Resonant interaction in common envelopes

The resonant interaction between an orbiting low-mass secondary star and the pulsational modes of the primary in a common envelope binary system is studied. When the secondary is very close to the envelope, and especially if it is inside the envelope, i.e., the system is in a common envelope phase, a rich spectrum of both g- and p-modes can be excited. During the common envelope phase high-order and high harmonic p-modes become important. By means of a simple one-zone model, the amplitudes of the forced oscillations are approximately estimated. It is claimed that if several conditions are met, then a brown dwarf secondary can cause nonnegligible axisymmetrical mass loss through its resonant interaction with a red giant primary's envelope. One implication of this for elliptical planetary nebulae is discussed.