The main body of the book has been concerned with the effects of axial rotation upon the structure and evolution of single stars. As was pointed out in Section 1.4, further challenging problems arise from the study of double stars whose components are close enough to raise tides on the surface of each other. Indeed, tidal interaction in a detached close binary will continually change the spin and orbital parameters of the system (such as the orbital eccentricity e, mean orbital angular velocity inclination m, and rotational angular velocity ^ of each component). Unless there are sizeable stellar winds emanating from the binary components, the total angular momentum will be conserved during these exchange processes. However, as a result of tidal dissipation of energy in the outer layers of the components, the total kinetic energy of a close binary system will decrease monotonically. Ultimately, this will lead to either a collision or an asymptotic approach toward a state of minimum kinetic energy. Such an equilibrium state is characterized by circularity (e = 0), coplanarity (m = 0), and corotation (^ = ^0); that is to say, the orbital motion is circular, the rotation axes are perpendicular to the orbital plane, and the rotations are perfectly synchronized with the orbital revolution.

To be specific, unless the binary components rotate in perfect synchronism with a circular orbital motion, each star senses a variable external gravitational field - thus becoming liable to oscillatory motions that may be described as an "equilibrium tide" and a "dynamical tide." The former is just the instantaneous shape obtained by assuming that strict mechanical equilibrium prevails, even though the forcing potential depends on time, that is to say, it is assumed that the forced oscillations of the star are rapidly damped out and do not affect the "equilibrium distortion." The latter refers to the dynamical response of the star to the tidal forcing of its natural modes of oscillation. As we shall see in Section 8.2, the effects of turbulent viscosity retarding the equilibrium tide play an important role in binary components with a deep connective envelope; these stars experience a torque that tends to induce synchronization. However, because viscosity is much too small in stars having an outer radiative envelope, a different mechanism must be invoked to explain the high degree of synchronism and orbital circularization that is observed in the early-type binaries. In Section 8.3 we shall see that radiative damping can produce in part the required torque by retarding the dynamical tide in these stars.

In the late 1970s, the theoretical predictions based on these two distinct mechanisms were in agreement with the (then current) observations. Unfortunately, as will be shown in Sections 8.2.2 and 8.3.1, they are unable to explain all of the most recent observational data reported in Section 1.4. This is the reason why in Section 8.4 we shall consider another braking mechanism, which is much more efficient than the two classical ones but has hitherto escaped notice. In my opinion, this third mechanism was overlooked for so long because too much reliance had been placed on the deep-rooted tradition of celestial mechanics, with the hydrodynamical aspect of the problem being neglected altogether. As we shall see in Section 8.4.2, this mechanism is operative in the early-type and late-type binaries alike. It involves a large-scale meridional flow, superposed on the motion around the rotation axis of the tidally distorted star. These transient, mechanically driven currents are caused by the forced lack of axial symmetry in a binary component; they cease to exist as soon as synchronization has been achieved in the star. They are thus quite different from the steady, thermally driven currents presented in Section 4.6, which, as we recall, are caused by the forced lack of spherical symmetry in the radiative envelope of a tidally distorted binary component. They are also quite different from the large-scale atmospheric motions presented in Sections 2.5.1 and 2.5.2; as we shall see in Section 8.5, however, these geostrophic (or astrostrophic) currents are of direct relevance to the study of contact binaries.

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