Final fates as a function of initial helium star mass and initial metallicity. The left panel corresponds to models without overshooting, while the right panel corresponds to models with overshooting across convective boundaries (f_OV = 0.014, 0.016). Hatched regions show models with ONe cores featuring residual carbon, which evolve either toward an ONe WD, a thermal runaway, or an ECSN. The boundary between ONe SNe Ia and ECSNe corresponds to models with average residual carbon mass fractions of X(¹²C)≃0.004 (see Sect. 4). The ZAMS masses (of solar metallicity models) were mapped based on Fig. 4 of Farmer et al. (2015). For M_ZAMS < 7.0 M_⊙ we extrapolated the mass using the fitting function M_ZAMS = 2(M_He, core + 2.45). For more details, see Sect. 3.