Particle acceleration in ultra-relativistic oblique shock waves

We perform Monte Carlo simulations of diffusive shock acceleration at highly relativistic oblique shock waves. High upstream flow Lorentz gamma factors (Gamma) are used, which are relevant to models of ultra-relativistic particle shock acceleration in active galactic nuclei (AGN) central engines and relativistic jets and gamma ray burst (GRB) fireballs. We investigate numerically the acceleration properties in the relativistic and ultra-relativistic flow regime (Gamma similar to 10-10(3)), such as angular distribution, acceleration time constant, particle energy gain versus number of crossings and spectral shapes. We perform calculations for sub-luminal and super-luminal shocks. For the first case, the dependence on whether or not the scattering is pitch angle diffusion or large angle scattering is studied. The large angle model exhibits a distinctive structure in the basic power-law spectrum which is not nearly so obvious for small angle scattering. However, both models yield significant 'speed-up' or faster acceleration rates when compared with the conventional, non-relativistic expression for the time constant, or alternatively with the time scale r(g)/c where r(g) is Larmor radius. The Gamma(2) energization for the first crossing cycle and the significantly large energy gain for subsequent crossings as well as the high 'speed-up' factors found, are important in supporting the Vietri and Waxman work on GRB ultra-high energy cosmic ray, neutrino and gamma-ray output. Secondly, for super-luminal shocks, we calculate the energy gain for a number of different inclinations and the spectral shapes of the accelerated particles are given. In this investigation we consider only large angle scattering, partly because of computational time limitations and partly because this model provides the most favourable situation for acceleration. We use high gamma flows with Lorentz factors in the range 10-40, which are relevant to AGN accretion disks and jet ultra-relativistic shock configurations. We closely follow the particle's trajectory along the magnetic field lines during shock crossings where the equivalent of a guiding centre approximation is inappropriate, constantly measuring its phase space co-ordinates in the fluid frames where E = 0. We find that a super-luminal 'shock drift' mechanism is less efficient in accelerating particles to the highest energies observed, compared to the first order Fermi acceleration applying in the sub-luminal case, suggesting that the former cannot stand as a sole acceleration mechanism for the ultra-high energy cosmic rays observed. (C) 2003 Elsevier Science B.V. All rights reserved