Anomalous transport of cosmic ray electrons

TL;DR

This paper models anomalous cosmic ray electron transport using continuous time random walks, analyzing how different diffusion regimes affect synchrotron emission and spectral softening in galaxy clusters.

Contribution

It introduces a formalism for modeling anomalous transport of cosmic ray electrons and applies it to explain observed synchrotron spectra in galaxy clusters.

Findings

Supra-diffusive transport explains the diffuse emission in the Coma cluster.

Sub-diffusive transport results in slower spectral index changes.

The model matches observed synchrotron spectral softening.

Abstract

Anomalous transport processes in which the variance of the distance travelled does not necessarily increase linearly with time are modelled using the formalism of continuous time random walks. We compute particle propagators which have the required dependence on space and time and use these to find the spatial dependence of the synchrotron radiation emitted by a population of continuously injected electrons. As the electrons are transported away from the source they cool, and the synchrotron spectrum softens. Sub-diffusive transport -- corresponding to stochastic trapping, or restriction of the transport across the average direction of a stochastic magnetic field -- produces a much slower rate of change of spectral index than does supra-diffusion -- which occurs when particles move almost without scattering, in a field containing large ordered regions. Application to the diffuse emission of the outer parts of the Coma cluster favours an interpretation in terms of supra-diffusion.