Synchrotron Model for the Infrared, Optical and X-Ray Emission of the   Crab Pulsar
  We develop a model for the infrared, optical and soft X-ray emission of the Crab pulsar in terms of anisotropic synchrotron emission by relativistic particles in an outer gap scenario with a single energy distribution. It is shown that such a distribution is naturally produced in an efficient pair cascade and that the energy of the primary particles are limited by synchrotron radiation. It is further shown that this synchrotron model is able to reproduce the spectral shape between the infrared and soft X-rays and also the corresponding luminosities. In particular, the long standing problem of the rapid spectral decline towards infrared frequencies is understandable as emission at very small pitch angles from low energy particles. Finally, we show that the scaling of our synchrotron model explains the observed correlation between the X-ray luminosity and the spin-down luminosity of the neutron star. 
A. R. Crusius-Waetzel, T. Kunzl, H. Lesch