Double-Core Evolution. IX. The Infall of a Main-Sequence Star through the Envelope of Its Intermediate-Mass Red Giant Companion

The common envelope phase of binary evolution is investigated for the formation of cataclysmic variable systems. An intermediate-mass red giant of 5 M_sun characterized by a ratio of core mass to total mass of ∼0.2 with main-sequence companions of 0.5 and 1 M_sun are considered. It is found that the ejection of the common envelope is favorable for binary systems consisting of red giants of large radii and massive companions. The survival of the system as a detached post-common envelope binary is sensitive to the structure of the red giant star. Provided that the common envelope exhibits a flat mass radius profile and that sufficient orbital energy is released to unbind the envelope, a long-period (P ≳ 0.3 yr) system can be transformed into a short-period system (P 1 day). The orbital separation of these systems as they emerge from the spiral in phase is estimated from the local minimum in the dimensionless quantity V = -d ln p/d ln r of the initial envelope. It is found that the orbital separations increase with the core mass of the progenitor red giant star. A basis for prescribing the outcome of common envelope evolution is presented.