Double core evolution. X. Through the envelope ejection phase

The evolution of binary systems consisting of an asymptotic giant branch star of mass equal to 3 M. or 5 M. and a main-sequence star of mass equal to 0.4 M. or 0.6 M. with orbital periods greater than or similar to 200 days has been followed from the onset through the late stages of the common-envelope phase. Using a nested grid technique, the three-dimensional hydrodynamical simulations of an asymptotic giant branch star with radii similar to 1 AU indicate that a significant fraction of the envelope gas is unbound (similar to 31% and 23% for binaries of 3 M. and 0.4 M., and 5 M. and 0.6 M., respectively) by the ends of the simulations and that the efficiency of the mass ejection process similar to 40%. During an intermediate phase, a differentially rotating structure resembling a thick disk surrounds the remnant binary briefly before energy input from the orbits of the companion and remnant core drive the mass away. While the original volume of the giant is virtually evacuated in the late stages, most of the envelope gas remains marginally bound on the grid. At the ends of our simulations, when the orbital decay timescale exceeds about 5 yr, the giant core and companion orbit one another with a period of similar to 1 day (2.4 days for a binary involving a more evolved giant), although this is an upper limit to the final orbital period. For a binary of 5 M. and 0.4 M., the common envelope may not be completely ejected. The results are not found to be sensitive to the degree to which the initial binary system departs from the synchronous state.