Shock-drift particle acceleration in superluminal shocks - A model for hot spots in extragalactic radio sources

Shock-drift acceleration at relativistic shock fronts is investigated using a fully relativistic treatment of both the microphysics of the shock-drift acceleration and the macrophysics of the shock front. By explicitly tracing particle trajectories across shocks, it is shown how the adiabatic invariance of a particle's magnetic moment breaks down as the upstream shock speed becomes relativistic, and is recovered at subrelativistic velocities. These calculations enable the mean increase in energy of a particle which encounters the shock with a given pitch angle to be calculated. The results are used to construct the downstream electron distribution function in terms of the incident distribution function and the bulk properties of the shock. The synchrotron emissivity of the transmitted distribution is calculated, and it is demonstrated that amplification factors are easily obtained which are more than adequate to explain the observed constrasts in surface brightness between jets and hot spots.