We discuss the existence of pulsing X-ray sources that consist of neutron stars in highly compact binary systems (orbital periods not more than Od3), undergoing accretion from low-mass late-type dwarf or degenerate-dwarf companions. An appropriate mass transfer rate can be driven by the decay of the orbit due to gravitational radiation, a self-excited wind, and/or the evolution of the companion. Such a system may result from the evolution of a cataclysmic variable, wherein a degenerate dwarf collapses to form a neutron star after accreting sufficient mass to exceed the Chandrasekhar limit. We apply this model to the 7s7 X-ray pulsar 3U 1626-67, and demonstrate that it can explain the apparent lack of Doppler shifts in the X-ray pulsations from this source. The model may also account for other observed properties of the source, including (1) the apparent faintness and large ultraviolet excess of the optical counterpart, (2) the lack of X-ray eclipses, and (3) an approximately 1000 s quasi-periodic oscillation in the source intensity that was recently observed with the SAS 3 satellite.
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Joss et al. (1978) studied this question.