The Net Advance of Physics: Gamma-Ray Pulsar Emission Models, by Alice K. Harding -- Section 4.

Outer Gap Models

Vacuum gaps may grow in the outer magnetosphere along null

charge surfaces, which separate regions of the opposite sign of the

corotation charge. Along open field lines threading this surface,

charges of one sign will escape through the light cylinder and

cannot be replaced, because charge coming from the polar cap

below has the opposite sign. Particles can be accelerated by the

resulting in the gap to energies limited by curvature radiation

reaction (Cheng, Ho & Ruderman 1986). In outer gap models, the

spectral cutoffs are due to this limit on the primary particle energy

and are predicted to be somewhat more gradual than the

attenuation cutoffs of polar cap models.

Unlike the case in polar cap models, the magnetic fields

in the outer gap are too weak for one-photon pair production

to play a significant role in the cascade. Instead, the

curvature photons undergo photon-photon pair production

with thermal X-rays from the polar caps (as in the case of

Vela or Geminga) or non-thermal X-rays produced by the cascade

(as in the Crab). In the Crab pulsar, the -ray emission is

produced by synchrotron self-Compton radiation from the pairs,

with the lower energy part of the spectrum dominated by the

synchrotron component and the higher energy spectrum dominated

by inverse Compton (Ho 1989). In Vela-like pulsars with periods

around 0.1 s, a large obliquity is required to bring the inner gap

radius closer to the neutron star. This has the dual purpose of

increasing the optical depth to pair production with thermal X-ray

photons (Romani 1996) and increasing the gap magnetic field,

which moves the ``death" line to longer periods (Chen & Ruderman

1993). The spectra of these pulsars will be primarily curvature

radiation and it is possible to reproduce the observed soft-hard-soft

variation through the profile (Romani 1996).

The -ray pulse profiles from the outer gaps have been

investigated, in a simple geometrical model, by Chiang & Romani

(1994), who assumed that the emission from gap accelerated

particles is beamed along magnetic field lines and also assumed a

spatial and energy dependence of the radiation. They were able to

produce double peaked profiles with bridge emission separated by

, similar to the Crab and Vela pulsars. The -rays from the

outer gap are emitted into fan beams with large solid angle

sr.

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