The dynamical orbital stability of the proposed 2+1+1 hierarchical eclipsing binary systems

Abstract

We performed a comprehensive dynamical stability analysis of the eclipsing binary systems proposed to have a $2+1+1$ hierarchical structure. Using the REBOUND N-body integration package, which includes the WHFast, IAS15, MERCURIUS, and TRACE integrators, and the MEGNO (Mean Exponential Growth Factor of Close Orbits) chaos indicator, we analysed the orbital configurations of these systems and their stability on long time scales. For TZ Boo, dynamical simulations based on two proposed orbital models show that configurations with two additional companions (models I and III) exhibit significant dynamical instability, with chaotic orbital behaviour occurring on short time scales ($\sim 10^3$ years). This instability is confirmed by MEGNO chaos parameters greater than 2 and the rapid divergence of the semi-major axes and eccentricities of the proposed companions. Similarly, the BB Peg and V539 Arae systems, despite being proposed to host two additional companions, also show pronounced chaotic behaviour on short timescales, as evidenced by high MEGNO values and instability times of about 708 and 458 years, respectively. In contrast, NSVS 7453183 exhibits significant dynamical stability over $10^8$ year simulations, supported by bounded oscillations in the orbital parameters and MEGNO values consistently below 2. The stability of the system was further validated by an analysis of the orbital parameter uncertainties, indicating the critical role of the high eccentricity dynamics in the outer companion. These results indicate the need to integrate dynamical analyses with observational constraints to assess the plausibility of additional companions in binary systems. While NSVS 7453183 provides a plausible quadruple system configuration, the results for TZ Boo, BB Peg, and V539 Arae suggest against over-reliance on $O-C$ diagram modelling without detailed stability evaluations.