Conceptual Framework for Orbital Instability in Contact Binary Star Systems: A Rigorous Multidimensional Analysis of HR 5171 A and Implications for Stellar Mergers

This conceptual paper presents an integrated multidisciplinary framework for analyzing orbital instability in massive contact binary star systems, with HR 5171 A as the primary case study. Using precise computational modeling, including branched evolutionary paths, mathematical derivations, and falsifiable hypotheses, we demonstrate that these systems are transient phases leading to stellar merger, contradicting assumptions of long-term equilibrium. Key mechanisms include tidal disruption near the Roche limit, hydrodynamic drag in common envelopes, angular momentum loss through mass ejection, Darwin tidal instability, energy balance via the α-formalism, mass-radius response exponents, and thermodynamic feedback. Supported by mathematical equations, reproducible Python simulations using observational data, sensitivity analyses, statistical measures, Bayesian inference for uncertainties, and links to observations (e.g., V1309 Scorpii merger) and theoretical models, we quantify the short timescales of these configurations. The framework applies to systems like VFTS 352 and MY Camelopardalis. Falsifiability is ensured through predictions of merger times, period changes, and gravitational wave signals. Implications include spacetime perturbations during mergers, producing detectable gravitational waves via LISA and LIGO. All claims are supported by peer-reviewed references with DOIs and URLs for integrity, reproducibility, and access.