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Non-thermal emission from standing relativistic shocks: an application to red giant winds interacting with AGN jets

Galactic and extragalactic relativistic jets have rich environments that are full of moving objects, such as stars and dense clumps. These objects can enter into the jets and generate shocks and non-thermal emission. We characterize the emitting properties of the downstream region of a standing shock formed due to the interaction of a relativistic jet with an obstacle. We focus on the case of red giants interacting with an extragalactic jet. We perform relativistic axisymmetric hydrodynamical simulations of a relativistic jet meeting an obstacle of very large inertia. The results are interpreted in the framework of a red giant whose dense and slow wind interacts with the jet of an active galactic nucleus. Assuming that particles are accelerated in the standing shock generated in the jet as it impacts the red giant wind, we compute the non-thermal particle distribution, the Doppler boosting enhancement, and the non-thermal luminosity in gamma rays. The available non-thermal energy from jet-obstacle interactions is potentially enhanced by a factor of $\sim 100$ when accounting for the whole surface of the shock induced by the obstacle, instead of just the obstacle section. The observer gamma-ray luminosity, including the flow velocity and Doppler boosting effects, can be ~300(g/10)^2 times higher than when the emitting flow is assumed at rest and only the obstacle section is considered, where g is the jet Lorentz factor. For a whole population of red giants inside the jet of an AGN, the predicted persistent gamma-ray luminosities may be potentially detectable for a jet pointing to the observer. Obstacles interacting with relativistic outflows, for instance clouds and populations of stars for extragalactic jets, or stellar wind inhomogeneities in microquasar jets and in winds of pulsars in binaries, should be taken into account when investigating the non-thermal emission from these sources.