Dynamical effects of mass exchange in close binary systems

Abstract

The problem of mass exchange in a close binary system is studied from the point of view of the evolution of the orbital elements. It is assumed that the original orbit is nearly circular and one of the components has expanded and fills the area inside the equipotential surface passing through the inner Lagrangian pointL ₁, losing mass to the other component. The mass is assumed to be ejected along the tangent to the equipotential surface passing throughL ₁ in retrograde orbits.

It is proved that the eccentricity remains very small. The semimajor axis increases in almost all cases where the mass is being transferred from the less massive to the more massive component, and decreases when the mass is being transferred from the more massive to the less massive component. It is also shown that if the more massive star evolves first and loses mass to its companion, the process of mass exchange continues automatically until the originally more massive component becomes the less massive one and the binary system remains in an almost static condition for long intervals of time, the less massive component occupying the area inside the equipotential surface passing throughL ₁ and surrounding the star.