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 σ, 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 B0, the electron spectral index s, and the angle of the toroidal axis with the line of sight, φ. I show integrated spectra and radial profiles for various cases, along with predicted variations of photon index Γ with radius in X-rays. Most models predict much smaller sizes in X-rays, and curves of Γ (r) which do not resemble observations. Further elaborations of the dynamics of PWNe seem necessary.