The Low-Mass Limit for Total Mass of W UMa-type Binaries

The observations of W UMa type stars show a well-defined short-period limit of 0.22 d, which is equivalent to a lower mass limit of approximately 1 solar mass for the total binary mass. It is currently believed that cool contact binaries are formed from detached binaries losing angular momentum (AM) via a magnetized wind. Orbital evolution of detached binaries with various component masses was followed until the primary component reached the critical Roche surface and the Roche lobe overflow (RLOF) began. It was assumed that the minimum initial, i.e. ZAMS, orbital period of such binaries is equal to 2 d and that the components lose AM just as single stars. According to the mass-dependent formula for AM loss rate of single stars, derived in this paper, the AM loss time scale increases substantially with decreasing stellar mass. The formula was applied to binaries with the initial primary component masses between 1.0 and 0.6 solar mass and two values of mass ratio q=1 and 0.5. Detailed calculations show that the time needed to reach RLOF by a 1 solar mass primary is of the order of 7.5 Gyr, but it increases to more than 13 Gyr for a binary with an initial primary mass of 0.7 solar mass. Binaries with less massive primaries have not yet had time to reach RLOF even within the age of the Universe. This sets a lower mass limit for the presently existing contact binaries