A Three‐dimensional Outer Magnetospheric Gap Model for Gamma‐Ray Pulsars: Geometry, Pair Production, Emission Morphologies, and Phase‐resolved Spectra

A three-dimensional pulsar magnetosphere model is used to study the geometry of outer magnetospheric gap accelerators, following seminal work of Romani and coworkers. The size of the outer gap is self-consistently limited by pair production from collisions of thermal photons from polar cap heating of backflow outer gap current with curvature photons emitted by gap-accelerated charged particles. In principle, there could be two topologically disconnected outer gaps. Conditions for local pair production such as local field line curvature, soft X-ray density, electric field, etc., support pair production inside an outer gap only between r in (ϕ) (the radius of the null surface at azimuthal angle ϕ) and r lim (ϕ) ≈ 6 r in (ϕ = 0) ≪ R L (the light cylinder radius). Secondary pairs, on the other hand, are produced almost everywhere outside the outer gap by collisions between curvature photons and synchrotron X-rays emitted by these secondary pairs. These processes produce a wide X-ray fan beam in the outgoing direction and a very narrow beam in the incoming direction for each outer gap. For pulsars with a large magnetic dipole inclination angle, part of the incoming γ-ray beam will be absorbed by the stellar magnetic field. If the surface magnetic field is dominated by a far off-center dipole moment (e.g., as in a proposed "plate tectonic" model), gravitational bending of photons from polar cap accelerators and their ultimate conversion into outflowing e ± pairs can result in the quenching of one of these two outer gaps. Various emission morphologies for the pulsar (depending on magnetic inclination angle and viewing angle) are presented. Double-peak light curves with strong bridges are most common. From the three-dimensional structure of the outer gap and its local properties, we calculate phase-resolved spectra of gamma-ray pulsars and apply them to observed spectra of the Crab pulsar.