Magnetohydrodynamic Models for the Structure of Pulsar-Wind Nebulae

The Crab Nebula is well-described at optical wavelengths and above by a steady-state magnetohydrodynamic model due to Kennel and Coroniti (1984). Can this class of model describe other pulsar-wind nebulae? I exhibit simple generalizations of KC models,for various values of sigma, the ratio of magnetic to particle flux input at the wind shock. I calculate the evolution of the electron spectrum and synchrotron emissivity in the nebula assuming spherical symmetry, a steady state, and a purely toroidal magnetic field. Emission profiles depend on the initial magnetic field B_0, the electron spectral index s, and the angle of the toroidal axis with the line of sight, phi. I show integrated spectra and radial profiles for various cases, along with predicted variations of photon index Gamma with radius in X-rays. Most models predict much smaller sizes in X-rays, and curves of Gamma(r) which do not resemble observations. Further elaborations of the dynamics of PWNe seem necessary.