The Effect of Diffusion on the Particle Spectra in Pulsar Wind Nebulae

Abstract

A possible way to calculate particle spectra as a function of position in pulsar wind nebulae is to solve a Fokker-Planck transport equation. This paper presents numerical solutions to the transport equation with the processes of convection, diffusion, adiabatic losses, and synchrotron radiation included. In the first part of the paper the steady-state version of the transport equation is solved as a function of position and energy. This is done to distinguish the various effects of the aforementioned processes on the solutions to the transport equation. The second part of the paper deals with a time-dependent solution to the transport equation, specifically taking into account the effect of a moving outer boundary. The paper highlights the fact that diffusion can play a significant role in reducing the amount of synchrotron losses, leading to a modification in the expected particle spectra. These modified spectra can explain the change in the photon index of the synchrotron emission as a function of position. The solutions presented in this paper are not limited to pulsar wind nebulae, but can be applied to any similar central source system, e.g. globular clusters.

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• On the Unusually Large Spatial Extent of the TeV nebula HESS J1825-137: Implication from the Energy-Dependent Morphology
• Multi-band Emission up to PeV Energy from the Crab Nebula in a Spatially Dependent Lepto-hadronic Model
• Hitomi X-ray Observation of the Pulsar Wind Nebula G21.5$-$0.9
• Exploiting Morphological Data from Pulsar Wind Nebulae via a Spatio-Temporal Leptonic Transport Code
• Pulsar Wind Nebulae