Instability of close triple systems with coplanar initial doubly circular motion

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Abstract
We consider the orbits of triple stars that are started with hierarchical, doubly circular motion, but which have a sufficiently short ratio of orbital periods that the system is close to instability. We discuss the nature of the unstable motion: this can be a straightforward series of ejections of one component, which ultimately escapes to infinity, but there are several other possibilities. For instance, one component may exchange back-and-forth between orbits around the second and the third components, possibly in perpetuity. Alternatively, there may be a number of exchanges followed by ejection and escape. We examine the choices between exchanges and ejections (or both), guided partly by the Szebehely & Zare criterion. In a very small region of our three-dimensional parameter space we have discovered a family of periodic orbits. The masses involved are approximately 1.0 + 0.016 for the inner binary, and 0.4 for the third body. The lightest body makes alternately two small and two large revolutions about the heaviest body, viewed in the frame where the two heaviest bodies are at rest. This pattern persists for at least several thousand revolutions but we defer an analysis of stability of these orbits to a future paper. We consider the application of our results to the close triple systems λ Tau and CH Cyg.

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