On secular stability of tidally distorted stars of arbitrary structure

Abstract

The aim of the present paper will be to develop a theory which should make it possible to investigate secular stability of close binary systems, consisting of tidally-distorted components of arbitrary internal structure, by a minimization of the potential energy of the system as a whole. In the second section which follows brief introductory remarks, appropriate expressions for the total potential energy of a close binary will be formulated. Section 3 will be concerned mainly with the nature of the tide-generating potential, and its effects on the shape of each star. In Section 4, the amplitudes of partial tides raised by this potential will be specified, for stars of arbitrary structure, correctly to terms of second order in superficial distortion; and in Section 5 we shall investigate the effects of interaction between rotation and tides to the same degree of approximation. The concluding Section 6 will then contain an explicit formulation of different constituents adding up to the total potential energy of the system, which can be used as a basis for its secular stability by the methods outlined already in our previous investigation (Kopal, 1973).