DOUBLE-CORE EVOLUTION .9. 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 gi ant of 5 M. characterized by a ratio of core mass to total mass of sim ilar to 0.2 with main-sequence companions of 0.5 and 1 M. are consider ed. 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 enve lope binary is sensitive to the structure of the red giant star. Provi ded that the common envelope exhibits a flat mass radius profile and t hat sufficient orbital energy is released to unbind the envelope, a lo ng-period (P greater than or similar to 0.3 yr) system can be transfor med into a short-period system (P less than or similar to 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 quantit y V = dln p/d lnr of the initial envelope. It is found that the orbita l separations increase with the core mass of the progenitor red giant star. A basis for prescribing the outcome of common envelope evolution is presented.