Structure and evolution of low mass W UMa type systems
  The structure and evolution of low mass W UMa type contact binaries are discussed by employing Eggleton's stellar evolution code. Assuming that these systems completely satisfy Roche geometry, we calculate the relative radii of both components of contact binaries in different contact depth between inner and outer Roche lobes. We obtain a radius grid of contact binaries, and can ensure the surfaces of two components lying on an equipotential surface by interpolation using this radius grid when we follow the evolution of the contact binaries. We assume that the energy transfer takes place in the different regions of the common envelope to investigate the effects of the region of energy transfer on the structure and evolution of contact binaries. We find that the region of energy transfer has significant influence on the structure and evolution of contact binaries, and conclude that the energy transfer may occur in the outermost layers of the common convective envelope for W-type systems, and this transfer takes place in the deeper layers of the common envelope for A-type systems. Meanwhile, if we assume that the energy transfer takes place in the outermost layers for our model with low total mass, and find that our model steadily evolves towards a system with a smaller mass ratio and a deeper envelope, suggesting that some A-type W UMa systems with low total mass could be considered as the later evolutionary stages of W-subtype systems, and that the surface temperature of the secondary excesses that of the primary during the time when the primary expands rapidly, or the secondary contracts rapidly, suggesting that W-subtype systems may be caused by expansion of the primary, or by the contraction of the secondary. 
Lifang Li, Zhanwen Han, Fenghui Zhang