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Here, we use Fermi Gamma-ray Space Telescope detections and upper limits on non-recycled pulsars obtained from the Large Area Telescope (LAT) to constrain how the gamma-ray luminosity L γ depends on the period P and the period derivative $$\dot{P}$$. We use a Bayesian analysis to calculate a best-fit luminosity law, or dependence of L γ on P and $$\dot{P}$$, including different methods for modeling the beaming factor. An outer gap (OG) magnetosphere geometry provides the best-fit model, which is $$L_\gamma \propto P^{-a} \dot{P}^{b}$$ where a = 1.36 ± 0.03 and b = 0.44 ± 0.02, similar to but not identical to the commonly assumed $$L_\gamma \propto \sqrt{\dot{E}} \propto P^{-1.5} \dot{P}^{0.5}$$. Given upper limits on gamma-ray fluxes of currently known radio pulsars and using the OG model, we find that about 92% of the radio-detected pulsars have gamma-ray beams that intersect our line of sight. By modeling the misalignment of radio and gamma-ray beams of these pulsars, we find an average gamma-ray beaming solid angle of about 3.7π for the OG model, assuming a uniform beam. Using LAT-measured diffuse fluxes, we place a 2σ upper limit on the average braking index and a 2σ lower limit on the average surface magnetic field strength of the pulsar population of 3.8 and 3.2 × 1010 G, respectively. We then predict the number of non-recycled pulsars detectable by the LAT based on our population model. Using the 2 yr sensitivity, we find that the LAT is capable of detecting emission from about 380 non-recycled pulsars, including 150 currently identified radio pulsars. Using the expected 5 yr sensitivity, about 620 non-recycled pulsars are detectable, including about 220 currently identified radio pulsars. As a result, we note that these predictions significantly depend on our model assumptions.

Source Citation

Perera, B. B. P., Mclaughlin, M. A., Cordes, J. M., Kerr, M., Burnett, T. H., & Harding, A. K. (2013). Modeling The Non-Recycled Fermi Gamma-Ray Pulsar Population. The Astrophysical Journal, 776(1), 61.