1996A&A...315..432T

To help determine the origin of millisecond pulsars, we compute the space velocities predicted by various models of their formation. It is difficult to produce a millisecond pulsar velocity greater than 270km/s with any model, unless the formation of the neutron star is accompanied by some form of asymmetric kick. If the accretion-induced collapse of a white dwarf is the sole formation mechanism, then kicks are essential to reproduce the high velocities of some of the millisecond pulsars observed. Our computations show that, in general, we expect those systems with shorter orbital periods to have larger velocities than those with longer periods, but any relation between the final orbital period and space velocity is fairly weak, especially if asymmetries are involved. We demonstrate that binary millisecond pulsars probably evolved through a common envelope before the formation of the neutron star, and that the energy used to expell the envelope is more than that available from the gravitational potential. More millisecond pulsar proper motions and distances will help to constrain the various formation models, but early indications are that low-velocity millisecond pulsars are over-represented in the sample, especially if the most recent estimates of kick velocities are used.