Mapping the Parameter Space of Triple Star Systems Stability, Tightness, and Angular Momentum

The dynamical stability of hierarchical multiple stellar systems represents a fundamental constraint on the formation and secular evolution of eclipsing binaries (EBs). A comprehensive dynamical analysis of 97 eclipsing systems with reliable parameters is presented. Using a refined catalogue spanning spectral types from M to B, the stability of each configuration is evaluated. Statistical analysis of the current sample reveals that 98% of the configurations satisfy the stability requirement S > 1, with a median stability factor of S~4.6. A primary finding of this study is a dynamical relaxation trend in the relationship between orbital tightness (aout/ain) and specific angular momentum (hin), where momentum variance decreases significantly as hierarchical spacing increases beyond aout/ain > 25. Furthermore, for short tertiary periods (Pout < 5 years), a scarcity of systems with low specific angular momentum is observed. These results demonstrate that the stability of hierarchical multiples is independent of inner binary morphology (contact vs. semi-detached), providing a robust quantitative baseline for future N-body simulations and the characterisation of complex stellar hierarchies in high-cadence surveys.