tokens: super asymptotic giant branch (AGB) star. In an He star in the binary system, there is no H-rich envelope and, thus, AGB phase does not occur. For such a situation, the CO core growth depends on the efficiencies of the He shell burning and the mass loss of the He envelope. Because the mass-loss process in the binary system is not fully understood and long-time calculation of the CO-core growth through the He-shell burning is required, it is not easy to evaluate whether a CO core less than 1.36 M ⊙ in the binary system grows up to the critical mass and explodes as an ultra-stripped EC SN. The mass range of CO cores for EC SNe was recently discussed for the primary stars in binary system (Poelarends et al. 2017 ; Siess Lebreuilly 2018 ). However, the mass range would be still model dependent and, thus, we are not sure whether the binary evolution affects the mass range of CO cores of EC SN progenitors. The investigation of the growth of the ONe core with thin He layer is important to clarify the possibility of the evolutionary path to an EC SN in close-binary systems. How is low-mass NS formed from EC SN progenitors and ultra-stripped SN progenitors that have a low-mass Fe core? In the case of EC SNe, the electron fraction in the ONe core is ∼0.48 at the central Ne ignition (Takahashi et al. 2013 , 2018 ). The electron fraction in the ONe core scarcely decreases until the central Ne ignition. On the other hand, progenitors of ultra-stripped SNe cause the electron capture during their evolution and, as a result, the electron fraction of the Fe core decreases. The electron fraction at the centre is ∼0.43 when the central density becomes ∼10 10 g cm −3 in the collapsed models in this paper. Thus, the Chandrasekhar mass of EC SN progenitors is heavier than that of the progenitors that have a low-mass Fe core of ultra-stripped SNe. The hydrodynamical simulation in our previous study (Yoshida et al. 2017 ) showed that the baryon mass of the PNS of an EC SN is 1.32 M ⊙ . 4 This mass is higher than the baryonic mass range of the NSs formed from CO137–CO144 models. 6 SUMMARY In this paper, we investigated the minimum mass of NSs based on astrophysical scenarios, i.e. stellar collapse and supernova explosion. We calculated the evolution of CO cores with masses 1.35–1.45 M ⊙ . The stars with CO-core masses higher than 1.36 M ⊙ form an Fe core after off-centre Ne, O, and Si-burnings. We found that low-mass CO cores, which eventually form an Fe core and subsequently collapse, could result in an NS with mass ∼1.17 M ⊙ , which is comparable with the lowest NS mass precisely measured. According to our stellar evolution simulations, the minimum mass of CO cores that produce an Fe core is ∼1.37 M ⊙ and below this value an ONe core is formed, which would lead to EC SN instead. Because of its higher value of Y e , an EC SN would produce more massive NSs than a core-collapse SN from an Fe core. Therefore, the minimum mass of NSs is expected to be determined by the
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