Pulsar statistics .4. Pulsar velocities

We have used Monte Carlo simulations of the Galactic pulsar population to reassess the kinematics of radio pulsars in light of the large number of recently published proper motions and the revised distance model. Our modelling of the observational selection effects that distort the observed sample is far more detailed and self-consistent than that of previous authors. This allows us to compare the observed sample of pulsars against samples of synthetic pulsars predicted by our model, the kinematic properties of which are well understood. We find no convincing evidence for a significant magnetic field-velocity correlation. In order to be consistent with the observed velocity distribution, we find that the mean birth velocity of pulsars must be similar to 500 km s(-1), about a factor of 3 higher than previously thought. Such high birth velocities have important implications on our understanding of magnetic field decay and the distribution of old neutron stars in the Galaxy. To establish the likely time-scale for magnetic field evolution, we consider models with short (10 Myr) and long (100 Myr) decay time-scales. The most compelling evidence against 10-Myr decay time-scales and for timescales greater than or similar to 100 Myr comes from the distribution of pulsars above the Galactic plane as a function of characteristic age. The sky distribution of old (greater than or similar to 100 Myr) neutron stars predicted by our model is inconsistent with that of the gamma-ray bursts observed by BATSE.