We compare the rotation rate of neutron stars in low-mass X-ray binaries (LMXBs) with the orbital period of the binaries. We find that, while short orbital period LMXBs span a range of neutron star rotation rates, all the long-period LMXBs have fast rotators. We also find that the rotation rates are highest for the systems with the highest mean mass accretion rates, as can be expected if the accretion rate correlates with the orbital period. We show that these properties can be understood by a balance between spin-up due to accretion and spin-down due to gravitational radiation. Our scenario indicates that the gravitational radiation emitted by these systems may be detectable by future ground-based gravitational wave detector
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