The Velocity Distribution of Isolated Radio Pulsars

We infer the velocity distribution of radio pulsars based on large-scale 0.4 GHz pulsar surveys. We do so by modelling evolution of the locations, velocities, spins, and radio luminosities of pulsars; calculating pulsed flux according to a beaming model and random orientation angles of spin and beam; applying selection effects of pulsar surveys; and comparing model distributions of measurable pulsar properties with survey data using a likelihood function. The surveys analyzed have well-defined characteristics and cover approx. 95% of the sky. We maximize the likelihood in a 6-dimensional space of observables P, dot-P, DM, absolute value of b, mu, F (period, period derivative, dispersion measure, Galactic latitude, proper motion, and flux density). The models we test are described by 12 parameters that characterize a population's birth rate, luminosity, shutoff of radio emission, birth locations, and birth velocities. We infer that the radio beam luminosity (i) is comparable to the energy flux of relativistic particles in models for spin-driven magnetospheres, signifying that radio emission losses reach nearly 100% for the oldest pulsars; and (ii) scales approximately as E(exp 1/2) which, in magnetosphere models, is proportional to the voltage drop available for acceleration of particles. We find that a two-component velocity distribution with characteristic velocities of 90 km/ s and 500 km/ s is greatly preferred to any one-component distribution; this preference is largely immune to variations in other population parameters, such as the luminosity or distance scale, or the assumed spin-down law. We explore some consequences of the preferred birth velocity distribution: (1) roughly 50% of pulsars in the solar neighborhood will escape the Galaxy, while approx. 15% have velocities greater than 1000 km/ s (2) observational bias against high velocity pulsars is relatively unimportant for surveys that reach high Galactic absolute value of z distances, but is severe for spatially bounded surveys; (3) an important low-velocity population exists that increases the fraction of neutron stars retained by globular clusters and is consistent with the number of old objects that accrete from the interstellar medium; (4) under standard assumptions for supernova remnant expansion and pulsar spin-down, approx. 10% of pulsars younger than 20 kyr will appear to lie outside of their host remnants. Finally, we comment on the ramifications of our birth velocity distribution for binary survival and the population of inspiraling binary neutron stars relevant to some GRB models and potential sources for LIGO.