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

Abstract

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 backÑow 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 Ðeld line curvature, soft X-ray density, electric Ðeld, etc., support pair production inside an outer gap only between (the radius of the null surface at azimuthal angle /) and r in (/) r lim (/) B 6r in (/ \ (the light cylinder radius). Secondary pairs, on the other hand, are produced almost everywhere 0) > R L 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 c-ray beam will be absorbed by the stellar magnetic Ðeld. If the surface magnetic Ðeld is dominated by a far o †-center dipole moment (e.g., as in a proposed "" plate tectonic ÏÏ model), gravitational bending of photons from polar cap accelerators and their ultimate conversion into outÑowing eB 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.

The Phase‐resolved X‐Ray Spectra of the Crab Pulsar

“…High-energy -ray emission is mainly produced by the Compton scattering. Cheng et al (2000) have used this model to explain the phase-dependent spectra and phase-average spectrum of high-energy -rays for the Crab pulsar. Therefore, in principle, our model can explain nonthermal radiation from Xrays to -rays.…”

Relativistic Effects and Polarization in Three High‐Energy Pulsar Models

“…we use the "retarded vacuum dipole" approximation, commonly encountered in previous research (eg. Romani & Yadigaroglu 1995;Arendt & Eilek 1998;Cheng et al 2000). However, to enable estimate of the importance of near lightcylinder magnetic field distortions, we also present a limited number of results for the static shape dipole.…”

“…In the recent version of the outer gap (OG) model (Romani & Yadigaroglu 1995;Cheng, Ruderman, Zhang (2000), hereafter CRZ2000) peaks in pulsar lightcurves are purely due to the caustic effects -a fact first emphasized by Romani & Yadigaroglu (1995) (hereafter RY95). However, an important additional factor which determines lightcurve shape in the OG model is the geometry of the acceleration region (outer gap).…”

VLBI imaging of a flare in the Crab nebula: more than just a spot

“…3) can be represented by a power-law expansion Δ r ∝ z m , which yields m ≈ 0.7. A jet viewing angle of 60 • (Cheng et al 2000;Komissarov & Lyutikov 2011) is assumed in these calculations. The expansion derived is consistent with the one expected for the jet boundary in a magnetically confined flow (Fendt 1997;Fendt & Memola 2001) with a weakly evolving poloidal magnetic field component.…”