Secondary components of W UMa-type contact binaries (CBs) have many special properties, two of them are excess in radius and luminosity. In order to make these specialties clear, we propose radial density distribution to roughly detect the interior structure of the secondaries in CBs. By comparing the radial density distribution between secondary components of CBs and main-sequence stars, we find the radial density distribution of secondaries in A-subtype CBs are similar to main-sequence stars whose masses higher than 1.8 Msun, which suggests that these two kinds of stars may have some evolutionary relationship. While secondary components of W-subtype CBs are closely connected with stars whose masses lower than 1.8 Msun. Then, we investigate the mass–luminosity relation of secondaries in CBs, the big differences between two subtypes suggests that the overluminosity of secondaries in these two subtypes are caused by two different reasons. Overluminosity in A-subtype is because the secondary components are evolved from initial more massive stars, while in W-subtype is due to energy transfer.

Period cut-off and period-color relation are two special characters of W UMa-type contact binaries. In the past, many authors noted these two properties, however, a comprehensive study was still lacking. In order to reveal a theoretical mechanism behind these two peculiarities, we collected 370 contact binaries whose orbital periods, mass ratios, masses and radii are compiled and attempted to make this idea come true by statistical means. Then, we obtained a lower limit (0.15 days) of orbital period by studying the correlation among four physical parameters (orbital period P, mass ratio q, mass of primary star M1 and separation between two components a). Furthermore, we used the most reliable parameters (P and q) to check our result, fortunately, all evidence indicated that our predicted value is credible. In the end, the reason why the period-color relation exist was also discussed.