One-dimensional Electric Field Structure of an Outer Gap Accelerator -   III. Location of the Gap and the Gamma-ray Spectrum
  We investigate a stationary particle acceleration zone in the outer magnetosphere of a spinning neutron star. The charge depletion due to a global current causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate curvature gamma-rays, some of which collide with the X-rays to materialize as pairs in the gap. As a result of this pair-production cascade, the replenished charges partially screen the electric field, which is self-consistently solved together with the distribution of particles and gamma-rays. If no current is injected at neither of the boundaries of the accelerator, the gap is located around the so-called null surface, where the local Goldreich-Julian charge density vanishes. However, we find that the gap position shifts outwards (or inwards) when particles are injected at the inner (or outer) boundary. We apply the theory to the nine pulsars of which X-ray fields are known from observations. We show that the gap should be located near to or outside of the null surface for the Vela pulsar and PSR B1951+32, so that their expected GeV spectrum may be consistent with observations. We then demonstrate that the intrinsically large TeV flux from the outer gap of PSR B0540-69 is absorbed by the magnetospheric infrared photons to be undetectable. We also point out that the electrodynamic structure and the resultant GeV emission properties of millisecond pulsars are similar to young pulsars. 
Kouichi Hirotani and Shinpei Shibata