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

Abstract

Ultra-compact massive galaxies (UCMGs) exhibit elevated stellar-to-dynamical mass ratios when dynamical masses are estimated using standard virial prescriptions. This discrepancy has been interpreted as non-homology driven by their compactness. This study investigates how the stellar-to-dynamical mass ratio depends on compactness (C), velocity dispersion ($σ_*$), stellar population properties (age, metallicity, and [Mg/Fe]), and star formation histories (SFHs). The analysis is based on a homogeneous sample of 482 UCMGs from the INSPIRE and E-INSPIRE surveys, extending to 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 IMF variations and recompute stellar-to-dynamical mass ratios using an empirical prescription where the virial coefficient varies with radius and stellar mass. Finally, I test modulation by stellar kinematics and population properties, including the degree of relicness (DoR), quantifiying the extremeness of the SFH. A statistically significant anti-correlation between compactness and the IMF-corrected stellar-to-dynamical mass ratio is recovered under a constant virial coefficient, but the relation flattens when a structure-dependent K is adopted. The data define a structural-dynamical manifold in the logC-log$σ_*$ space. Velocity dispersion sets the dominant axis of variation, and the corresponding plane accounts for ~62% of the variance in stellar-to-dynamical mass ratio. The stellar-to-dynamical mass ratio in UCMGs is governed primarily by the depth of the gravitational potential traced by $σ_*$, rather than C alone. At fixed size, systems with higher velocity dispersion show lower stellar-to-dynamical mass ratios. Non-homology therefore reflects coupled dynamical and evolutionary processes rather than purely geometric compactness.

Figures (9)

• Figure 1: Distribution of compactness ($\mathcal{C} = R_{\rm e}/R_{\rm Shen}$; left panel) and virial dynamical mass ($M_{\rm dyn}$, $K=5$; right panel) for the full sample of 482 UCMGs. Vertical dashed lines indicate the median values, while dotted lines mark the 16th and 84th percentiles.
• Figure 2: Comparison between stellar masses derived assuming a Kroupa IMF and those corrected according to the empirical IMF–DoR relation. Points are colour-coded by DoR and the dashed line indicates the one-to-one relation.
• Figure 3: Comparison between dynamical masses computed assuming a constant virial coefficient ($K=5$) and those obtained using the structure-dependent calibration of PeraltaDeArriba+14. The dashed line indicates the one-to-one relation. Points are colour-coded by compactness.
• Figure 4: Stellar-to-dynamical mass ratio as a function of compactness under different assumptions. In all panels, points are colour-coded by DoR, while grey symbols indicate non-corrected masses, with arrows marking correction-driven shifts. Top: IMF-corrected stellar masses with a constant virial coefficient $K=5$. Middle: Structure-dependent virial coefficient $K=K_{\rm PdA}$ with Kroupa stellar masses. Bottom: Fully adjusted configuration combining $K=K_{\rm PdA}$ with IMF-corrected stellar masses.
• Figure 5: Residuals of the compactness--mass relation, $\Delta \log_{10}(M_\star/M_{\rm dyn})$, as a function of stellar population and formation-history indicators: DoR (top left), mass-weighted age (top right), metallicity [M/H] (bottom left), and SSP-like [Mg/Fe] (bottom right). Grey points represent individual galaxies. Red symbols indicate binned medians with 16--84% intervals, and red lines show robust linear fits. Spearman coefficients are reported in each panel.