Gamma-ray emission from pulsars: strength of the acceleration field in the outer gap

We study the gamma-ray emission from an outer-gap accelerator around a rotating neutron star. Assuming the existence of global currents in the magnetosphere, the charge depletion causes a large electric field along the magnetic field lines. This electric field accelerates migratory electrons and positrons, which radiate gamma-rays via curvature radiation. These gamma-rays produce radiating particles by colliding with the X-rays, maintaining a pair-production cascade in the gap accelerator. Imposing a gap-closure condition that a single pair produces one pair in the gap on average, we explicitly solve the strength of the acceleration field and demonstrate how the luminosity of the curvature-radiated, GeV photons depends on the pulsar parameters such as the surface temperature, the rotational frequency and the magnetic moment. It is predicted that J0437-4715 is a possible candidate to be detected by a next-generation gamma-ray telescope like GLAST. We further explicitly show that the TeV flux emitted from the outer gap of a typical rotation-powered pulsar is too weak to be detected by current ground-based telescopes.