Published online by Cambridge University Press: 25 May 2016
Recent three-dimensional studies of the common-envelope phase of binary evolution have provided important insights into its theoretical description. The role of non-axisymmetric effects associated with gravitational torques is essential for understanding all aspects of the evolution. For successful ejection of the common envelope and survival of the remnant compact binary it is required that the orbital period of the progenitor system is long, so that one of the components of the system is in the red giant or red supergiant stage of evolution. Not only must there be sufficient energy released from the orbit to unbind the common envelope, but it is also necessary that a sufficiently steep density gradient exist above the evolved core of the giant. If these conditions are satisfied, the time scale for orbital decay in the region above the core exceeds the time scale for mass loss from the common envelope and merger is avoided. The implications of these results for the formation of cataclysmic variables (CVs), low-mass X-ray binaries (LMXBs), and the descendants of high-mass X-ray binaries (HMXBs) are discussed.