest-mass lowest-Z models. Models of Z=1e-10 and Z=1e-8 in a narrow initial mass range around 5 Msun experience the cessation of thermal pulses, and their final fates as type-I1/2 supernovae cannot be discarded. All the models of initial mass of about 6-7 Msun experience a corrosive second dredge-up and undergo significant metal enrichment in their envelopes. This allows them to develop a solar-like TP-AGB or TP-super-AGB, ultimately becoming white dwarfs. Except for those undergoing the cessation of thermal pulses, all of our models show the nucleosynthetic signatures of both efficient third dredge-up and hot-bottom burning, with the activation of the NeNa cycle and the MgAlSi chains. This leads to the creation of vast amounts of CNO, with typical [N/Fe] > 4), and the characteristic abundance signature [N/Fe] > [C/Fe] > [O/Fe]. Due to differences in input physics (mostly related to convection and convective boundaries), our nucleosynthetic yields present dramatic differences with respect to recent results existing in the literature for intermediate-mass models of similar metallicities.