Monte Carlo methods are used to simulate the properties of the Galactic population of rotation-powered pulsars in a model where the gamma rays are produced by energetic electrons that Comptonscatter photons near the pulsar polar cap. We use results of radio pulsar statistical studies to assign the initial magnetic field, spatial, and velocity distributions of neutron stars at birth. Gamma-ray and radio fluxes are calculated for an observer at Earth and are used to determine the expected number of detectable gamma-ray pulsars. The results are compared with the observed properties of the seven known gamma-ray pulsars. We investigate models where the polar-cap angle is 1, 2, and 4 times larger than the nominal polar-cap angle determined by the open field lines of an aligned dipole magnetic field and where the initial rotation period is 20 or 30 ms. We find that the distance, period, age, magnetic field, and gamma-ray flux distributions of the observed gamma-ray pulsars are best represented by a model where the initial pulse period is 30 ms and the polar cap angle is 4 times larger than the nominal angle. For this model, we predict approx >2-4 radio-quiet pulsars that emit gamma rays at flux levels of the known gamma-ray pulsars. The emission of unresolved gamma-ray pulsars is found to contribute to the diffuse Galactic gamma-ray continuum at the 5%-10% level.
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