Double core evolution. IV. The late stages of evolution of a 2 M_⊙ red giant with a 1 M_⊙ companion

We report on the results of hydrodynamical simulations of the late phase of the common envelope stage of a binary consisting of a 2 M_⊙ red giant and a 1 M_⊙ main-sequence companion. The numerical results demonstrate that sufficient energy is released from the orbit to eject the mass within the common envelope without requiring the main-sequence companion to spiral into the white dwarf core of the red giant star. At the end of the simulation the orbital decay time scale increases rapidly to more than 160 yr. The long decay time scale reflects the removal of mass from the common envelope and its subsequent spin-up to near corotation. The ratio of the orbital decay time scale to the mass-loss time scale from the common envelope increases to more than 700 and the mass contained within the common envelope decreases to ∼0.01 M_⊙ or less. It is argued that further orbital decay will be small and that the final binary period will be 1.2 days.