Spatial dependence of high energy electrons and their radiations in pulsar wind nebulae

We investigate the spatial dependence of high energy electrons and their radiations in pulsar wind nebulae（PWNe）.By assuming a time-dependent broken power-law injection and spatial dependence of convection velocity,magnetic field strength and diffusion coefficient on the radial distance of an expanding system,we numerically solve the Fokker-Planck transport equation including convection,diffusion,adiabatic loss and radiative loss in spherical coordinates,and investigate the effects of magnetic field,PWN age,maximum energy of electrons,and diffusion coefficient on electron spectra and non-thermal photon emissions.Our results indicate that（1） electron spectra and the corresponding photon spectra are a function of radial distance r of the expanding system;（2） for a given expansion velocity,the increase of the PWN age causes a slower decrease of the convection velocity(V ∝ r-β) and a more rapid decrease of the magnetic field strength(B ∝ r-1+β),but a more rapid increase of the diffusion coefficient(κ∝ r1-β) because the index β decreases with the PWN age;and（3） the lower energy part of the electron spectra is dominated by convection and adiabatic loss,but the higher energy part is dominated by the competition between synchrotron loss and diffusion,and such a competition is a function of radial distance.Therefore the diffusion effect has an important role in the evolution of electron spectra as well as non-thermal photon spectra in a PWN.