Eccentric orbit generalization and simultaneous solution of binary star light and velocity curves

This paper discusses the computation of binary star light and radial velocity curves, including the effects of eccentric orbits and nonsynchronous rotation. Logical relations needed to impose physical constraints (semidetached condition, etc.) are specified. Some of the more important mathematical relations are also given. One can now model semidetached, detached, double-contact, and X-ray binaries for arbitrary rotation rates and orbital eccentricity. Contact binaries can also be modeled, but are restricted to the synchronous, circular orbit case. In all cases the figures of the components and the surface gravity fields are described by surfaces of constant potential energy. An essentially rigorous treatment is given of the solution constraint imposed by X-ray eclipse durations in eccentric orbit cases, assuming photospheric eclipses. Attention is drawn to a previously unrecognized morphological type of close binary, for which the name double-contact binary is suggested. This is a binary in which both stars fill their limiting lobes and at least one spins faster than synchronously, so that the components do not touch, even at one point. Some proposed members of this group are β Lyr, V356 Sgr, and perhaps U Cep. As examples of program applications, light curves are computed for SW Lyn and radial velocity curves for HD 77581 (4U 0900-40). One can show that the photometry of SW Lyn does not permit an eccentricity as large as has been reported, and that there is no photometric evidence for e ≠ 0. Radial velocity distortions for HD 77581 due to proximity effects are small enough to neglect, considering the scatter of the best present observations. Values of X-ray eclipse duration (Θe) for two rotation rates and two values of e are given. In order to overlap the range of observational Θe values, the rotation should be slow (perhaps half-synchronism) and e should not exceed about 0.10. Several kinds of evidence point to a recent rapid increase in radius of HD 77581. A method is given by which simultaneous differential corrections solutions of light and radial velocity curves can be made. Proper weighting schemes are especially crucial to the success of such solutions.