Analytic study of 1D diffusive relativistic shock acceleration

Published 18 October 2017 © 2017 IOP Publishing Ltd and Sissa Medialab
, , Citation Uri Keshet JCAP10(2017)025 DOI 10.1088/1475-7516/2017/10/025

1475-7516/2017/10/025

Abstract

Diffusive shock acceleration (DSA) by relativistic shocks is thought to generate the dN/dE∝ Ep spectra of charged particles in various astronomical relativistic flows. We show that for test particles in one dimension (1D), p−1=1− ln [γd(1+βd)]/ ln [γu(1+βu)], where βud) is the upstream (downstream) normalized velocity, and γ is the respective Lorentz factor. This analytically captures the main properties of relativistic DSA in higher dimensions, with no assumptions on the diffusion mechanism. Unlike 2D and 3D, here the spectrum is sensitive to the equation of state even in the ultra-relativistic limit, and (for a J{üttner-Synge equation of state) noticeably hardens with increasing 1<γu<57, before logarithmically converging back to pu)=2. The 1D spectrum is sensitive to drifts, but only in the downstream, and not in the ultra-relativistic limit.

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10.1088/1475-7516/2017/10/025