Authors: Nicolas Poupart
We develop a hierarchical formulation for evaluating gravitational binding energy from the internal organization of matter, volume conservation, and mass--energy equivalence. Rather than relying only on pairwise interaction terms defined relative to infinity, the proposed estimator assigns an intrinsic energy scale to compact configurations of matter. We then test whether the corresponding mass-equivalent contribution can reproduce the effective dark mass inferred in galaxies.We test this formulation using SPARC rotation-curve data together with independent GALEX and SDSS photometric observations. Stellar population mixtures are reconstructed from dynamical information alone, without using photometric data as input, and are then used to predict integrated galaxy colors. The resulting colors show significant correlations with observations, indicating that the reconstructed populations encode non-trivial information about stellar structure.A systematic exploration of the estimator reveals structured regions of high-quality solutions in parameter space. In particular, the results favor a hierarchical recursive interpretation in which class-level binding energies are preserved, while the global heterogeneous aggregate may contribute with an effective virial factor. The dynamical reconstruction varies only weakly across a broad range of parameters, whereas the photometric constraints provide greater discrimination between candidate forms.These results suggest that gravitational binding energy provides a physically motivated contribution to the effective dark mass inferred in galaxies, while also explaining why dynamical information can encode stellar population structure.
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