Shock acceleration and steep-spectrum synchrotron sources

Abstract

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 effected by small irregularities in an otherwise uniform magnetic field. Motivated by polarization measurements, we investigate particle acceleration in highly disordered magnetic fields, following particle trajectories numerically. We find that mildly relativistic shocks give rise to synchrotron emission with a spectral index α ~0.5–0.7 (S_υ∝ υ^−α), in excellent agreement with low-frequency optically thin synchrotron emission from active galaxies. For highly relativistic shock speeds (u/c ≥ 0.9) the spectrum steepens (α > 1), and may be relevant in explaining emission from blazars. In terms of the Lorentz factor of the shock, we find a rough relation α≃(3γ+ 1)/8. This trend may also be connected with the observed steepening of synchrotron spectra with radio power observed in powerful radio sources.