Overconstraint of the Lensing–Gas Offset Evolution in Dissociative Galaxy Cluster Mergers

Observations of dissociative galaxy cluster mergers reveal spatial offsets between gravitational lensing mass peaks and the X-ray emitting intracluster gas. Recent studies have shown that the magnitude of this lensing–gas offset decreases systematically with time since first core passage, consistent with a single exponential relaxation on gigayear timescales. In this work, we perform an explicit model-selection analysis of the observed offset evolution. Using weighted least-squares fitting and standard information-criterion diagnostics (AIC, AICc, BIC), we compare a minimal single-timescale relaxation model to extended models incorporating either a time-independent offset component or multiple relaxation timescales. We find that all extended models collapse to the minimal form: additional parameters fail to acquire independent empirical meaning and are penalized without improving the goodness of fit. The data therefore support a single, overconstrained temporal signature characterized by one effective relaxation timescale. This result is purely empirical and independent of any specific physical interpretation of the relaxation mechanism. It places strong constraints on interpretations of lensing–gas offsets in dynamically disturbed systems and demonstrates that the observed signal does not admit additional dynamically independent contributions within the present data.