Abstract

In this paper a model for /3 Lyrae is developed which attempts to account for the complex photometric and spectroscopic phenomena and which is consistent with dynamics. In the introduction the dimensions of the system are discussed, and the conclusion is reached that the components have a common envelope (they form a "contact binary"). In section 2 it is shown that con- tact binaries with unequal components are unstable. It is shown that matter streams from A to B as long as the masses are unequal; that L~m and z~(Spectra1 type) are abnormally large for the mass ratio; and that a system of currents will be set up (Fig. ~, b). These currents account for the sateffite compo- nents of spectral lines observed near the primary minimum of /3 Lyrae. If the common envelope attains great height and/or if the currents attain large velocities, ejection of matter from the outer point of B will take place. This ejection is considered to supply the source of the mysterious B5 spectrum and to cause the asymmetry and irregularity of the photometric minimum. Ejection of another type (type A), arising in a separated binary composed of one giant and one dwarf star, is also considered, and its application to peculiar emission stars with composite spectra is stressed. The theory of both types of ejection based on Jacobi's integral is given in section 4. The orbits of ejected particles are determined in sections 5-7. Section 5 contains the first-order theory for the vicinity of the point of ejection; Figures 6 and 7 illustrate the results. Numerical integrations are used in sections 6 and 7 with Figures 8-12 showing the orbits obtained. Section 8 gives applications to /3 Lyrae and other stars. A schematic picture of the gaseous tail in which ~ Lyrae winds itself is given in Figure 13. The effect is that of a giant pinwheel with one streamer. The shadow cast by B on the streamer appears to play an im- portant role in the spectral features, as it appears to de-ionize the gas. The change of period in $ Lyrae is also considered. It appears that both the process of mass transfer from A to B and the ejection from B would tend to shorten the period. The effect on the period of the pressure at the interface of the com- ponents is examined in the addendum