Modelling Plerion Spectra and their Evolution

We review recent theoretical developments on pulsar winds, their nebulae and relativistic shock acceleration, and show how they illuminate unsolved problems in plerion spectra, in particular the multiple spectral breaks in the Crab and the low-frequency breaks of plerions such as G 21.5-0.9 and 3C 58. Recent work on Fermi acceleration theory at relativistic shocks shows that a particle spectral index of 2.2-2.3, compatible with the X-ray spectra of plerions, results under a wide variety of assumptions. If pulsar winds contain ions as well as electrons and positrons, the mechanism of Hoshino et al. (1992), which yields harder spectra, would operate at lower energies and may explain the flat radio spectral indices of plerions. This scenario implies wind parameters in the Crab compatible with the pulsar wind acceleration model of Lyubarsky & Kirk (2001). Recent hydrodynamical simulations of plerion evolution inside SNR blast waves demonstrate that the passage of the reverse shock rapidly compresses the plerion. Using a simple isobaric model, we investigate the influence of the resulting magnetic field compression and decrease in shock radius on the evolution of the plerion spectrum. We suggest that the passage of the reverse shock may explain the low-frequency breaks in 3C 58 and G 21.5-0.9, as well as the increase in 3C 58's radio flux