Nonlinear Particle Acceleration in Relativistic Shocks

Monte Carlo techniques are used to model nonlinear particle acceleration in parallel collisionless shocks of various speed, including mildly relativistic ones. When the acceleration is efficient, the backreaction of accelerated particles modifies the shock structure and causes the compression ratio, r, to change from test-particle values. Modified shocks with Lorentz factors less than about 3, can have compression ratios greater than 4 and the momentum distribution of energetic particles no longer follows a power law relation. For faster shocks, r depends on the shock Lorentz factor but can drop below 3, giving self-consistent spectra considerably steeper than the so-called `universal' test-particle result of N(E) proportional to E^{-2.3}. In the ultra-relativistic limit (i.e., Lorentz factors greater than about 50), shocks undergoing efficient particle acceleration may adjust enough to conserve energy and momentum without lowering r and the compression ratio may again approach the test-particle value of 3