W Ursae Majoris stars can be understood as contact binary stars with a common envelope (Lucy 1968). They subdivide into two types: The A-type are earlier inspectral class than about F5, are believed to have radiative envelopes, and associate primary (deeper) eclipse minimum with transit eclipse. The W-type have spectral classes later than F5, are believed to have convectlve envelopes, and associate primary minimum with occultation eclipse. Controversy has surrounded the explanation of W-type light curves.
Four distinct models have been introduced to describe the envelopes or photospheres of W UMa stars. (1) The Rucinski hot secondary model directly explains W-type light curves on a postulational basis. Since 70%-90% of the emitted radiation from the secondary (less massive) component is believed to reach the secondary via circulation currents from the primary, there is an apparent thermodynamic mystery why the secondary should be hotter. (2) The Lucy Thermal Relaxation Oscillation (TRO) model argues that the secondary component is perpetually out of thermal equilibrium and that the components are in contact only during part of a given TRO cycle. During contact the photosphere is supposed to be barotropic. In this case primary minimum always associates with transit eclipse, in disagreement with observation for W-type systems. (3) The Shu et al. thermal discontinuity (DSC) model also argues for a barotropic photosphere but differs from Lucy on the gravity brightening exponent. The changes are insufficient to produce W-type light curves, (4) Webbink (1977), and, separately, Nariai (1976), argue for a baroclinic envelope. If the baroclinicity extends to the photosphere there is a possibility that W-type l i g h t curves could be explained. In particular, the Webbink scenario produces a hot secondary.