Vibrational stability of the components of close binary systems

The aim of the present paper will be to extend our previous investigation of the vibrational stability of rotating configurations (Kopal, 1981) to a similar investigation of the stability of the components of close binary systems which not only rotate, but also distort each other by tidal action. To this end, differential equations which govern first-order oscillations of arbitrary spherical-harmonic symmetry will be set up in Clairaut coordinates in which the radial coordinate is replaced by the potential which remains constant over level surfaces of equilibrium configurations; introduced by us in an earlier paper (Kopal, 1980), and their form detailed for surface distorted by second-, third-, and fourth-harmonic tides raised by the external mass; and their boundary conditions established. A solution of such differential boundary-value problems arising in connection with the stars of arbitrary structure remains, of course, a task for automatic computers. It may only be added that the tide-generating potential Ψ _T established in this paper should enable us to study, by the same method, not only free, but also forced oscillations of the components of close binary systems, arising from orbital eccentricity of the respective couples, dynamical tides, or other causes likely to be operative in such systems.