2017ApJ...834...43L

A self-consistent and spatially dependent model is presented to investigate the multiband emission of pulsar wind nebulae (PWNe). In this model, a spherically symmetric system is assumed and the dynamical evolution of the PWN is included. The processes of convection, diffusion, adiabatic loss, radiative loss, and photon-photon pair production are taken into account in the electron's evolution equation, and the processes of synchrotron radiation, inverse Compton scattering, synchrotron self-absorption, and pair production are included for the photon's evolution equation. Both coupled equations are simultaneously solved. The model is applied to explain observed results of the PWN in MSH 15-52. Our results show that the spectral energy distributions (SEDs) of both electrons and photons are all a function of distance. The observed photon SED of MSH 15-52 can be well reproduced in this model. With the parameters obtained by fitting the observed SED, the spatial variations of photon index and surface brightness observed in the X-ray band can also be well reproduced. Moreover, it can be derived that the present-day diffusion coefficient of MSH 15-52 at the termination shock is κ₀=6.6×10²⁴ cm² s^–1, the spatial average has a value of {bar}κ=1.4×10²⁵ cm² s^–1, and the present-day magnetic field at the termination shock has a value of B₀=26.6 µG and the spatial averaged magnetic field is {bar}B=14.9 µG. The spatial changes of the spectral index and surface brightness at different bands are predicted.