The gravity-darkening of highly distorted stars in close binary systems

From a quantitative analysis of the photometric ellipticity effect, values of the exponent of gravity-darkening have been empirically deduced for the components of sixteen W UMa systems with accurate cross-correlation spectroscopic mass ratios. In the analysis, the exponents for both components of a W UMa system are assumed to be the same. In view of the generally unstable nature of their light curves and the consequent difficulty to find an unique set of the fractional radii of both components, -values have been derived for various equipotential surfaces with boundary cases set at the inner and outer Roche lobes.The results indicate that if the fill-out factors are less than 0.5 (as is so for most of the actual cases), the deduced -values are all greater than Lucy's conventional value of 0.32. The empirical -values as a whole are found to increase with the mean effective temperature of the components and, furthermore, they show a tendency to decrease with increasing mass ratio, particularly for A-type systems. Thus, a W UMa system consisting of two components of quite different masses has a large empirical -value. These observational evidences indicate that the structure of the photosphere of contact components of W UMa systems is significantly different from that of normal Main-Sequence stars of similar spectral type and may provide a clue to solve puzzles of W UMa stars.