On the period-density relations and lower period limit of contact binaries

The theoretical relations between the orbital period and mean densities of component stars of contact binaries are deduced. It is found that the orbital period of a contact binary is inversely proportional to the square root of the mean densities of component stars with the slopes as functions of mass ratio and fill-out factor of system. A test of 148 well-studied contact binaries with physical parameters determined from comprehensive photometric and spectroscopic solutions shows that the upper limit of secondaries' mean densities depends strongly on the total masses, M 1 + M 2, of the contact systems. For a low-mass contact system with ( M + M 2) = 2 M circle dot, the maximum mean density of the secondary is strictly lower than that of a 5 Gyr star with a mass of (M + M 2)/2. Taking this as the basic constraint, the derived period-density relation was applied to simulate the orbital period distribution of low-mass contact binaries over the total-mass range of 1-2 M circle dot. It reproduces a period cut-off at 0.12-0.16 d, depending on the fill-out factor.