Mass transfer in eccentric binary stars

The concept of Roche lobe overflow is fundamental to the theory of interacting binaries. Based on potential theory, it is dependent on all the relevant material corotating in a single frame of reference. Therefore if the mass losing star is asynchronous with the orbital motion or the orbit is eccentric, the simple theory no longer applies and no exact analytical treatment has been found. We use an analytic approximation whose predictions are largely justified by smoothed particle hydrodynamic simulations (SPH). We present SPH simulations of binary systems with the same semi-major axis a = 5.55 R-circle dot, masses M-1 = 1 M-circle dot, M-2 = 2 M-circle dot and radius R-1 = 0.89 R-circle dot for the primary star but with different eccentricities e = 0.4, 0.5, 0.6 and 0.7. In each case the secondary star is treated as a point mass. When e = 0.4 no mass is lost from the primary while at e = 0.7 catastrophic mass transfer, partly through the L-2 point, takes place near periastron. This would probably lead to common-envelope evolution if star 1 were a giant or to coalescence for a main-sequence star. In between, at e >= 0.5, some mass is lost through the L-1 point from the primary close to periastron. However, rather than being all accreted by the secondary, some of the stream appears to leave the system. Our results indicate that the radius of the Roche lobe is similar to circular binaries when calculated for the separation and angular velocity at periastron. Part of the mass loss occurs through the L-2 point.