Diffusive acceleration in relativistic shocks: Particle feedback

Yotam Nagar, Uri Keshet

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The spectral index s of high-energy particles diffusively accelerated in a non-magnetized relativistic shock, such as in a γ-ray burst afterglow, depends on the unknown angular diffusion function D, which itself depends on the particle distribution function f if acceleration is efficient. We develop a relaxation code to compute s and f for an arbitrary functional D that depends on f. A local D(f)$ dependence is motivated and shown, when rising (falling) upstream, to soften (harden) s with respect to the isotropic case, shift the angular distribution towards upstream (downstream) directions, and strengthen (weaken) the particle confinement to the shock; an opposite effect on s is found downstream. However, variations in s remain modest even when D is a strong function of f, so the standard, isotropic-diffusion results remain approximately applicable unless D is both highly anisotropic and not a local function of f. A mild, ∼0.1 softening of s, in both 2D and 3D, when D(f) rises sufficiently fast, may be realized in ab initio simulations.

Original languageEnglish
Pages (from-to)329-336
Number of pages8
JournalMonthly Notices of the Royal Astronomical Society
Issue number1
StatePublished - 1 Feb 2021


  • acceleration of particles
  • gamma-ray burst: General
  • magnetic fields
  • shock waves


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