Double and single recycled pulsars: an evolutionary puzzle?

We investigate the statistics of isolated recycled pulsars and double neutron star binaries in the Galactic disc. Since recycled pulsars are believed to form through accretion and spin-up in close binaries, the isolated objects presumably originate from disrupted progenitors of double neutron stars. There are a comparable number of double neutron star systems compared to isolated recycled pulsars. We find that standard evolutionary models cannot explain this fact, predicting several times the number of isolated recycled pulsars than those in double neutron star systems. We demonstrate, through population synthesis calculations, that the velocity distribution of isolated recycled pulsars is broader than for binary systems. When this is accounted for in a model for radio pulsar survey selection effects, which include the effects of Doppler smearing for the double neutron star binaries, we find that there is a small (similar to 25 per cent) bias towards the detection of double neutron star systems. This bias, however, is not significant enough to explain the observational discrepancy if standard (Sigma = 265 km s-1) neutron star natal kick velocities are invoked in binary population syntheses. Population syntheses in which the 1D Maxwellian velocity dispersion of the natal kick is Sigma similar to 170 km s-1 are consistent with the observations. These conclusions further support earlier findings the neutron stars formed in close interacting binaries receive significantly smaller natal kicks than the velocities of Galactic single pulsars would seem to indicate.