A mechanism for producing short-period binaries

When three point masses form a hierarchical triple system, the short-period orbit can be severely modified by the long-period orbit if the two orbits are inclined to each other by more than about 39 degrees deg (sin(-1) root 2/5). Such an inclination can induce 'Kozai cycles' (Kozai, 1962), in which the eccentricity of the inner orbit cycles by a large amount while its period and therefore semimajor axis remains roughly constant. During those periastra when the eccentricity is largest, tidal friction may become important, and this can result in a secular shrinkage of the orbit, until it becomes circularised at a period of a few days. However, apsidal motion due to either GR or to the quadrupolar distortion of the components (if they are no longer treated as point masses) can reduce the range of eccentricity. We explore the limits on outer and inner orbital period that these perturbations imply. If the components are F/G/K/M dwarfs, then rotationally-driven dynamo activity can become important at the short periods that can occur in the right circumstances. It can cause the period to shorten further. The result may be a contact binary, and/or a merger in which the two stars of the inner pair coalesce to form a single rapidly rotating star. We suggest that this may be the origin of AB Dor, a very rapidly rotating K dwarf that is probably about 50 Myr old.