Galactic populations of radio and gamma-ray pulsars in the polar cap model

We simulate the characteristics of the Galactic population of radio and $\gamma$-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 ${10}^9$ years. 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. $\gamma$-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 $\gamma$-ray beams of 1 steradian solid angle, our model predicts that EGRET should have seen 7 radio-loud and 1 radio-quiet, $\gamma$-ray pulsars. With much improved sensitivity, GLAST, on the other hand, is expected to observe 76 radio-loud and 74 radio-quiet, $\gamma$-ray pulsars of which 7 would be identified as pulsed sources. We also explore the effect of magnetic field decay on the characteristics of the radio and $\gamma$-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 (9 pulsed) $\gamma$-ray pulsars. The lower flux threshold allows GLAST to detect $\gamma$-ray pulsars at larger distances than those observed by the radio surveys used in this study.