Gamma‐Ray Emission Properties from Mature Pulsars in the Galaxy and in the Gould Belt

We study the $\gamma$-ray emission properties of pulsars by using a newself-consistent outer gap model. The outer gap can exist in pulsars with ageover million years old if the effect of magnetic inclination angle as well asthe average properties of the outer gap are considered. The mature $\gamma$-raypulsars, whose ages are between 0.3 to 3 million years old, are able to move upto high galactic latitude. Moreover, their $\gamma$-ray luminosity are weakerand their spectra are softer than those of younger $\gamma$-ray pulsars in thegalactic plane significantly. We use a Monte Carlo method to simulate thestatistical properties of $\gamma$-ray pulsars in the Galaxy as well as in theGould Belt. We find that $\gamma$-ray pulsars located at $\mid b \mid <5^{\circ}$ and located at $\mid b \mid > 5^{\circ}$ have very differentproperties. High galactic latitude $\gamma$-ray pulsars are dominated by maturepulsars with longer periods, weaker fluxes and softer spectra. If the pulsarbirth rate in the Galaxy and the Gould Belt are $\sim 10^{-2}yr^{-1}$ and $\sim2\times 10^{-5}yr^{-1}$ respectively, there are 42 and 35 radio-quiet$\gamma$-ray pulsars for $\mid b \mid < 5^{\circ}$ and $\mid b \mid >5^{\circ}$ respectively. Radio-quiet $\gamma$-ray pulsars from the Gould Beltare 2 and 13 for $\mid b \mid < 5^{\circ}$ and $\mid b \mid > 5^{\circ}$respectively. We suggest that a good fraction of unidentified EGRET$\gamma$-ray sources may be these radio-quiet $\gamma$-ray pulsars. Furthermore$\gamma$-ray pulsars located at $\mid b \mid > 5^{\circ}$ satisfies $L_{\gamma}\propto L^{\beta}_{sd}$ whereas $L_{\gamma} \propto L^{\delta}_{sd}$ for$\gamma$-ray pulsars in the galactic plane, where $\beta \sim 0.6$ and $\delta\sim 0.3$ respectively.Comment: 24 pages, 21 figures, accepted to be published in Ap