Several observations are revealing the widespread occurrence of mildly relativistic wide-angle AGN winds strongly interacting with the gas of their host galaxy. Such winds are potential cosmic-ray accelerators, as supported by gamma-ray observations of the nearby Seyfert galaxy NGC 1068 with the Fermi gamma-ray space telescope. The non-thermal emission produced by relativistic particles accelerated by the AGN-driven wind observed in the circum-nuclear molecular disk of such galaxy is invoked to produce the gamma-ray spectrum. The AGN wind model predicts a hard spectrum that extend in the very high energy band which differs significantly from those corresponding to other models discussed in the literature, like starburst or AGN jet. We present dedicated simulations of observations through the Cherenkov Telescope Array (CTA), the next-generation ground based gamma-ray observatory, of the very high energy spectrum of the Seyfert galaxy NGC 1068 assuming the AGN wind and the AGN jet models. We demonstrate that, considering 50 hours of observations, CTA can be effectively used to constrain the two different emission models, providing important insight into the physics governing the acceleration of particles in non-relativistic AGN-driven outflows. This analysis strongly motivates observations of Seyfert and starburst galaxies with CTA in order to test source population models of the extragalactic gamma-ray and neutrino backgrounds.
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