Aims. The goal of the paper is to present a detailed study of the propagation of low velocity (5 to 25 km s-1) stationary molecular shocks in environments illuminated by an external ultraviolet (UV) radiation field. In particular, we intend to show how the structure, dynamics, energetics, and chemical properties of shocks are modified by UV photons and to estimate how efficiently shocks can produce line emission. Methods. We implemented several key physico-chemical processes in the Paris-Durham shock code to improve the treatment of the radiative transfer and its impact on dust and gas particles. We propose a new integration algorithm to find the steady-state solutions of magnetohydrodynamics equations in a range of parameters in which the fluid evolves from a supersonic to a subsonic regime. We explored the resulting code over a wide range of physical conditions, which encompass diffuse interstellar clouds and hot and dense photon-dominated regions (PDR). Results. We find that C-type shock conditions cease to exist as soon as G0 > 0.2 (nH/cm-3)^1/2. Such conditions trigger the emergence of another category of stationary solutions, called C*-type and CJ-type shocks, in which the shocked gas is momentarily subsonic along its trajectory. These solutions are shown to be unique for a given set of physical conditions and correspond to dissipative structures in which the gas is heated up to temperatures comprised between those found in C-type and adiabatic J-type shocks. High temperatures combined with the ambient UV field favour the production or excitation of a few molecular species to the detriment of others, hence leading to specific spectroscopic tracers such as rovibrational lines of H2 and rotational lines of CH+. Unexpectedly, the rotational lines of CH+ may carry as much as several percent of the shock kinetic energy.
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