Orbital period cut-off of W UMa-type contact binaries

Period cut-off and period-colour 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 365 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 d) of orbital period by studying the correlation among four physical parameters (orbital period P, mass ratio q, mass of primary star M-1, 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-colour relation exists was also discussed.