Radiation- and pair-loaded shocks

We consider the structure of mildly relativistic shocks in dense media, taking into account the radiation and pair loading, and diffusive radiation energy transfer within the flow. For increasing shock velocity (increasing post-shock temperature), the first important effect is the efficient energy redistribution by radiation within the shock that leads to the appearance of an isothermal jump, whereby the flow reaches the finial state through a discontinuous isothermal transition. The isothermal jump, on scales much smaller that the photon diffusion length, consists of a weak shock and a quick relaxation to the isothermal conditions. Highly radiation-dominated shocks do not form isothermal jump. Pair production can mildly increase the overall shock compression ratio to $\approx 10$ (from $4$ for matter-dominated shocks and $7$ of the radiation-dominated shocks).