Driving Outflows with Relativistic Jets and the Dependence of AGN Feedback Efficiency on ISM Inhomogeneity

We examine the detailed physics of the feedback mechanism by relativistic AGN jets interacting with a two-phase fractal interstellar medium in the kpc-scale core of galaxies using 29 3D grid-based hydrodynamical simulations. The feedback efficiency, as measured by the amount of cloud-dispersal generated by the jet-ISM interactions, is sensitive to the maximum size of clouds in the fractal cloud distribution but not to their volume filling factor. Feedback ceases to be efficient for Eddington ratios P_jet/L_edd<10^-4, although systems with large cloud complexes ~50 pc require jets of Eddington ratio in excess of 10^-2 to disperse the clouds appreciably. Based on measurements of the bubble expansion rates in our simulations we argue that sub-grid AGN prescriptions resulting in negative feedback in cosmological simulations without a multi-phase treatment of the ISM are good approximations if the volume filling factor of warm phase material is less than 0.1 and the cloud complexes are smaller than ~25 pc. We find that the acceleration of the dense embedded clouds is provided by the ram pressure of the high velocity flow through the porous channels of the warm phase, flow that has fully entrained the shocked hot-phase gas it has swept up, and is additionally mass-loaded by ablated cloud material. This mechanism transfers 10% to 40% of the jet energy to the cold and warm gas, accelerating it within 10 to 100 Myr to velocities that match those observed in a range of high and low redshift radio galaxies hosting powerful radio jets.