A Cyclic Thermal Instability in Contact Binary Stars

We show analytically that contact binary stars coupled by a common sconvective envelope, the Lucy model, are almost invariably unstable when ssubjected to mass transfer: if either component begins to exchange mass, sit will continue to do so. A detailed sequence of models is calculated swhich follows the thermal evolution of a 2 M0 contact binary of normal sPopulation I abundances (X = 0.70, Z = 0.02), starting at nearly equal smass. The initial instability develops into a cyclic exchange of mass swith the mass fraction oscillating between 0.56 < M1/(M1 + M2) < s0.62 with a period of 10 years. The system achieves thermal equilibrium son the average, but individually both stars are perpetually out of sequilibrium. The instability is of a general nature and such oscillating ssystems can satisfactorily populate the short-period, red region of the spenod- relation for W UMa stars. Subject headings: stars: binaries - sstars: mass loss - stars: W Ursae Majoris