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

Neutron stars in high-mass X-ray binaries (HMXBs) generally accrete from the wind 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, we investigate the spin period distribution of wind-fed X-ray pulsars with a supergiant companion star, using a population synthesis method. We find that the modeled distribution of supergiant HMXBs in the spin period - orbital period diagram is consistent with observations provided that the winds from the donor stars have relatively low terminal velocities ($\lesssim 1000$ kms$^{-1}$). The measured wind velocities in several supergiant HMXBs seem to favor this viewpoint. The predicted number ratio of wind-fed X-ray pulsars with persistent X-ray luminosities higher and lower than $4\times 10^{36}$ ergs$^{-1}$ is about $1:10$.