Roche-lobe overflow in the vicinity of the inner Lagrangian point in close binary systems

Abstract

The formation of flows in the vicinity of the inner Lagrangian point has been computed for various close binary systems (from short-period U Gem to long-period β Lyr systems). The dependence of the masstransfer rate through the inner Lagrangian point on the degree of Roche-lobe overflow is derived. One new aspect of this work is the use of Kurucz stellar model atmospheres when constructing the initial configuration of the outer layers of the mass-losing star and also the use of the “large particles” numerical method of Belotserkovski$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}$ and Davydov. The application of these stellar model atmospheres provides a more realistic description of the stream than do polytropic models. The computations show that the influence of the Coriolis and centrifugal forces on the rate of mass transfer is negligible and does not exceed a few percent. In certain specific cases (β Per and W UMa), the stream models differ strongly from those of Lubow and Shu. The degree of Roche-lobe overflow and the rate of mass transfer indicated by observations are such that the atmospheric layers of the mass-losing star are nearly always located at the inner Lagrangian point. The only exceptions are compact binary systems and U Gem stars, in which the inner Lagrangian point resides in layers of the mass-losing star that are denser than its atmospheric layers, and the β Per system, in which the mass-losing atmosphere is located inside its Roche lobe. The numerical dependences of the mass-transfer rate on the degree of Roche-lobe overflow differ from the analytical dependences for both large and small overflows. This is due to differences between the Kurucz model stellar atmospheres and the polytropic models used in previous analytical calculations and also to the presence of dynamical effects connected with the mass transfer in the computations. The polytropic indices corresponding to the best agreement between the numerical and analytical dependences are 4.5 for β Lyr, 2.4–2.6 for the cataclysmic binaries, and 3.1–3.3 for the remaining stars. These polytropic indices indicate that the Roche lobes of the mass-losing stars in close binary systems are usually overflowing.