Super- and massive AGB stars – IV. Final fates – initial-to-final mass relation

We explore the final fates of massive intermediate-mass stars by computing detailed stellar models from the zero age main sequence until near the end of the thermally pulsing phase. These super-AGB and massive AGB star models are in the mass range between 5.0 and 10.0 M⊙ for metallicities spanning the range Z=0.02−0.0001. We probe the mass limits Mup, Mn and Mmass, the minimum masses for the onset of car- bon burning, the formation of a neutron star, and the iron core-collapse supernovae respectively, to constrain the white dwarf/electron-capture supernova boundary. We provide a theoretical initial to final mass relation for the massive and ultra-massive white dwarfs and specify the mass range for the occurrence of hybrid CO(Ne) white dwarfs. We predict electron-capture supernova (EC-SN) rates for lower metallicities which are significantly lower than existing values from parametric studies in the litera- ture. We conclude the EC-SN channel (for single stars and with the critical assumption being the choice of mass-loss rate) is very narrow in initial mass, at most ≈ 0.2 M⊙. This implies that between ∼ 2−5 per cent of all gravitational collapse supernova are EC-SNe in the metallicity range Z=0.02 to 0.0001. With our choice for mass-loss pre- scription and computed core growth rates we find, within our metallicity range, that CO cores cannot grow sufficiently massive to undergo a Type 1.5 SN explosion.