The role of beam geometry in population statistics and pulse profiles of radio and gamma-ray pulsars

We present results of a pulsar population synthesis study that incorporates a number of recent developments and some significant improvements over our previous study. We have included the results of the Parkes multi-beam pulsar survey in our select group of nine radio surveys, doubling our sample of radio pulsars. We adopted with some modifications the radio beam geometry of Arzoumanian, Chernoff & Cordes (2002). For the $\gamma$-ray beam, we have assumed the slot gap geometry described in the work of Muslimov & Harding (2003). To account for the shape of the distribution of radio pulsars in the $\dot P-P$ diagram, we continue to find that decay of the magnetic field on a timescale of 2.8 Myr is needed. With all nine surveys, our model predicts that EGRET should have seen 7 radio-quiet (below the sensitivity of these radio surveys) and 19 radio-loud $\gamma$-ray pulsars. AGILE (nominal sensitivity map) is expected to detect 13 radio-quiet and 37 radio-loud $\gamma$-ray pulsars, while GLAST, with greater sensitivity is expected to detect 276 radio-quiet and 344 radio-loud $\gamma$-ray pulsars. When the Parkes multi-beam pulsar survey is excluded, the ratio of radio-loud to radio-quiet $\gamma$-ray pulsars decreases, especially for GLAST. The decrease for EGRET is 45%, implying that some fraction of EGRET unidentified sources are radio-loud $\gamma$-ray pulsars. In the radio geometry adopted, short period pulsars are core dominated. Unlike the EGRET $\gamma$-ray pulsars, our model predicts that when two $\gamma$-ray peaks appear in the pulse profile, a dominant radio core peak appears in between the $\gamma$-ray peaks. Our findings suggest that further improvements are required in describing both the radio and $\gamma$-ray geometries.