A binary in which a slightly evolved star starts mass transfer to a neutron star can evolve towards ultra-short orbital periods under the influence of magnetic braking. This is called magnetic capture. We investigate in detail for which initial orbital periods and initial donor masses binaries evolve to periods less than 30–40 minutes within the Hubble time. We show that only small ranges of initial periods and masses lead to ultra-short periods, and that for those only a small time interval is spent at ultra-short periods. Consequently, only a very small fraction of any population of X-ray binaries is expected to be observed at ultra-short period at any time. If 2 to 6 of the 13 bright X-ray sources in globular clusters have an ultra-short period, as suggested by recent observations, their formation cannot be explained by the magnetic capture model.
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