Broadband Photon Spectrum and its Radial Profile of Pulsar Wind Nebulae

The observed radial profiles of the X-ray emission from Pulsar Wind Nebulae (PWNe) have been claimed to conflict with the standard one-dimensional (1-D) steady model. However, the 1-D model has not been tested to reproduce both the volume-integrated spectrum and the radial profile of the surface brightness, simultaneously. We revisit the 1-D steady model and apply it to PWNe 3C 58 and G21.5-0.9. We find that the parameters of the pulsar wind, the radius of the termination shock $r_{\rm s}$ and magnetization $\sigma$, greatly affect both the photon spectrum and radial profile of the emission. We have shown that the parameters constrained by the entire spectrum lead to a smaller X-ray nebula than observed one. We have also tested the case that reproduces only the observations in X and gamma-rays, ignoring the radio and optical components. In this case, there are parameter sets that reproduce both the spectrum and emission profile, but the advection time to the edge of the nebula becomes much smaller than the age. Our detailed discussion clarifies that the standard 1-D steady model has severe difficulty to reproduce both the volume-integrated spectrum and the surface brightness simultaneously. This implies that the model should be improved by taking into account extra physical processes such as spatial diffusion of particles. Additionally, we calculate the surface brightness profile of the radio, optical and TeV gamma-rays. The future observations in these wavelengths are also important to probe the spatial distributions of the relativistic plasma and the magnetic field of PWNe.