Test-Particle Diffusive Shock Acceleration in Relativistic Shocks

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We present results from a fully relativistic Monte Carlo simulation of diffusive shock acceleration (DSA) in unmodified (i.e., test-particle) shocks. The computer code uses a single algorithmic sequence to smoothly span the range from nonrelativistic speeds to fully relativistic shocks of arbitrary obliquity, providing a powerful consistency check. We show the dependence of the particle spectrum, which can differ strongly from the canonical f(p) proportional to p⁻⁴.²³ result, on the obliquity and on the strength and ``fineness'' of scattering for a range of shock Lorentz factors. The Monte Carlo results are also shown to be consistent with a simple relation for the spectral index given by Keshet and Waxman (2005) in parallel shocks when the diffusion is ``fine'' and isotropic.