2011MNRAS.415.1827T

We have performed a Monte Carlo simulation of the Galactic population of pulsars and γ-ray observations. We apply a two-layer outer-gap model, which has been developed by Wang, Takata & Cheng, of the γ-ray emission process, and study the radiation characteristics as a function of the magnetic inclination angle (α) and the Earth viewing angle (ζ). In our model, the γ-ray flux and the spectral cut-off energy tend to decrease as the inclination and viewing angles deviate from 90°. The emerging spectrum above 100 MeV becomes soft with a photon index p∼ 1.8-2 for ζ -> 90 °and p∼ 1.2-1.3 for ζ ≪ 90°. Our simulation predicts that pulsars with larger inclination angles (α= 70-90°) and larger viewing angles (ζ= 70-90°) have been preferentially detected by the Fermiγ-ray telescope, and hence the observed pulse profiles of the γ-ray pulsars have a double-peak structure rather than a single-peak one. In the simulation, most γ-ray millisecond pulsars are categorized as radio-quiet γ-ray pulsars, because their radio fluxes are under the sensitivities of the major radio surveys. Even if we drastically increase the radio sensitivity by a factor of 10, the number of radio-selected millisecond pulsars detected by Fermi 10-year observations is still much lower than the expected number of γ-ray-selected millisecond pulsars, indicating that radio-quiet millisecond pulsars must contribute to Fermi unidentified sources and/or γ-ray background radiation. We argue that γ-ray pulsars observed with a smaller viewing angle (ζ ≪ 90°) will appear as low-efficiency γ-ray pulsars. For example, the unique radiation properties of the low-efficiency γ-ray pulsar PSR J0659+1414 can be explained by our present gap model with a viewing geometry of α∼ζ= 40°-50°.