One-dimensional electric field structure of an outer gap accelerator — II. γ-ray production resulting from inverse Compton scattering

We study the structure of a stationary and axisymmetric charge-deficient region (or a potential gap) in the outer magnetosphere of a spinning neutron star. A large electric field along the magnetic field lines is created in this potential gap and accelerates migratory electrons (e−) and/or positrons (e+) to ultrarelativistic energies. Assuming that the gap is immersed in a dense soft photon field, these relativistic e± radiate γ-ray photons via inverse Compton (IC) scattering. These γ-rays, in turn, produce yet more radiating particles by colliding with ambient soft photons, leading to a pair-production cascade in the gap. The replenished charges partially screen the longitudinal electric field, which is self-consistently solved together with the distribution of e± and γ-ray photons. It is demonstrated that the voltage drop in the gap is not more than 1010 V when the background X-ray radiation is as luminous as 1037 erg s−1. However, this value increases with decreasing X-ray luminosity and attains 1012 V when the X-ray radiation is 1036 erg s−1. In addition, we find useful expressions of the spatial distribution of the particle fluxes and longitudinal electric field, together with the relationship between the voltage drop and the current density. Amazingly, these expressions are valid not only when IC scattering dominates but also when curvature radiation dominates.