Approximate estimate of the dimensionless spin a_* of the resultant BH as a function of the He-rich initial mass and orbital period, denoted by the color of the filled circles. The star symbols, sharing the same color bar with a_*, refer to the ratio of the He-rich star’s mass at the central carbon exhaustion to its initial mass, i.e. M_final/M_init. For a given initial mass of the He-rich star, this quantity remains the same whatever the orbital period because in this estimation, stars are evolving as if they were single stars. Left panel: 0.01 Z_⊙, middle panel: 0.1 Z_⊙, right panel: Z_⊙. In these approximate estimates, the mass of the BH companion is assumed to be 10 M_⊙, while the orbital separation is assumed to remain constant. We also assume that tides instantaneously synchronize the spin of the He-rich star with the orbital angular velocity. The solid black line denotes the lower limit in orbital period, below which a He-rich star at a given specific mass would overfill its Roche lobe at ZAHeMS.