Abstract
The observations of gamma-ray emission from pulsars with the Fermi-LAT detector and the detection of the Crab pulsar with the VERITAS array of Cherenkov telescopes at energies above 100 GeV make it unlikely that curvature radiation is the main source of photons above GeV energies in the Crab and many other pulsars. We outline a model in which the broad UV-X-ray component and the very high energy \gamma-ray emission of pulsars are explained within the Synchrotron-Self-Compton (SSC) framework. We argue that the bulk of the observed radiation is generated by the secondary plasma, which is produced in cascades in the outer gaps of the magnetosphere. We find that the inverse-Compton (IC) scattering occurs in the Klein-Nishina regime, which favors synchrotron photons in the UV band as target field for the scattering process. The primary beam is accelerated in a modest electric field, with a field strength that is of the order of a few percent of the magnetic field near the light cylinder. Overall, in the Klein-Nishina regime of the IC scattering the particle distribution in the gap does not evolve towards a stationary distribution and thus is intrinsically time-dependent. We point out that in a radiation reaction-limited regime of particle acceleration the gamma-ray luminosity L_{\gamma} scales linearly with the pulsar spin-down power \dot{E}, L_\gamma ~ \dot{E}, and not proportional to \sqrt{\dot{E}} as expected from potential-limited acceleration.
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