Mass-Transfer Stream Trajectories

Mass-Transfer Stream Trajectories

In their spectroscopic studies of accretion disks around Algol systems, Otto Struve and Su-Shu Huang discovered that the observance of H$\alpha$ emission lines was related to the orbital period of the systems in question. With these observations, they were able to separate the systems into two groups: short-period and long-period systems. Struve distinguished each group by the H$\alpha$ emission-line feature. In the short-period systems, Struve was only able to observe H$\alpha$ lines during primary eclipse. These transient features were observable when the stellar light was minimized during primary eclipse. On the other hand, the long-period systems displayed permanent H$\alpha$ lines throughout the entire orbital cycle, and were observable in the full light of the system.

As Kuiper (1941) suggested, the formation of a gaseous region around one of the components can be created by the transfer of mass from one star to the other. The motion of this gaseous material is dictated by the gravitational field of the two stars and other particles in the gaseous cloud. The gravitational effects of individual particles in the gaseous region are negligible as compared to the two stellar components. Therefore, the trajectory of a small particle from the L1 point towards the gainer star can be calculated from the restricted three-body equations or 2-dimensional hydrodynamical models.

The first formal treatment of the gas dynamics in semi-detached systems was published by Lubow & Shu (1975). Assuming that the components rotate synchronously, Lubow & Shu utilized the Roche model to describe the ejection of matter through the L1 point. Near the L1 point, the matter stream must accelerate from subsonic velocities to supersonic velocities to be carried through the L1 point. As the matter stream exits through the L1 point, the stream will be deflected by the Coriolis effect into a narrow stream. The angle of deflection is determined by the mass ratio of the system. These authors also analyzed the orbital region around the gainer star. The matter stream does not directly fall onto the surface of the gainer star. On the other hand, the excess angular momentum deflects the stream around the gainer star.