The acceleration of cosmic rays in shock fronts - II

The acceleration to relativistic energies of the high-energy tail of the particle distribution produced by a shock front is discussed. In order to be accelerated, particles need to be able to pass through the shock without being strongly deflected and it is argued, using the Earth's bow shock as an example, that a shock front produces large numbers of protons, and probably electrons also, which satisfy this condition. The resulting energy spectrum of these initially non-relativistic particles is calculated. It yields an estimate of the density of cosmic ray particles in a shocked gas and indicates that a large proportion of the random energy produced by a shock is given to accelerated particles. The synchrotron radio emission from the energetic electrons in a shocked gas is calculated, and the theoretical and observed flux densities of two supernova remnants (Tycho's SNR and Cas A) are compared and found to agree satisfactorily. The implications for the minimum energy of radio sources are considered, and the effect of multiple shocks on the cosmic ray density evaluated.