2017MNRAS.472.2926L

Observations of two pulsar wind nebulae (PWNe) 3C 58 and G21.5-0.9 indicate that they have mostly symmetric spherical morphologies, emit photons from radio to γ-rays and have the radial variations of the photon indices in X-ray band. The spatially radiative properties of 3C 58 and G21.5-0.9 are modelled in the frame of a spatially dependent model. Combining with the dynamical evolution of each PWN, the time evolution of the spectral energy distributions (SEDs) and the radial variations of the photon indices of 3C 58 and G21.5-0.9 are calculated. Our modelling results show that observed multiband SEDs and the radial variations of the photon indices in X-ray band of these two PWNe can be reproduced well. From the modelling results, the values for the present-day diffusion coefficient and magnetic field are derived, including the values at the termination shock and the spatial average. The spatial changes of the present-day photon indices at different bands are predicted and our results show that the photon indices obviously vary with radial distance in almost all of energy range except that in radio and GeV γ-ray bands.