Shock acceleration and steep-spectrum synchrotron sources

The acceleration of particles by the Fermi mechanism is widely invoked to explain the synchrotron emission from active galaxies and supernova remnants, and for the origin of cosmic rays. Previous studies have generally assumed that the scattering of the particles is affected by small irregularities in an otherwise uniform magnetic field. Motivated by polarization measurements, particle acceleration in highly disordered magnetic fields are investigated, following particle trajectories numerically. It is found that mildly relativistic shocks give rise to synchrotron emission with a spectral index α ∼ 0.5-0.7, in excellent agreement with low-frequency optically thin synchrotron emission from active galaxies