A Dynamical Stability Study of Triple-Star Systems Using Physical and Geometrical Parameters

The dynamical stability of 141 triple-star systems is investigated. These systems are selected from the updated catalog of multiple stars systems (i.e., the MSC catalog). The distribution of eccentricity for inner and outer orbits is plotted. This diagram shows that the inner orbits are almost circular while the outer ones are oval, indicating higher eccentricity. This confirms that triple-star systems are also hierarchical. The dynamical stability of all systems is investigated using five different criteria. Observational stability parameters and their critical values are calculated using orbital values and the masses of components. In addition, the stability margin against the eccentricity of the outer orbit is plotted. This diagram shows that by increasing the eccentricity of the outer orbit, the distance from the stability limit also increases. Therefore, the higher the eccentricity of the outer orbit is, the more unstable the system becomes. Furthermore, by some investigations, we found that the dependence on the eccentricity of the inner orbit through the factor 1=(1 − ein) stabilizes many systems in some criteria, and this modifies the corresponding criteria. The results of the investigations show that almost all triple-star systems are stable and have a hierarchical structure. Only five systems (with WDS indexes: 18126-7340, 06467+0822, 02022- 2402, 08391-5557, and 00247-2653) are unstable in at least three criteria. The reasons for the instability of these systems are most likely the observational errors or the unreal theoretical criteria. Finally, the introduced five criteria are ordered according to their credibility and precision.