Spatial Development of Energetic Particle Spectra in Pulsar Wind Nebulae

TL;DR

This paper introduces a spatially-dependent model for pulsar wind nebulae that accounts for magnetic field structure and particle transport, improving upon previous uniform-source models.

Contribution

It extends existing nebula models by incorporating spatial dependence and magnetic field effects into the particle transport equations.

Findings

Shows the impact of magnetic field structure on particle spectrum evolution.

Provides a numerical solution framework for spatially-dependent particle transport.

Applicable to systems similar to pulsar wind nebulae, like globular clusters.

Abstract

The evolution of the non-thermal emission emitted by pulsar wind nebulae is generally calculated using spatially-independent particle transport models. Although useful, these models implicitly assume that the source of non-thermal particles is located uniformly throughout the system, contrary to the nature of pulsar wind nebulae where the source is located at the centre of the system. Additionally, it is not possible to take into account the spatial properties of the magnetic field and flow velocity, or the effects of diffusion and gradient and curvature drifts in these models. In this paper we present an extension to the current nebula models by including a spatial dependence in our numerical solutions of a Fokker-Planck particle transport equation. These solutions also show the effect that the magnetic field structure has on the evolution of the particle spectrum. Although applied within the context of pulsar wind nebulae, the presented solutions are equally valid for any similar central source system such as globular clusters.