Surface Forms and Mass Loss for the Components of Close Binaries-General Case of Non-Synchronous Rotation.

Abstract

The problem considered is that of determining the surface forms, the limiting surfaces, and the properties relating to mass loss for non-synchronously rotating components of close binaries. Attention is confined to systems for which the orbital motion is circular and for which the components can be treated as Roche models whose internal motions are largely included in uniform rotations about fixed axes through their centers of mass. The surface forms are derived in a first approximation in which deviations irom uniform rotation are neglected in the equation of motion; the surface forms in this approximation follow from the hydrostatic equation for the appropriate uniformly rotating frame. (The well-known theories for synchronously rotating components of close binaries and for uniformly rotating single stars are clearly particular cases of this first approximation.) The remainder of the paper is devoted to a discussion of the limitations of this first approximation and to a consideration of the nature and magnitude of the deviations from it that are to be expected. Some general implications of these results for the evolution of members of close binaries are briefly noted.