We present a long-term numerical three-dimensional simulation of a relativistic outflow designed to be compared with previous results from axisymmetric, two-dimensional simulations, with existing analytical models and state-of-art observations. We follow the jet evolution from 1~kpc to 200~kpc, using a relativistic gas equation of state and a galactic profile for the ambient medium. We also show results from smaller scale simulations aimed to test convergence and different three-dimensional effects. We conclude that jet propagation can be faster than expected from axisymmetric simulations, covering tens of kiloparsecs in a few million years, until the dentist drill effect produced by the growth of helical instabilities slows down the propagation speed of the jet head. A comparison of key physical parameters of the jet structure as obtained from the simulations with values derived from observations of FRII sources reveals good agreement. Our simulations show that shock heating can play a significant role in the feedback from active galaxies, confirming previous 2D results. A proper description of galactic jets as a relativistic scenario, both dynamical and thermodynamical, reveals an extremely fast and efficient feedback process reheating the ICM, and therefore, with dramatic consequences on the galactic evolution. Our results point towards FRII jets as the source of the energetic electrons observed in radio relics.
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