We investigate the lowest mass stars that produce Type-II supernovae, motivated by recent results showing that a large fraction of type-II supernova progenitors for which there are direct detections display unexpectedly low luminosity (for a review see e.g. Smartt 2009). There are three potential evolutionary channels leading to this fate. Alongside the standard ‘massive star’ Fe-core collapse scenario we investigate the likelihood of electron capture supernovae (EC-SNe) from super-AGB (S-AGB) stars in their thermal pulse phase, from failed massive stars for which neon burning and other advanced burning stages fail to prevent the star from contracting to the critical densities required to initiate rapid electron-capture reactions and thus the star's collapse. We find it indeed possible that both of these relatively exotic evolutionary channels may be realised but it is currently unclear for what proportion of stars. Ultimately, the supernova light curves, explosion energies, remnant properties (see e.g. Knigge et al. 2011) and ejecta composition are the quantities desired to establish the role that these stars at the lower edge of the massive star mass range play.

In this review I am discussing the current state of simulating the internal evolution of AGB stars. Recent work on AGB stars include the effect of rotation, magnetic fields and internal gravity waves, as well as thermohaline mixing induced by the 3He + 3He pp-chain reaction. Hydrodynamic simulations of the interior convection of AGB stars are now becoming available, giving insights to convective boundary mixing, for example for He-shell flash convection. At very low metallicity convective-reactive events are encountered in AGB stars (as well as in massive stars), and the necessity of hydrodynamic simulations to address this difficult phase of stellar evolution is emphasized.

The evolution of central stars of planetary nebulae can proceed in several distinct ways, either leading to H-deficiency or to H-normal surface composition. Several new simulations of the evolution channels that lead to H-deficiency are now available, mainly the born-again scenarios that are triggered by a He-shell flash during the hot pre-white dwarf evolution phase. A realistic AGB progenitor evolution is important for correct HRD tracks, that allow mass determinations. New hydrodynamic simulations of He-shell flash convection including cases with H-ingestion are now performed, and allow a determination of the convective extra-mixing efficiency. This has direct consequences for the intershell abundance distribution of AGB stars that can be observed in the H-deficient CSPN.

We model the nucleosynthesis during a radiative interpulse phase of a rotating 3 M⊙ Asymptotic Giant Branch (AGB) star. We find an enhanced production of the neutron source species 13C compared to non-rotating models due to shear mixing of protons and 12C at the core-envelope interface. We estimate that the resulting total production of heavy elements by slow neutron capture (s-process) is too low to account for most observations. This due to the fact that rotationally induced mixing during the interpulse phase causes a pollution of the 13C pocket layer with the neutron poison 14N. As a result we find a maximum neutron exposure of τmax = 0.04 mbarn–1 in the s-process layer of our solar metallicity model with rotation. This is about a factor of 5 … 10 less than required to reproduce the observed stellar s-process abundance patterns. We compare our results with models that include hydrodynamic overshooting mixing, and with simple parametric models including the combined effects of overshooting and mixing in the interpulse. Within the parametric model a range of mixing efficiencies during the interpulse phase correlates with a spread in the s-process-efficiency. Such a spread is observed in AGB and post-AGB stars as well as in pre-solar SiC grains.

H-deficient post-AGB objects, e.g. PG1159 type star K1-16 and born-again AGB star Sakurai's object, have been reported to be significantly iron-deficient. We find that the iron deficiencies expected due to neutron-capture nucleosynthesis during either the progenitor AGB evolution and/or the neutron burst that occurs as a result of the rapid burning of protons during a post-AGB He-flash are generally in line with observations.

We present a stellar evolution model sequence of the past and future evolution of the post-AGB born again star Sakurai's object (V 4334 Sgr). In order to match the short evolutionary time scale we have to assume that the convective ingestion of hydrogen-rich envelope material into the He-flash convection zone proceeds slower than predicted by the mixing length theory. For the future we predict a swift second evolution through the central star region before a second born-again evolution occurs.

The carbon and nitrogen isotopic ratios of pre-solar SiC grains of type A+B suggest a proton-limited nucleosynthetic process as encountered, for instance, during the very late thermal pulse of post-AGB stars. We study the nuclear processes during this phase and find carbon and nitrogen isotopic ratios which can reproduce those of A+B grains. These results are still preliminary because they depend on uncertain factors such as the details of mixing during the post-AGB thermal pulse, the rates of some nuclear reactions, and the assumptions on mixing during the progenitor AGB phase.

We discuss the occurrence of the s-process during the radiative interpulse phase of rotating AGB stars. Due to differential rotation, protons are mixed into 12C-rich layers after thermal pulses, in the course of the so called third dredge up episode. We follow the time evolution of key isotope abundances in the relevant layers with a post-processing code which includes time dependant mixing and nucleosynthesis. In rotating AGB models, the mixing persists during the entire interpulse phase due to the steep gradient of angular velocity at the envelope-core interface. As the layers containing protons and 12C, which are formed this way, become hotter, a 13C-pocket is formed in a natural way. However, in this situation also 14N is formed and spread over the entire 13C-pocket. We include the neutron consuming 14N(n,p) reaction in our network and determine to what extent it reduces the production of trans-iron elements. We propose that rotation may be responsible for the spread of efficiencies of the 13C neutron source as required by observations.

While the basic properties of AGB stellar evolution are well established, comprehensive observational studies of late phases of intermediate mass stars continue to generate puzzles for current stellar models. Here, I review current techniques to model AGB stars, and I discuss important aspects of current research of AGB (and post-AGB) stellar evolution with a particular focus on how these interrelate.