Excitation of gravity waves in common envelopes

We study the excitation of gravity waves by a low-mass companion orbiting inside the envelope of a giant star, concentrating on brown dwarfs inside the envelope of asymptotic giant branch stars. Efficient g-wave excitations occur only after the brown dwarf has spiraled-in to the radiative zone, well inside the envelope, of the asymptotic giant branch star. The brown dwarf excites g-waves when its orbital radius is about 3-10 solar radii. At this stage of the evolution the envelope mass is below 0.1 solar mass. The g-waves propagate inward from the secondary orbit, carrying angular momentum and energy. We find that the angular momentum transport leads to an efficient spin-up of the inner envelopes. The differential rotation between the envelope and core and nonlinear wave effects, can cause a mixing of heavy elements from the core to the envelope.