Spin magnitude χ₂ of the BH formed through the direct core collapse of the He star (left panel) and the corresponding total angular momentum of the progenitor star (right panel) as a function of the central helium abundance. The binary system consists of a 20 M_⊙ BH and a 20 M_⊙ He star with different initial rotation rates (blue: ω_i = 0; orange: initially synchronized with the orbit; green: ω_i = 0.3 ω_crit; red: ω_i = 0.6 ω_crit; purple: ω_i = 0.9 ω_crit). All models assume an initial orbital period of 1.0 d; the 0.5 d case is provided for comparison in Fig. A.2. Results for He stars at 0.01 Z_⊙ are nearly identical to those at 0.1 Z_⊙, and are therefore not shown here.