The Stability of Contact Binary Stars

A contact binary system consists of two stars orbiting so closely they share an outer atmosphere. Approximately one in two hundred solar-type stars have a smaller companion in contact (W UMa systems). Hence, they are common and long-lived. Realistic computation of the evolution of both stars including their interaction has not yet been achieved. It has long been thought that such systems are generally unstable on a thermal timescale to mass transfer (e.g., Flannery 1976, ApJ, 205, 217). Oscillations in the direction of mass transfer were suggested as a means by which they might nonetheless be long-lived. If so, however, computation of evolution over nuclear timescales would be difficult for stars that are never allowed to relax thermally.

Molnar et al. (2022, AAS Mtg #240, 308.01) presented MESA evolutionary computations of the primary star that included mass transfer, showing that the systems are largely stable (excepting for large mass ratios). Molnar et al. (2023, DDA Mtg #54, 400.01) explored the unstable cases further, showing that they would evolve towards stability on a thermal timescale without overflowing the L₂ point.

We extend that work further here, showing how to compute the boundaries (in system mass versus mass ratio space) of unstable systems. We also show how the physical conditions (temperature and pressure) of the primary star at the equipotential that includes the L₁ point set a boundary condition on the secondary star that in turn sets the rate of mass transfer. Systems with greater fillout factor will drive a greater mass transfer rate. Equilibrium is established when the fillout factor drives mass transfer at the rate needed to accommodate the growing primary star. An important new consequence of this idea is that stellar structure calculations for the secondary star with this imposed boundary condition can in principle determine the unique fillout factor a given system will have as a function of time in its evolution. That is to say, fillout factor is not an independent parameter. Future work is to add this condition to MESA and compute the first contact binary systems with two fully realistic stars.