Energy transfer and its effects on the secondaries in W Ursae Majoris type contact binaries

Based on the physical parameters of 133 W Ursae Majoris (W UMa) type contact binaries, energy transfer and its effects on the secondaries in W UMa contact binaries are investigated. Relations are given between the mass ratio (q) for W UMa contact binaries and the relative energy transfer rates, i.e. U-1, the ratio of the transferred luminosity to the surface luminosity of the primary, and U-2, the ratio of the transferred luminosity to the nuclear luminosity of the secondary. The theoretical curves(U-1 versus q and U-2 versus q) are derived based on various assumptions: that the two components in each W UMa system are nearly identical in effective temperature and just fill their inner Roche lobes, and the primaries are zero-age main-sequence stars. Although these curves can reflect the distribution of U-1 and U-2 versus q, some observational systems deviate significantly from these curves. This results mainly from the difference in effective temperatures of the components of W UMa systems. The radius and the density of the secondary are related to the relative energy transfer rate U-2: the higher U-2, the greater the expansion and the lower the density of the secondary in a W UMa system. In addition, it is found that the temperature difference of W UMa binary components is correlated with the relative energy transfer rate U-1 and decreases with increasing U-1. This might suggest that there is a thermal coupling between the two components in W UMa contact binaries, and that the classification of W UMa contact binaries into A or W types depends on the energy transfer from the primary to the secondary. The temperature difference of W UMa binary components is poorly correlated with the mass of the primary. This suggests that the properties of the common envelope of a W UMa contact binary might not have a significant effect on the energy transfer between the two components.