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Neutron stars in high-mass X-ray binaries (HMXBs) generally accrete from thewind matter of their massive companion stars. Recently Shakura et al. (2012)suggested a subsonic accretion model for low-luminosity ($<4\times 10^{36}$ergs$^{-1}$), wind-fed X-ray pulsars. To test the feasibility of this model, weinvestigate the spin period distribution of wind-fed X-ray pulsars with asupergiant companion star, using a population synthesis method. We find thatthe modeled distribution of supergiant HMXBs in the spin period - orbitalperiod diagram is consistent with observations provided that the winds from thedonor stars have relatively low terminal velocities ($\lesssim 1000$kms$^{-1}$). The measured wind velocities in several supergiant HMXBs seem tofavor this viewpoint. The predicted number ratio of wind-fed X-ray pulsars withpersistent X-ray luminosities higher and lower than $4\times 10^{36}$ergs$^{-1}$ is about $1:10$.

Can the Subsonic Accretion Model Explain the Spin Period Distribution of Wind-fed X-ray Pulsars?