Double-core evolution. V. Three-dimensional effects in the merger of a red giant with a dwarf companion

The evolution of the common envelope phase of a binary system consisting of a 4.67 M_⊙ red giant and a 0.94 M_⊙ dwarf is studied using smoothed particle hydrodynamics. We demonstrate that the three-dimensional effects associated with the gravitational tidal torques lead to a rapid decay of the orbit on timescales ≲1 yr. The relative orbit of the two cores in the common envelope is initially eccentric and tends to circularize as the orbital separation of the two cores decreases. The angular momentum lost from the orbital motion is distributed throughout the common envelope, and the double core does not evolve to a state of co-rotation for the evolutionary time followed. The energy dissipated from the relative orbit and deposited in the common envelope results in the ejection of ∼13% of the mass of the envelope. The mass is ejected in all directions, but there is a preference for mass ejection in the orbital plane of the binary system. For example, ∼80% of the ejected mass lies within 30° of the binary orbital plane. Because gravitational forces are long range, most of the energy and angular momentum is imparted to a small fraction of the common envelope resulting in an efficiency of the mass ejection process of ∼15%. The core of the red giant executes significant displacement with respect to the center of mass of the system and contributes nearly equally to the total energy dissipation rate during the latter phases of the evolution. The degree of departure from synchronism of the initial binary system can be an important property of the system which can affect the outcome of the common envelope phase.