Modelling the evolution of pulsar wind nebulae

Abstract

This study focusses on modelling important aspects of the evolution of pulsar wind nebulae using two different approaches. The first uses a hydrodynamic model to simulate the morphological evolution of a spherically-symmetric composite supernova remnant that is expanding into a homogeneous interstellar medium. In order to extend this model, a magnetic field is included in a kinematic fashion, implying that the reaction of the fluid on the magnetic field is taken into account, while neglecting any counter-reaction of the field on the fluid. This approach is valid provided that the ratio of electromagnetic to particle energy in the nebula is small, or equivalently, for a large plasma β environment. This model therefore allows one to not only calculate the evolution of the convection velocity but also, for example, the evolution of the average magnetic field. The second part of this study focusses on calculating the evolution of the energy spectra of the particles in the nebula using a number of particle evolution models. The first of these is a spatially independent temporal evolution model, similar to the models that can be found in the literature. While spatially independent models are useful, a large part of this study is devoted to developing spatially dependent models based on the Fokker-Planck transport equation. Two such models are developed, the first being a spherically-symmetric model that includes the processes of convection, diffusion, adiabatic losses, as well as the non-thermal energy loss processes of synchrotron radiation and inverse Compton scattering. As the magnetic field geometry can lead to the additional transport process of drift, the previous model is extended to an axisymmetric geometry, thereby allowing one to also include this process.