The minimum mass ratio of W Ursae Majoris binaries

The minimum mass ratio for tidal stability of a contact binary containing two unevolved main-sequence stars is calculated to be 0.09 in the case of a mostly radiative primary, and is higher if an appreciable fraction of the mass lies in a convective envelope. At least one observed system, AW UMa, has a mass ratio just below this value ($q=0.075$), implying, if the system is stable, that the primary must be slightly evolved and must have a very shallow convective envelope. Contact binaries with mass ratios significantly below that of AW UMa should not be observed, since they are tidally unstable and quickly merge into a single, rapidly rotating object, on a timescale ~10³--10⁴\,yr.