NEUTRON-STARS AND MILLISECOND PULSARS FROM ACCRETION-INDUCED COLLAPSE IN GLOBULAR-CLUSTERS

We examine the limits on the number of millisecond pulsars which could be formed in globular clusters by the generally accepted scenario (in which a neutron star is created by the supernova of an initially massive star and subsequently captures a companion to form a low-mass X-ray binary which eventually becomes a millisecond pulsar). We find that while the number of observed low-mass X-ray binaries can be adequately explained in this way, the reasonable assumption that the pulsar luminosity function in clusters extends below the current observational limits down to the luminosity of the faintest millisecond pulsars in the field suggests a cluster population of millisecond pulsars which is substantially larger than the standard model can produce. Alleviating this problem by postulating much shorter lifetimes for the X-ray binaries requires massive star populations sufficiently large that the mass loss resulting from their evolution would be likely to unbind the cluster. We argue that neutron star formation in globular clusters by accretion-induced collapse of white dwarfs may resolve the discrepancy in birthrates.