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.

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We present a model of X-ray emission from rotation-powered pulsars, which in general consist of one nonthermal component, two hard thermal components, and one soft thermal component. The nonthermal X-rays come from synchrotron radiation of eB pairs created in the strong magnetic Ðeld near the neutron star surface by curvature photons emitted by charged particles on their way from the outer gap to the neutron star surface. The Ðrst hard thermal X-ray component results from polar-cap heating by the return current in the polar gap. The second hard thermal X-ray component results from polar-cap heating by the return particles from the outer gap. Because of cyclotron resonance scattering, most of the hard thermal X-rays will be e †ectively reÑected back to the stellar surface and eventually reemitted as soft thermal X-rays. However, some of the hard thermal X-rays can still escape along the open magnetic Ðeld lines, where the e`/e~pair density is low. Furthermore, the characteristic blackbody temperatures of the two hard X-ray components emitted from the polar-cap area inside the polar gap and the polarcap area deÐned by the footprints of the outer-gap magnetic Ðeld lines are strongly a †ected by the surface magnetic Ðeld, which can be much larger than the dipolar Ðeld. In fact, the strong surface magnetic Ðeld can explain why the e †ective blackbody radiation area is nearly 2 orders of magnitude larger than that deduced from the dipolar Ðeld for young pulsars (2 orders of magnitude less for old pulsars). Our model indicates how several possible X-ray components may be observed, depending on the magnetic inclination angle and viewing angle. Using the expected X-ray luminosity and spectra, we explain the observed X-ray spectra from pulsars such as Geminga, PSR B1055[52, PSR B0656]14, and PSR B1929]10.