Electron-positron pair creation in relativistic shocks: Pair plasma in thermodynamic equilibrium

The thermodynamics of the relativistic shock wave in which electron-positron pairs are produced in the post-shock matter is studied in the temperature range 5×${10}^9$ K≲T≲${10}^{12}$ K, where the baryons are nonrelativistic and electron-positron pairs are the only leptons created. The post-shock matter with pairs in thermodynamic equilibrium are classified according to whether or not the energy density of the radiation (the pairs and the photons) exceeds that of the baryons. The post-shock matter without pairs in thermal equilibrium is also considered in the case where it is composed of a relativistic two-temperature electron-ion plasma. The relevant time scales for such processes as temperature relaxation, pair production, and cooling are examined in order to establish the temperature region where such a plasma can exist. Analytic relations between the pre-shock and post-shock quantities are obtained in certain limits of these three cases. The shocks with and without pairs in the post-shock matter are then compared.