A Self-Consistent and Spatially Dependent Model of the Multiband Emission of Pulsar Wind Nebulae

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 , the spatial average has a value of , and the present-day magnetic field at the termination shock has a value of and the spatial averaged magnetic field is . The spatial changes of the spectral index and surface brightness at different bands are predicted.