X-ray emission of a pulsar wind nebula (PWN) is a group of particles with the highest energy among the non-thermal electron-positrons present in the nebula. The standard emission model of PWNe predicts that such high energy particles lose their energy immediately by radiative cooling and that the emission region of X-rays is smaller than those of lower frequencies. However, as 3C 58 and G21.5-0.9, some PWNe have been discovered in which the emission region of X-rays and radio extend to the almost same extent, and it has been pointed out that the conventional model has room for reconsideration.
We investigate the validity of the model by simultaneously calculating the emission spectrum integrating over the entire nebula and the radial profile of the X-ray surface brightness. Our detailed analysis reveals that the conventional model cannot explain observational facts of 3C 58 and G21.5-0.9. Furthermore, in order to improve the model, we construct a model of PWNe in consideration of spatial diffusion due to a disturbed magnetic field. We show that entire spectra and X-ray surface brightness profiles are reproduced simultaneously by our new model. The model implies the existence of a large gamma-ray halo which consists of particles diffusely escaped out of the nebula. The halo could spread to a degree that it can be resolved spatially by the Cherenkov Telescope Array.