Beyond compactness:. A structural--dynamical--evolutionary manifold for the stellar-to-dynamical mass ratio in ultra-compact massive galaxies

Ultra-compact massive galaxies (UCMGs) often exhibit elevated stellar-to-dynamical mass ratios when dynamical masses are estimated using standard virial prescriptions. This discrepancy has been interpreted as evidence for structural non-homology driven primarily by their compactness. This study investigates how the stellar-to-dynamical mass ratio depends on compactness (), and star formation histories. The analysis is based on a homogeneous catalogue of 482 UCMGs from the internal kinematics (σ_⋆), stellar population properties (mass-weighted age, metallicity, and Mg/Fe and surveys, extending to significantly smaller sizes than previously analysed samples. I first derive the compactness–mass relation assuming a constant virial coefficient (K=5). I then correct stellar masses for initial mass function (IMF) variations and recompute stellar-to-dynamical mass ratios using an empirical prescription in which the virial coefficient varies as a function of radius and stellar mass. Finally, I test whether the relation is modulated by stellar kinematics and population properties, including the degree of relicness (DoR), which quantifies the extremeness of the star formation history. A statistically significant anti-correlation between compactness and the IMF-corrected stellar-to-dynamical mass ratio is recovered when a constant virial coefficient is adopted, even within the relatively narrow range of, łog σ_⋆) space. Velocity dispersion sets the dominant axis of variation, and the corresponding plane accounts for sim62% of the variance in stellar-to-dynamical mass ratio. Including stellar age increases the explained variance to sim63%, revealing a secondary evolutionary modulation. In contrast, DoR, metallicity, and spanned by nearby UCMGs. The relation substantially flattens when a structure-dependent K is adopted, in agreement with previous literature. Beyond this one-dimensional behaviour, the data define a structural–dynamical manifold in the (łog C Mg/Fe do not retain independent explanatory power once stellar age is included. The stellar-to-dynamical mass ratio in UCMGs is governed primarily by the depth of the gravitational potential, traced by stellar velocity dispersion, rather than by compactness alone. At fixed size, systems with higher σ_⋆ exhibit systematically lower stellar-to-dynamical mass ratio, indicating that dynamical structure regulates the apparent mass imbalance in the ultra-compact regime. Compactness largely reflects this dynamical scaling, while stellar age introduces a coherent secondary modulation linking the structural manifold to the evolutionary state of the galaxy. Non-homology in UCMGs therefore encodes coupled dynamical and assembly processes rather than purely geometric compactness.