The spectrum of particles accelerated in relativistic, collisionless shocks

Details The spectrum of particles accelerated in relativistic, collisionless shocks The spectrum of particles accelerated in relativistic, collisionless shocks

2004-08-25

arxiv.org/abs/astro-ph/0408489v1

Phys.Rev.Lett. 94 (2005) 111102

Astronomy and Astrophysics

Astrophysics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.94.111102

We analytically study diffusive particle acceleration in relativistic, collisionless shocks. We find a simple relation between the spectral index s and the anisotropy of the momentum distribution along the shock front. Based on this relation, we obtain s = (3beta_u - 2beta_u*beta_d^2 + beta_d^3) / (beta_u - beta_d) for isotropic diffusion, where beta_u (beta_d) is the upstream (downstream) fluid velocity normalized to the speed of light. This result is in agreement with previous numerical determinations of s for all (beta_u,beta_d), and yields s=38/9 in the ultra-relativistic limit. The spectrum-anisotropy connection is useful for testing numerical studies and for constraining non-isotropic diffusion results. It implies that the spectrum is highly sensitive to the form of the diffusion function for particles travelling along the shock front.

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