Introduction

If binary stars simply executed their orbits according to Newtonian theory for point masses, then interest in their properties would have waned long ago, save for the need to improve determinations of stellar masses. The universe is rather more exciting, however, and at least the close binary stars (as defined in Chapter 1) display all manner of perturbations and interactions that guarantee that they will continue to provide an abundance of astrophysical phenomena that will require explanation. In this chapter we consider a sequence of progressively greater departures from the point-mass, spherical-star model that we used in Chapters 2 and 3.

We consider, firstly, a theory of mild perturbations, or deviations from the idealized spherical shape for a star, which theory can fully explain the observed phenomena of apsidal motion, the circularization of orbits, and the synchronization of stellar axial-rotation periods and orbital periods. The stars in such binary systems become tidally locked, such that two stellar hemispheres face each other, and two are permanently averted. The logical extension of these perturbations is to the Roche model for binary stars that is applicable to tidally locked systems in circular orbits. Here the stars can be virtually spherical in shape when their radii (R) are small relative to their separation (a)(R/a < 0.10), and they appear no different from those in the earlier point-mass theory. But the Roche model also permits stars to become seriously distorted from spherical shape, with R/a > 0.20, far beyond the limitations of the earlier perturbation theory.