We have developed a computer code (Tauris & Bailes 1996) to follow the evolution of a binary system from the zero-age main sequence to its “final” state as a binary millisecond pulsar (BMSP), at all stages keeping careful track of the mass and orbital separation of the two stars.
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 270 km s−1 with any model, unless the formation of the neutron star is accompanied by some form of asymmetric kick. We obtain average 3-D system velocities of 〈v
recoil〉= 99.6, 137.6 and 160.7 km s−1 using Gaussian kicks of 〈v
kick〉=0, 200 and 450 km s−1 (σ=0, 100 and 200 km s - 1, respectively). 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.