In addition to merger, mass transfer occurs if either star fills its Roche Lobe by expanding during the later stages of evolution. The Roche Lobes are spherical surfaces surrounding each star where the force of gravitational attraction is equal and opposite. Models show that in systems such as these, any material that passes beyond the Roche-lobe of the star will flow onto the binary companion, often by way of an accretion disk (recall the illustration on the previous page). This occurs as material from the primary star streams through the inner Lagrangian point where the gravity of the two stars cancels.
When the Roche lobe filling star is a giant with a convective envelope of material surrounding the core, or is significantly more massive than the companion, then the transferred material may not be captured by the companion but accumulate in a region that surrounds both stars called a common envelope. The BSE models the resulting common envelope (CE) event, which accounts for possibility of the expulsion of the common envelope as the two form either close/contact binaries or the cores spiral into one another during a merger.
The documentation of mass transfer provided by the BSE throughout the simulations of this study were used to make correlations with binary periods to predict formation pathways of particular observed BSs in the open cluster NGC 188 (see the results sections for more details).
This illustration depicts the outerlayers of the primary stars expanding not only beyond its Roche Lobe, but also beyond that of the secondary. The result is a common envelope of material surrounding both stars