Dynamical Stability Analysis of UZ Lyr and Z Dra Binary Systems with Potential Additional Bodies

In this study, we investigate the orbital stability of the UZ Lyr and Z Dra systems using N-body simulations with the REBOUND package. Specifically, we used the Mean Exponential Growth Factor of Nearby Orbits (MEGNO) and the Wisdom-Holman Symplectic Integrator (WHFast) to analyze the dynamical stability of these binary star systems, which may host additional planetary bodies. The results for UZ Lyr show that the system becomes dynamically unstable after about 104 years, entering a chaotic regime as indicated by the MEGNO stability map. On shorter timescales, however, the system appears to be quasi-stable. The results reveal the inherent difficulties in forecasting long-term orbital stability based on short-term simulations. Similarly, for the Z Dra system, we investigate four proposed models from previous studies. Our simulations show that while single light travel time (LTT) effect models remain stable, models with two LTTs exhibit pronounced instability on short timescales, as confirmed by both WHFast and MEGNO analyses. The results suggest that while additional bodies may provide a better empirical fit to observed timing variations, such configurations are often dynamically unstable. This study highlights the importance of long-term dynamical analysis when evaluating the potential presence of additional objects in binary systems.