Spectral theory of mixed shocks : application to Cygnus A type hot spots.

A theory of classical shocks in a mixed fluid composed of a thermal classical plasma, containing most of the mass density is investigated. The structure of the shock and the cosmic ray spectrum is derived for an arbitrary ratio between the downstream pressures, in the case where magnetic pressure is negligible. It turns out that the energy spectral index remains close to 2 in the strong shock limit. A strong collisionless shock mainly heats protons, but a limitation due to the finite width of the shock layer (compared to the relativistic electron diffusion length) is exhibited. Such a theory is suitable for application to radio source hot spots and predicts a synchrotron spectrum which extends up to X-rays. A consistent model for Cygnus A type hot spots is presented, including a thermal plasma of protons carrying an amplified magnetic field, the relativistic component contributing only to a small fraction of the mass density. The paper is divided into two parts: the first one is devoted to the theory of mixed shocks and acceleration of relativistic particles, the second to its application to Cygnus A type hot spots, which are probably the largest shocks in nature.