Galactic Populations of Radio and Gamma-Ray Pulsars in the Polar Cap Model

We simulate the characteristics of the Galactic population of radio and γ-ray pulsars using Monte Carlo techniques. At birth, neutron stars are spatially distributed in the Galactic disk, with supernova-kick velocities, and randomly dispersed in age back to 10⁹ yr. They are evolved in the Galactic gravitational potential to the present time. From a radio luminosity model, the radio flux is filtered through a selected set of radio-survey parameters. γ-ray luminosities are assigned using the features of recent polar cap acceleration models invoking space-charge-limited flow, and a pulsar death valley further attenuates the population of radio-loud pulsars. Assuming a simple emission geometry with aligned radio and γ-ray beams of 1 sr solid angle, our model predicts that EGRET should have seen seven radio-loud and one radio-quiet γ-ray pulsars. With much improved sensitivity, GLAST, on the other hand, is expected to observe 76 radio-loud and 74 radio-quiet γ-ray pulsars, of which seven would be identified as pulsed sources. We also explore the effect of magnetic field decay on the characteristics of the radio and γ-ray pulsar populations. Including magnetic field decay on a timescale of 5 Myr improves agreement with the radio pulsar population and increases the predicted number of GLAST-detected pulsars to 90 radio-loud and 101 radio-quiet (nine pulsed) γ-ray pulsars. The lower flux threshold allows GLAST to detect γ-ray pulsars at larger distances than those observed by the radio surveys used in this study.