Abstract We have investigated the relation between the orbital period Porb and the spin period Ps of neutron stars in OB/X-ray binaries. By simulating the time-development of the mass loss rate and radius expansion of a 20M⊙ donor star, we have calculated the detailed spin evolution of the neutron star before steady wind accretion occurs (that is, when the break spin period is reached), or when the OB star begins evolving off the main sequence or has filled its Roche lobe. Our results are compatible with the observations of OB/X-ray binaries. We find that in relatively narrow systems with orbital periods less than tens of days, neutron stars with initial magnetic field B0 stronger than about 3×1012 G can reach the break spin period to allow steady wind accretion in the main sequence time, whereas neutron stars with B0 < 3×1012 G and/or in wide systems would still be in one of the pulsar, rapid rotator or propeller phases when the companion evolves off the main sequence or fills its Roche lobe. Our results may help understand the various characteristics of the observed OB/neutron star binaries along with their distributions in the Ps-Porb diagram.

Keywords binaries: close -- stars: evolution -- stars: pulsars -- stars: supergiants -- stars: winds, outflows

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