A model for the spatial distribution of relativistic electrons in the Crab Nebula

We extend the homogeneous model for the synchrotron emission from plerions to allow more realistic predictions of the surface brightness profiles of the Crab Nebula at radio, optical and X-ray frequencies. Abandoning the assumption of a uniform particle distribution, we assume that particles are injected into the synchrotron nebula only in the vicinity of the pulsar. Their distribution is then determined, to zeroth order, by MHD propagation in an azimuthal magnetic field of spatially constant but time-dependent intensity. A good agreement with observations across the electromagnetic spectrum is obtained if the finite extension of the particle injection region and particle diffusion with respect to the azimuthal field lines are taken into account.