Prerequisites for BH formation by fallback in a successful SN explosion. Left panel: compact remnant type left behind the explosion is constrained in the (μ₄M₄, ξ_2.5) plane. The lower boundary in ξ_2.5, demarcating the region over which only NSs are obtained, is indicated by a red horizontal line. The upper boundary in ξ_2.5, above which NS and fallback BH remnants coexist, is also indicated by a red horizontal line. For ξ_2.5 values in between, the linear ξ_2.5-to-μ₄M₄ fit model (represented by a diagonal dashed red line) sets the minimal ξ_2.5 value for fallback to occur depending on μ₄M₄. Right panel: compact remnant type is also constrained by the ratio M₄/M_CO. The M₄/M_CO < 0.6 condition for fallback to occur is represented by a red horizontal line through the (M₄, M₄/M_CO) plane. In both panels, the parameter space region that permits the coexistence of NSs and fallback BHs is shown in grey, while the region that constraints the remnant to be a NS is shown in orange.