Jet--ISM Interactions in Gaseous Disks: Simulating Kinetic Feedback in the Radio Galaxy 3C 326 N

Several radio galaxies, such as 3C,326,N, show signatures of jet--ISM coupling, but a complete theoretical framework for explaining them is still lacking. Interpreting these observations requires a detailed understanding of the gas distribution, geometry, and outflow energetics. In this paper, we use three-dimensional relativistic hydrodynamic simulations to investigate jet--ISM coupling in inhomogeneous gaseous disks, exploring a parameter space spanning different cloud configurations, jet powers, and central disk densities. Our simulations incorporate a numerical turbulence injection scheme that maintains vertical support in the disk, preventing the unphysical collapse encountered in previous studies. We find that jet--ISM coupling is strongly governed by the underlying cloud configuration, leading to distinct outflow morphologies, velocity dispersions, and kinetic energies. Simulations with small-scale (l c,max=50 pc) clouds produce the highest velocity dispersions and kinetic energies, whereas large-scale cloud configurations (l c,max=250 pc) yield the lowest values, with mixed cloud distributions exhibiting intermediate behavior. In addition, mixed cloud configurations give rise to asymmetric jet propagation, naturally producing unequal lobe lengths similar to those observed in radio galaxies. We compare our fiducial simulation (a 10 45, erg,s-1 jet interacting with a mixed cloud configuration) with observations of 3C,326,N, focusing on the morphology of the jet-driven bubble, synthetic emission and the gas kinematics. Our results successfully reproduce the observed properties, providing strong evidence that jet--ISM interactions can account for the wide bubble and the complex gas kinematics observed in this system.