Dynamical Orbital Stability Analyses of Eclipsing Binaries with Additional Companions

Abstract

In the study, the dynamical stability of 41 eclipsing binary (EB) systems proposed to host one or two additional bodies was examined, as reported in the literature. Using the REBOUND N-body integration package, we employed the WHFast and IAS15 integrators alongside the MEGNO (Mean Exponential Growth Factor of Nearby Orbits) indicator to conduct detailed orbital stability simulations over a period of 10 Myr. For systems exhibiting signs of instability on shorter timescales, MEGNO analyses were performed to identify chaotic behavior more effectively. Of the 41 systems analyzed, all 31 systems with a single proposed additional body demonstrated stable (non-chaotic) orbital configurations. Conversely, among the 10 systems proposed to host two additional bodies, only FK Aql exhibited stability, while the remaining systems displayed chaotic behavior, highlighting the challenges of maintaining long-term stability in multi-companion configurations. MEGNO analyses for FK Aql over 10⁸ years confirmed its placement in a dynamically stable region, with MEGNO chaos parameter values (\(\langle Y\rangle \leqslant 2\)), consistent with its orbital stability timeline. In contrast, MEGNO maps for the remaining multi-companion systems corroborated their chaotic timelines, confirming their instability. The combination of orbital stability timelines and MEGNO maps provides complementary insights into the long-term dynamics of these systems. This approach underscores the necessity of incorporating stability analyses into studies of binary systems to refine our understanding of their complex gravitational interactions.