The conventional picture of disk accretion onto magnetized neutron stars has been challenged by the spin changes observed in a few X-ray pulsars, and by theoretical results from numerical simulations of disk-magnetized star interactions. These indicate possible accretion during the propeller regime and the spin-down torque increasing with the accretion rate. Here we present a model for the accretion torque exerted by the disk on a magnetized neutron star, assuming accretion continues even for rapid rotators. The accretion torque is shown to have some different characteristics from that in the conventional model, but in accord with observations and numerical calculations of accretion-powered magnetized neutron stars. We also discuss its possible applications to the spin evolution in X-ray pulsars.

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We use the evolutionary population synthesis method to investigate the statistical properties of the wind-fed neutron star (NS) compact (P orb < 10 days) high-mass X-ray binaries (HMXBs) in our Galaxy, based on different spin-down models. We find that the spin-down rate in the supersonic propeller phase given by assuming that the surrounding material is treated as forming a quasi-static atmosphere or by assuming that the characteristic velocity of matter and the typical Alfvén velocity of material in the magnetospheric boundary layer are comparable to the sound speed in the external medium is too low to produce the observed number of compact HMXBs. We also find that the models suggested by assuming that the infalling material is ejected with the corotation velocity at the magnetospheric radius when the magnetospheric radius is larger than the corotation radius and by simple integration of the magnetic torque over the magnetosphere with a larger spin-down rate than that given by Davies & Pringle (1981) or Illarionov & Sunyaev (1975) can predict a reasonable number of observed wind-fed NS compact HMXBs. Our calculated results indicate that subsonic propeller phase may not exist at all by comparing with the observed particular distributions of wind-fed NS compact HMXBs in the P s − P orb diagram. However, the spin-down rate suggested by Wang & Robertson (1985); Dai, Liu & Li (2006);Jiang & Li (2005) and that given by Davidson & Ostriker (1973) both seem reasonable to produce the observed distribution of wind-fed NS compact HMXBs in the P s − P orb diagram. We cannot find which spin-down rate seems more reasonable from our calculations.

We investigate the birthrate problem for low-mass X-ray binaries (LMXBs) and millisecond radio pulsars (MRPs) in this paper. We consider intermediate-mass and low-mass X-ray binaries (I/LMXBs) to be the progenitors of MRPs, and calculate their evolutionary response to the cosmic star formation rate (SFR) both semi-analytically and numerically. With a typical value (1 Gyr) of the LMXB lifetime, one may expect comparable birthrates of LMXBs and MRPs, but the calculated number of LMXBs is an order of magnitude higher than that observed in the Galaxy. Instead, we suggest that the birthrate problem could be solved if most MRPs have evolved from faint to rather than bright LMXBs. The former may have a population of 10 4 in the Galaxy.close binaries, general pulsars, star formation, X-ray stars