1ST-ORDER FERMI PARTICLE-ACCELERATION BY RELATIVISTIC SHOCKS

We present Monte Carlo calculations of test particle spectra and acceleration times from first-order Fermi particle acceleration for parallel shocks with arbitrary flow velocities, and in particular for relativistic shocks. We give results for compression ratios up to 7 and for shock velocities, u1, up to 0.98c. We display complete spectra for several injection energies ranging from thermal to considerably superthermal. Far above the injection energy, the spectra are well approximated by a power law. In this region, the spectra are always harder than for nonrelativistic shocks; as the shock velocity approaches c, the spectral index, σ, approaches 1 [N(E)α E-σ] for large compression ratios r. We give approximate analytic expressions for the spectral slope as a function of u1 and r. The acceleration time as a function of particle energy is found to be less than for nonrelativistic shocks, by a factor that increases with u1, and it is about 3 for u1 = 0.98c. Monte Carlo techniques are used with two different scattering operators: pitch-angle (small deflection) diffusion and large-angle (isotropic) scattering, the scattering being elastic in both cases. We confirm earlier results that the spectrum for pitch-angle diffusion is considerably steeper than for large-angle scattering, for the same shock parameters. Our pitch-angle scattering operator assumes deflections are isotropic within a small cone about the particle's direction of motion. The Monte Carlo techniques we employ do not rely on the diffusion approximation and can treat anisotropic distributions, whether from thermal particles in all shocks or in shocks with relativistic flows speeds. Essentially the same Monte Carlo code has been tested extensively against spacecraft observations at the Earth's bow shock. We briefly discuss applications of these results to relativistic shocks expected to exist in pulsar winds and active galactic nuclei.