Analytical Study of Diffusive Relativistic Shock Acceleration

Abstract

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. Accurate analytic expressions for the spectral index s are derived using few (2-6) low-order moments of the shock-frame angular distribution. For isotropic diffusion, previous results are reproduced and justified. For anisotropic diffusion, s is shown to be sensitive to D, particularly downstream and at certain angles, and a wide range of s values is attainable. The analysis, confirmed numerically, can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by GRB afterglow observations.

4 pages, 2 figures, PRL accepted, minor changes

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• Relativistic Shocks: Particle Acceleration and Magnetization
• Ion dynamics and acceleration in relativistic shocks
• Interpretation and implication of the non-detection of GeV spectrum excess by Fermi gamma-ray Space Telescope in most GRBs
• Constraints on the Local Sources of Ultra High-Energy Cosmic Rays
• Hard Electron Energy Distribution in the Relativistic Shocks of GRB Afterglows
• Diffusive shock-acceleration: breakdown of spatial diffusion and isotropy
• Analytic study of 1D diffusive relativistic shock acceleration
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• The spectrum of Cosmic Rays escaping from relativistic shocks
• Maximally-hard spectra from diffusive shock-acceleration in pulsar-wind nebulae
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• Diffusive shock acceleration in $N$ dimensions
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• Synchrotron break frequencies of mildly-to-highly relativistic outflows observed off-axis