A note on the stability of hierarchical triple stars with initially circular orbits

We compute the dynamical evolution of hierarchical triple stars in which both orbits are initially circular, and determine the lower limit to the ratio of periods (outer/inner) for which there is dynamical stability. This ranges from 6.3 to 2.4, as the distant body's mass (in units of the inner binary) ranges from 100 to 0.01. We discuss a variety of types of behaviour that we find when the period ratio varies near its critical value.