Pair creation at shocks. Application to the high energy emission of compact objects

We investigate the effect of pair creation on a shock structure. Particles, accelerated in the shock via the first order Fermi process, are supposed to cool by inverse Compton process on external soft photons, resulting in a cut-off power law shape of the particle distribution function. The high energy photons produced are thus able to create pairs, through photon-photon annihilation. The increase of the pair pressure may then be sufficient to modify the shock profile. We show that there is even a limit of the pair pressure (of the order of 20% of the ram pressure of the upstream flow) above which the shock cannot exist any longer. Conversely, significant changes of the flow velocity profile will also modify the spectral index and the high energy cut--off of the particle distribution function. Hence the number of particles able to trigger the pair creation process will change, modifying the pair creation rate accordingly. Taking into account these different processes, we self-consistently derive the flow velocity profile and the particle distribution function. We show that, in some region of the parameter space, the system can converge towards stationary states where pair creation and hydrodynamical effects balance. We discuss the application of this model to explain the high energy emission observed in compact objects. We show that hard X-ray spectra ($\alpha_{X}< 1.$) are only obtained for small pair pressure and we don't expect any strong annihilation line in this case. We suggest also a possible variability mechanism if the soft photon compactness depends itself on the pair density of the hot plasma, such as expected in reillumination models.