Spatially Radiative Properties Of Pulsar Wind Nebulae

Pulsar wind nebulae(PWNe)are the very high energy y-ray sources.It is gen-erally believed that a PWN is created by the interaction of the pulsar wind with the non-relativistic ejecta of the ambient supernova remnant.A termination shock is formed in the interaction,and then the particles are accelerated to extreme relativistic energy at the shock.From the termination shock,the high energy particles are injected into the nebula,and emit photons ranging from radio to TeV y-rays during the evolution of the PWN.Observations reveal that the photon indices and surface brightness of some PWNe in the X-ray band change with radial distance,which provide very useful information for us to set up the model for describing radiative features of PWNe.In this thesis,the spatially radiative properties of PWNe are investigated theoretically,and main results are as follows.The importance of diffusion effect in a particle propagation model is studied in de-tails.Under the assumption that the system is spherically symmetric and expands with a constant velocity,the Fokker-Planck transport equation,which describes the evolution of electrons in the PWN,is numerically solved using the Douglas Alternating Direction Implicit method in spherical coordinates,where the processes of convection,diffusion,radiative loss,and adiabatic loss of the electrons are included.The effects of magnetic field,PWN age,maximum energy of the electrons,and diffusion coefficient on elec-tron spectra and non-thermal photon spectra.Our results indicate that electron spectra and the corresponding photon spectra are both the functions of radial distance.The lower energy part of the electron spectra is dominated by convection and adiabatic loss of the electrons,but the higher energy part is dominated by the competition between synchrotron loss and diffusion of the electrons,and such a competition is a function of radial distance and time due to the magnetic field and diffusion coefficient are both time and spatial dependent.Therefore the diffusion effect has an important role in the spatial evolution of electron spectra as well as non-thermal photon spectra in a PWN.A self-consistent and spatially dependent model is presented to investigate the multi-band emission of the PWN.In the frame of the dynamical evolution and one di-mensional magnetohydrodynamic model,the electron evolution is described as Fokker-Planck transport equation,which includes the processes of convection,diffusion,adia-batic loss,radiative loss,and photon-photon pair production of the electrons;the photon evolution is given by the photon conservation equation including the processes of syn-chrotron radiation,inverse Compton scattering,synchrotron self-absorption,and the pair production of the photons.The electron spectra and corresponding non-thermal photon spectra of the PWN are obtained through numerically solving the coupled equations.The model is applied to explain observed results of the PWN in MSH 15-52.Our results show that both the spectral energy distributions(SEDs)and the radial variations of the photon index and surface brightness in X-ray band of the PWN can be well reproduced.Moreover,the model predicts that the spectral indices obviously vary with radial dis-tance in X-ray and TeV bands,but only have slightly changes in radio and GeV bands.The spatially radiative properties of 3C 58 and G21.5-0.9 are modelled in the frame of the self-consistent and spatially dependent model.Our modelling results show that both the multi-band observations and the radial variations of the photon indices in X-ray band of the two PWNe can be well reproduced.Combining with the dynamical evolution of the 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.From our calculations,both the multi-band SEDs and radial photon indices of PWN have significant difference as time increase;the model predict that the photon indices obviously increase with the increase of radial distance in X-ray and TeV bands,but the spatial changing characteristics are not identically.