The Effective Viscoelastic Model (EVM) introduces an effective relaxation parameter β thatquantifies the degree to which a galaxy has approached the Radial Acceleration Relation (RAR)attractor. While previous work demonstrated that β exhibits non-random structure acrossSPARC galaxies, its physical interpretation remained unresolved.Using 171 galaxies from the SPARC sample, we investigate the empirical distribution andphysical correlates of β. We introduce a three-class relaxation taxonomy consisting of Class Imemory-suppressed systems (N = 25, 15%), Class II resolved relaxation systems (N = 100, 58%,median βII = 0.902), and Class III saturated/high-memory systems (N = 46, 27%). Significantbut weak correlations are found between β and the radial dynamical timescale (Trad, ρ =−0.190), baryonic acceleration (log gbar, ρ = +0.160), residual rotation-curve scatter (MAD, ρ =−0.187), and a velocity-gradient proxy (ρ = +0.195). However, neither individual observablesnor optimized composite memory scores provide strong predictive power (composite ρ = −0.023,multivariate R2 ≃ 0.17).These results indicate that β cannot be reduced to any single present-state observable. In-stead, β behaves as an emergent dynamical state variable encoding the cumulative assembly andrelaxation history of a galaxy. The EVM therefore interprets galaxy-to-galaxy diversity in β asa manifestation of non-equilibrium gravitational memory rather than stochastic scatter aroundthe RAR.We derive observational predictions for disturbed systems, interacting galaxies, low-surface-brightness populations, and high-redshift disks, providing future tests for IFU surveys such asMaNGA and SAMI, as well as JWST and SKA observations.
Chang-Sik Kim (Tue,) studied this question.