| Summary: | A method for the computer synthesis of theoretical light curves and like profiles for close binary stars in general has been developed and applied to the W Ursae Majoris stars. The geometry has been calculated using the centrally-condensed Roche model, for which a formulation in terms of cylindrical coordinates has been developed. Limb darkening has been computed using second order fits to the atmosphere grid of Kurucz, Carbon and Gingerich, and Hγ profiles have been taken from the same grid. A simple correction has been made to account for variations over the photosphere of each component.
Lucy’s model of a common convective envelope has been assumed for the W Ursae Majoris systems, and the “reflection affect has been computed for it also. Theoretical values obtained by Lucy and Rucinski for the gravity darkening exponent and the effective albedo respectively have been used. It has been found this method that the “reflection” effect should be small fir W Ursae Majoris stars.
The computer routines in FORTRAN IV for generating the Roche geometry have been systematically checked against polished tables, and the synthesis routines have been checked against well-known analytical methods for the simplified case of spherical components.
Consistent fits have been obtained to the observed light curves of four W. Ursae Majoris systems: BD+30°2163, V566 Oph, RR Cen, and RZ Tau, with mass-ratios respectively of 0.179±0.08, 0.238±0.005, 0.180±0.010 and 0.380±0.010. Less consistent fits have been obtained for several other systems. The common envelopes of these systems were found to lie between their inner and outer Lagrangian surfaces. A theoretical relation between the angle of internal contact for totally eclipsing systems and the inclination was obtained, and used in the fitting of models for the systems studied in this work.
The observed H profile of BD+30°2163 was found to be considerably narrower than the theoretical one, and this disparity is attributed tentatively to a composition not typical of Population I.
Masses and absolute magnitudes were computed approximately using the empirical mass-luminosity law for main sequence single stars, and the systems were placed on the Hertzsprung-Russel diagram
|
|---|
