2005A&A...429..489Z

Based on a new self-consistent outer gap model, we statistically study luminosity properties of γ-ray pulsars with ages of ≤2x10⁷yr in the Galaxy as well as those with ages of ≤5x10⁶yr in the Gould belt using a Monte Carlo method, where the γ-ray beaming effect has been included. Generally, the relation between γ-ray luminosity, L_γ, and pulsar spin-down power, L_sd, can be expressed as L_γ ∝L^δ_sd, where δ is a parameter that depends on the galactic latitude and the γ-ray threshold. For a given γ-ray threshold (for example, the EGRET threshold or GLAST threshold), the parameter δ is an increasing function of the galactic latitude. For the EGRET threshold, δ changes smoothly with the galactic latitude. For the GLAST threshold, however, δ has a minimum at |b|≤5°, and δ increases by a factor of ∼2 at the range of |b|=5°-10° relative to δ at |b|≤ 5°, and then increases smoothly as the galactic latitude further increases. The reason for this is that high galactic latitude γ-ray pulsars are dominated by mature pulsars. In fact, the ratio of γ-ray pulsars with their ages of >10⁶yr to all simulated γ-ray pulsars also increases with the galactic latitude. For the γ-ray pulsars produced in a fixed range of galactic latitude, the parameter δ increases slightly with the sensitivity of γ-ray detector.