Statistical study of dynamic behavior of triple star systems using available stability criteria

Abstract

The present study investigates 141 dynamically stable triple-star systems. These systems are chosen from the latest multiple star systems catalog (MSC). The eccentricity distribution for the outer and inner orbits is obtained. According to the eccentricity diagram, the outer orbits are oval, which indicates higher eccentricity, while the inner orbits are almost circular. Therefore, the hierarchical configuration of triple-star systems is confirmed. Five different criteria are considered to study the dynamic stability of multiple star systems. Observation-based stability factor values and the corresponding critical values can be determined from mass and orbital values of the components. Moreover, the plot of stability margin versus the outer orbit eccentricity is drawn. According to this plot, an increase in the outer orbit eccentricity increases the distance from the stability boundary. Consequently, a high outer orbit eccentricity leads to a high system instability. Our investigations show that in some criteria, many systems are stabilized by considering the dependence on the inner orbit eccentricity as 1/(1−ein) so that the related criteria are modified. Additionally, nearly all triple-star systems have hierarchical configurations and are stable. However, in at least three criteria, there are only five unstable systems with the WDS indices 00247-2653, 08391-5557, 02022-2402, 06467+0822, and 18126-7340. The instability of these systems can be attributed, with high probability, to observation errors or the unrealistic theoretical criteria. At the end, the credibility and accuracy of the mentioned five criteria are considered as the basis for ordering them.