Mean motion resonances and the stability of a circumbinary disk in a triple stellar system

We numerically investigated the orbital stability of a circumbinary disk in a 3-D triple stellar system. We verified that there is a stable region (protected region) in which highly eccentric and/or inclined orbits can remain stable. In this paper we identify two-body mean motion resonances as a powerful mechanism to increase the eccentricity of the particle on short time-scales (10 kyr or less) and produce a longer-lived high-eccentricity population. These resonances are of high order and have not been previously considered in triple stellar systems. We show that this powerful mechanism can lead to regions containing instabilities and gaps. This process also produces a number of highly eccentric particles whose orbits remain stable. We show that there are limit values of eccentricity and semi-major axis for an orbit to be within the stability region. These quantities represent the dynamical effects of the inner binary and third star companion on a circumbinary disk. The value of this limit depends on the system parameters and should be considered in estimates of the stability, formation, and survival of bodies in triple systems.