On Particle Acceleration around Shocks. I.

2002/12/31 by Mario Vietri, M. Vietri · 6 citations
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Cosmology and Gravitation Theories #Gamma-ray bursts and supernovae #astro-ph

paper · pdf · doi:10.1086/375534

published as Astrophys.J. 591 (2003) 954-961 · Accepted for publication in ApJ; minor changes only

arxiv created 2003/03/28 · openalex publication_date 2003/07/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We derive a relativistically covariant (although not manifestly so) equation for the distribution function of particles accelerated at shocks, which applies also to extremely relativistic shocks and arbitrarily anisotropic particle distributions. The theory is formulated for arbitrary pitch-angle scattering and reduces to the well-known case for small-angle scatterings via a Fokker-Planck approximation. The boundary conditions for the problem are completely reformulated introducing a physically motivated Green's function; the new formulation allows derivation of the particle spectrum both close and far away from the injection energy in an exact way, while it can be shown to reduce to a power law at large particle energies. The particle spectral index is also recovered in a novel way. Contact is made with the Newtonian treatment.

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