Inhomogeneous models for plerions: the surface brightness profile of the Crab Nebula

We extend the homogeneous model for the synchrotron emission from plerions to allow more realistic predictions of the surface brightness distribution at different 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 by MHD propagation in a magnetic field of spatially constant but time-dependent intensity. This highly simplified model reproduces the integrated spectrum and the synchrotron surface brightness profile of the Crab Nebula at radio frequencies. However, when applied to higher frequencies, it underestimates the extension of the emitting region, suggesting that particle diffusion with respect to the magnetic field lines must occur.