We investigate the physical mechanisms of tidal heating and satellite disruption in cold dark matter host haloes using N-body simulations based on cosmological initial conditions. We show the importance of resonant shocks and resonant torques with the host halo to satellite heating. A resonant shock (torque) couples the radial (tangential) motion of a satellite in its orbit to its phase space. For a satellite on a circular orbit, an inner Lindblad resonance (ILR)-like resonance dominates the heating and this heating results in continuous satellite mass loss. We estimate the requirements for simulations to achieve these dynamics using perturbation theory. Both resonant shocks and resonant torques affect satellites on eccentric orbits. We demonstrate that satellite mass loss is an outside-in process in energy space; a satellite's stars and gas are thus protected by their own halo against tidal stripping. We simulate the evolution of a halo similar to the Large Magellanic Cloud (LMC) in our Galactic dark matter halo and conclude that the LMC stars have not yet been stripped. Finally, we present a simple algorithm for estimating the evolution of satellite mass that includes both shock heating and resonant torques.
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