Low-velocity shocks: signatures of turbulent dissipation in diffuse irradiated gas

w Context. Large-scale motions in galaxies (supernovae explosions, galaxy collisions, galactic shear etc.) generate turbulence, which allows a fraction of the available kinetic energy to cascade down to small scales before it is dissipated. Aims. We establish and quantify the diagnostics of turbulent dissipation in mildly irradiated diffuse gas in the specific context of shock structures. Methods. We incorporated the basic physics of photon-dominated regions into a state-of-the-art steady-state shock code. We examined the chemical and emission properties of mildly irradiated (G(0) = 1) magnetised shocks in diffuse media (n(H) = 10(2) to 10(4) cm(-3)) at low-to moderate velocities (from 3 to 40 km s(-1)). Results. The formation of some molecules relies on endoergic reactions. Their abundances in J-type shocks are enhanced by several orders of magnitude for shock velocities as low as 7 km s(-1). Otherwise most chemical properties of J-type shocks vary over less than an order of magnitude between velocities from about 7 to about 30 km s(-1), where H-2 dissociation sets in. C-type shocks display a more gradual molecular enhancement with increasing shock velocity. We quantified the energy flux budget (fluxes of kinetic, radiated and magnetic energies) with emphasis on the main cooling lines of the cold interstellar medium. Their sensitivity to shock velocity is such that it allows observations to constrain statistical distributions of shock velocities. We fitted various probability distribution functions (PDFs) of shock velocities to spectroscopic observations of the galaxy-wide shock in Stephan's Quintet and of a Galactic line of sight which samples diffuse molecular gas in Chamaeleon. In both cases, low velocities bear the greatest statistical weight and the PDF is consistent with a bimodal distribution. In the very low velocity shocks (below 5 km s(-1)), dissipation is due to ion-neutral friction and it powers H-2 low-energy transitions and atomic lines. In moderate velocity shocks (20 km s(-1) and above), the dissipation is due to viscous heating and accounts for most of the molecular emission. In our interpretation a significant fraction of the gas in the line of sight is shocked (from 4% to 66%). For example, C+ emission may trace shocks in UV irradiated gas where C+ is the dominant carbon species. Conclusions. Low- and moderate velocity shocks are important in shaping the chemical composition and excitation state of the interstellar gas. This allows one to probe the statistical distribution of shock velocities in interstellar turbulence.