Distributions of the orbital periods of the ∼25 OB+NS binaries in our fiducial synthetic SMC population. Upper left: Predicted period distribution (yellow histogram), where the ∼21 OB+NS binaries in which the OB stars rotates faster than 95% of their critical rotational velocity are indicated by shading (labelled ‘OBe’). The period distribution of observed BeXBs in the SMC (Haberl & Sturm 2016) is plotted as purple line. Upper right: A zoom-in of the upper left panel. The B star + radio pulsar binary J0045-7319 (Bell et al. 1995) and the supergiant X-ray binary SMC X-1 (Rawls et al. 2011; Falanga et al. 2015) are indicated by arrows. Lower left: The same predicted distribution as in the top panels, with the colours indicating which of the systems formed through Case A and Case B mass transfer (blue and orange, respectively), with the corresponding total numbers given in the legend. Lower right: The same predicted distribution as in the top panels, with the colours indicating which type of SN, and therefore which NS kick distribution, was assumed for the different systems [green for electron-capture SN; red for helium-envelope-stripped SN (CCSN-C); purple for hydrogen-envelope-stripped SN (CCSN-He); cf. Sect. 2.6]. The predicted total numbers related to different SN types are given in the legend.